time-domain ab initio modeling of photoinduced dynamics at ... · time-domain ab initio modeling of...

PC66CH24-Prezhdo ARI 11 March 2015 10:22

Time-Domain Ab InitioModeling of PhotoinducedDynamics at NanoscaleInterfacesLinjun Wang,1,3 Run Long,2 and Oleg V. Prezhdo1

1Department of Chemistry, University of Southern California, Los Angeles,California 90089-0482; email: [email protected] of Physics and Complex & Adaptive Systems Laboratory, University College Dublin,Belfield, Dublin 4, Ireland3Department of Chemistry, University of Rochester, Rochester, New York 14627

Annu. Rev. Phys. Chem. 2015. 66:549–79

First published online as a Review in Advance onJanuary 22, 2015

The Annual Review of Physical Chemistry is online atphyschem.annualreviews.org

This article’s doi:10.1146/annurev-physchem-040214-121359

Copyright c© 2015 by Annual Reviews.All rights reserved

Keywords

time-dependent density-functional theory, nonadiabatic moleculardynamics, inorganic and organic interfaces, nanoscale materials, chargeand exciton dynamics

Abstract

Nonequilibrium processes involving electronic and vibrational degrees offreedom in nanoscale materials are under active experimental investigation.Corresponding theoretical studies are much scarcer. The review starts withthe basics of time-dependent density functional theory, recent developmentsin nonadiabatic molecular dynamics, and the fusion of the two techniques.Ab initio simulations of this kind allow us to directly mimic a great vari-ety of time-resolved experiments performed with pump-probe laser spec-troscopies. The focus is on the ultrafast photoinduced charge and excitondynamics at interfaces formed by two complementary materials. We con-sider purely inorganic materials, inorganic-organic hybrids, and all organicinterfaces, involving bulk semiconductors, metallic and semiconducting nan-oclusters, graphene, carbon nanotubes, fullerenes, polymers, molecular crys-tals, molecules, and solvent. The detailed atomistic insights available fromtime-domain ab initio studies provide a unique description and a compre-hensive understanding of the competition between electron transfer, thermalrelaxation, energy transfer, and charge recombination processes. These ad-vances now make it possible to directly guide the development of organicand hybrid solar cells, as well as photocatalytic, electronic, spintronic, andother devices relying on complex interfacial dynamics.

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FSSH:fewest-switchessurface hopping

QHD: quantizedHamiltonian dynamics

1. INTRODUCTION

Interfacial electron transfer processes (1) are fundamental to many areas of research, includingphotovoltaics (2, 3), photocatalysis (4, 5), photosynthesis (6, 7), photochemistry (8, 9), electrolysis(10, 11), molecular electronics (12, 13), and spintronics (14, 15). As shown in Figure 1, efficientelectron transfer at nanoscale interfaces needs to compete with thermal relaxation, energy trans-fer, charge recombination, and other dynamical processes, which ultimately determine the overalldevice efficiency. Numerous efforts have been devoted to exploring the nonequilibrium natureand mechanisms of these dynamical processes. Time-resolved experiments, such as transient ab-sorption spectroscopy (16, 17) and optical second harmonic generation techniques (18–20), havebeen widely used to obtain the timescale for each dynamical channel. On the theoretical side,nonadiabatic molecular dynamics (NAMD) provides the most popular and reliable solution (21,22). Over the past few decades, a suite of NAMD simulation approaches has been developed andimplemented, aimed at modeling the dynamical events in the time domain and at the atomisticlevel of detail (23–29), as they occur in experiment and nature.

This review covers the basics of the theory underlying various NAMD strategies availablein literature. We present the standard approaches, including mean-field (MF) (30–32), fewest-switches surface hopping (FSSH) (21, 33), and quantized Hamiltonian dynamics (QHD) (34,35). Tully’s FSSH approach has retained its popularity owing to its appealing simplicity, ease ofimplementation, and computational efficiency (22, 36, 37). Because of its great success, FSSH has

Thermalrelaxation

Energytransfer

Electrontransfer

Chargerecombination

Figure 1Photoinduced processes competing with electron transfer between a donor and an acceptor, includingthermal relaxation, energy transfer, and charge recombination. The energy levels of the donor (acceptor) areshown as red (blue) solid horizontal lines. The electron and hole are represented by solid and open circles,respectively.

550 Wang · Long · Prezhdo

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SC-FSSH:self-consistentfewest-switchessurface hopping

FSH: flexible surfacehopping

GFSH: global fluxsurface hopping

SQUASH:second-quantizedsurface hopping

SMF: stochastic meanfield

DISH:decoherence-inducedsurface hopping

CPF: coherencepenalty functional

attracted a lot of attention, and various situations requiring improvements have been identified.When high density of states (DOS) come into play, in particular in nanoscale materials, standardFSSH encounters the so-called trivial, or unavoided, crossing problem (38–41). It can be overcomewith several modern developments, including self-consistent fewest-switches surface hopping (SC-FSSH) (42) and adaptive flexible surface hopping (FSH) (43, 44). In addition, FSSH lacks thecapability of describing the superexchange mechanism of population transfer, which can be wellcaptured by the global flux surface-hopping (GFSH) (45) and second-quantized surface-hopping(SQUASH) (46) methods developed recently. Decoherence is another issue that needs to beconsidered for proper descriptions of slow transitions between states separated by significantenergy gaps (47–49). Decoherence can be taken into account by the stochastic mean-field (SMF)(50), decoherence-induced surface-hopping (DISH) (51), and coherence penalty functional (CPF)(52) methods.

Ab initio density functional theory (DFT) provides a rigorous and efficient means for de-scribing the electronic structure of systems comprising most chemical elements. In recent years,time-dependent density functional theory (TDDFT) has been extensively combined with NAMDand applied to a broad range of inorganic and organic systems undergoing charge separation, elec-tron and energy transfer, energy relaxation, charge recombination, chemical reactions, and othernonequilibrium processes (23–29). Inorganic materials generally exhibit strong bonding and highelectrical conductivity. Their large dielectric constants result in strong electric field screening andreduced Coulomb binding between electrons and holes (53). In contrast, organic systems are gen-erally loosely packed with small charge mobility due to weak electron-electron coupling and strongelectron-phonon interactions (54–57). Small dielectric constants result in strong Coulombic bind-ing of electron-hole pairs, and excitons tend to be localized (58–60). The fundamentally differentproperties of organic and inorganic materials are described by either chemistry or physics, whichdiffer in concepts and language: compare the terms orbitals, electron correlation, and vibrations,used by chemists, with the terms band structure, excitons, and phonons, employed by physicists.Thus, significant challenges arise for a unified description of organic and inorganic components,and their hybrids.

The state-of-the-art simulation tool combining TDDFT and NAMD generates a detailedtime-domain atomistic representation of the interfacial charge and exciton dynamics that arefundamental to a wide variety of applications. Studies performed by the Prezhdo group on quantumdots (QDs) and interfaces involving TiO2 have been reviewed previously (23–29). The currentreview focuses on interfaces formed by two complementary materials, including purely inorganicinterfaces, organic-inorganic hybrids, and all organic systems (see Figure 2). Only work publishedin 2010 or later is included.

A functional interface for photovoltaic or photocatalytic applications typically comprises aphoton absorber and an electron acceptor. Different absorber-acceptor combinations exhibitdistinct features. Exemplifying inorganic interfaces, we use an ab initio time-domain simulationto show that hot electrons can be extracted from QDs prior to relaxation (61), that electron-holerecombination can be minimized by tuning QD size and bridge length (62), that the mechanism ofelectron injection from a CdSe nanoparticle into nanoscale TiO2 depends on the dimensionalityof the latter (63), and that plasmon-driven charge separation on TiO2 sensitized with plasmonicnanoparticles has a 50% chance of already occurring during light absorption (64). Consideringorganic-inorganic hybrids, we reveal why graphene, a metal, can be used as a TiO2 sensitizer(65); that atomic defects can be both detrimental and beneficial for charge separation (66); howa long, insulating bridge can accelerate electron transfer (67); that nanoscale materials exhibita new, Auger-assisted type of electron transfer (68); that dimensionality is inverted when a QDand conjugated polymer form a heterojunction (69); and that the low efficiency of photocatalytic

www.annualreviews.org • Ab Initio Modeling of Photoinduced Dynamics 551

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a b c

Inorganicinterfaces

Organic-inorganicinterfaces

d e Y

CdX

gf

e–e–

hvj k h

Organicsystems

i

Figure 2Inorganic interfaces, organic-inorganic hybrids, and organic systems discussed in the review: (a) a PbSe quantum dot (QD) on a TiO2surface, (b) CdSe QD attached to either a TiO2 QD or TiO2 nanobelt, (c) Au20 cluster on a TiO2 surface, (d ) graphene on TiO2,(e) RhB molecule interacting with a PbS QD, ( f ) C60 bound to a CdSe QD, ( g) CdX QD interacting with a Y molecule (X = S, Se,and Te; Y = AQ, MV2+, and MB+), (h) P3HT on a CdS QD, (i ) GaN-H2O interface, ( j ) pentacene-C60 composite, and (k) aP3HT–carbon nanotube system.

water splitting by GaN results from unfavorable competition between charge relaxation andtransfer (70). Finally, for organic interfaces, we demonstrate that optically dark states governthe rates and yields of singlet fission and charge transfer at a pentacene/C60 interface (71) andillustrate how the asymmetry of electron and hole transfer at a polymer/nanotube interface canbe used to optimize solar cell performance (72). The mechanisms of all processes involved inthe photo-initiated dynamics are established, the key electronic states and phonon modes arecharacterized, and the interplay between the productive and unfavorable channels of photoin-duced electron and energy flow is described. The reviewed time-domain ab initio simulationsprovide important insights into the fundamental chemical physics of electron transfer and relatedprocesses on the nanoscale and generate valuable guidelines for the design and improvement ofphotovoltaic and photocatalytic devices.

2. SIMULATION APPROACHES

2.1. Time-Domain Density Functional Theory

The wave function, which determines all observable properties through the calculation of expec-tation values, is the central concept of quantum mechanics (73). However, it is still a forbiddingtask to find out the true many-electron wave function for large systems. The Hohenberg-Kohn


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theorems have shown that the desired properties of any system under the influence of a static ex-ternal potential can be obtained directly from the electron density, which is a function of only threecoordinates (74). This many-electron problem can be further reduced approximately to a tractablepicture of noninteracting electrons moving in an effective potential, resulting in the Kohn-Sham(KS) framework of DFT (75). With proper choices of exchange-correlation (XC) functionals,DFT finds an increasingly broad application in physics, chemistry, biology, and materials sciencefor the atomistic interpretation and prediction of complex system behavior (76).

When the external perturbation, including electromagnetic field and vibrational motions,evolves in time, the Runge-Gross theorem has shown that the three-dimensional (3D) electrondensity is also sufficient to describe the time-dependent response of the system (77). The resultingtheory is known as TDDFT (78). Within the KS representation, the electron density at time t,ρ(r, t), is given as a summation over all occupied single-electron KS orbitals, {ϕi (r, t)} (78),

ρ(r, t) =N e∑i=1

∣∣ϕi (r, t)∣∣2

, (1)

where Ne is the total number of electrons, and r expresses the assembly of 3Ne electronic coordi-nates. The time-dependent variational principle can be applied to the KS energy (78),

E =N e∑i=1

〈ϕi | K (r) |ϕi 〉 +N e∑i=1

〈ϕi | V (r; R) |ϕi 〉 + e2

2

∫∫ρ(r)ρ(r′)|r − r′| d 3rd 3r′ + Exc{ρ(r)}, (2)

where K(r) is the kinetic energy operator of noninteracting electrons, V (r; R) is the electron-nuclear attraction that relies on both electronic coordinates r and nuclear coordinates R, andExc{ρ} is the XC functional taking into account the many-body interactions. The result is a systemof coupled single-particle KS equations of motion (EOM) (78–80),

i�∂ϕi (r, t)

∂t= H (r; R, {ϕ})ϕi (r, t), (3)

where the Hamiltonian H (r; R, {ϕ}) is a functional of the overall density and, therefore, all occu-pied KS orbitals.

The adiabatic KS basis can be viewed as a numerical tool for solving the time-dependentKohn-Sham (TDKS) equations given in Equation 3 (81). Expansion of the TDKS orbitals in theadiabatic KS basis, {ϕ j (r; R)},

ϕi (r, t) =N e∑j=1

c i j (t)∣∣ϕ j (r; R)

⟩, (4)

yields a set of EOM for the expansion coefficients (21),

i�∂

∂tc i j (t) =

N e∑k

c ik(t)(εkδ j k + d j k · R), (5)

where εk is the corresponding energy of the adiabatic KS state, ϕk(r; R). The last term in Equation 5is the nonadiabatic coupling (NAC) (82–86),

d j k · R = −i�⟨ϕ j (r; R)

∣∣ ∇R∣∣ϕk(r; R)

⟩ · R = −i�⟨ϕ j (r; R)

∣∣ ∂

∂t∣∣ϕk(r; R)

⟩, (6)

which arises from the dependence of the adiabatic KS orbitals on the nuclear coordinates R (87).Solving the TDKS equations in the adiabatic KS basis shifts the computational effort to the highlyoptimized step of solving the time-independent DFT problem (88).


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CPA: classical pathapproximation

Slater determinants formed from single-electron KS orbitals can be viewed as an approxima-tion to the many-electron adiabatic states (88). A state basis is needed to perform NAMD, asdiscussed in the next subsection. The NACs between the Slater determinants are nonzero onlyif the determinants differ by one orbital. As a result, the propagation involves very sparse matri-ces, allowing the use of large many-electron basis sets. At the level of the TDKS equations, theadiabatic KS representation makes no approximations and can be viewed as a particular choice ofbasis set. It carries a number of advantages associated with the fact that adiabatic KS orbitals areroutinely computed by most electronic structure codes. The KS representation of excited statesassumes that the error made in the calculation of the potential energy surface (PES) due to themissing TDDFT correction is constant in time, and therefore, it is independent of the structuralchanges. Thus, the adiabatic KS states can be viewed as a zeroth order to the linear responsetime-dependent density functional theory (LR-TDDFT) adiabatic states (89). In practice, the KSexcitation is generally the leading term in the expression for the excitations calculated with LR-TDDFT (90). The agreement between the KS and LR-TDDFT descriptions is better for pureDFT functionals than for hybrid functionals. Larger systems with a greater number of electronsexhibit better agreement as well. The errors introduced with the KS description of electronicexcitations should be compared with other approximations, such as those involved in the choiceof the DFT functional and in the classical description of vibrational motions, neglecting zero-point energy contributions to the NAC and decoherence in the electronic subsystem induced byquantum vibrations (81).

2.2. Nonadiabatic Molecular Dynamics

NAMD provides a generalization of ordinary molecular dynamics (MD) to include transitionsbetween electronic states. This is achieved in a self-consistent way: The nuclear motions drive theelectronic evolution, for instance, by TDDFT, and the electronic evolution influences the classicalnuclear dynamics (33). The latter can be carried out in an MF manner, leading to the Ehrenfestapproximation (30). Correlations between the dynamics of nuclei and the electron can be builtin using surface-hopping (SH) techniques (21). Typically, NAMD is performed in the adiabaticbasis (91, 92). Adiabatic states are readily available from electronic structure calculations, and theygive better results with SH approaches. In the following subsections, we discuss in detail variousNAMD methods. Table 1 gives a brief description for each method, followed by advantages,weaknesses, and suggested applications.

2.2.1. Classical path and Ehrenfest approximations, quantized Hamilton dynamics. Theclassical path approximation (CPA) (93) provides a particularly simple solution to the quantumback-reaction problem, that is, the influence of the electronic evolution on the classical nuclei.CPA assumes that the classical trajectory is independent of electronic dynamics, whereas theelectronic dynamics still depends on the classical coordinates. CPA is appropriate if electron-phonon interactions are much weaker than electron-electron couplings (94), or the energy ofthe nuclei is sufficiently greater than that of the electrons, such that the electron–nuclear energyexchange does not affect the nuclear evolution appreciably. CPA is also valid if the PESs that areassociated with different electronic states differ only slightly, in comparison, for instance, with theamplitude of nuclear fluctuations due to thermal or zero-point energy.

The Ehrenfest approximation is another attractive choice for NAMD simulations owing toits straightforward and rigorous foundations (30–32). There, the force applied on the classicalparticles is based on the gradient of the expectation value of the Hamiltonian acting on thetime-evolving wave function. If the energy flow between electronic and nuclear subsystems is


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Tab

le1

Asu

mm

ary

ofth

edi

scus

sed

nona

diab

atic

mol

ecul

ardy

nam

ics

met

hods

,the

irad

vant

ages

,wea

knes

ses,

and

sugg

este

dap

plic

atio

ns

Met

hod

Des

crip

tion

Adv

anta

ges

Wea

knes

ses

Sugg

este

dap

plic

atio

nsC

lass

ical

path

appr

oxim

atio

n(C

PA

)N

oin

fluen

ceof

elec

tron

icev

olut

ion

onth

edy

nam

ics

ofcl

assi

caln

ucle

i

Pre

com

pute

dnu

clea

rtr

ajec

tory

,al

low

ing

mul

tiple

real

izat

ions

ofel

ectr

onic

evol

utio

n

Feed

back

from

elec

tron

sto

nucl

eiis

lost

Hig

h-en

ergy

proc

esse

s

Mea

n-fie

ldap

prox

imat

ion

(Ehr

enfe

st)

Ave

rage

forc

efr

omal

lele

ctro

nic

stat

eson

clas

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lnuc

lei

Rig

orou

s,si

mpl

e,im

prov

emen

ton

CP

AC

anno

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ture

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ucle

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rrel

atio

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dth

erm

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amic

equi

libri

um;o

verc

oher

ent

Shor

t-tim

edy

nam

ics

inm

ost

case

s;sy

stem

sw

ithhi

ghde

nsity

ofel

ectr

onic

stat

es

Qua

ntiz

edH

amilt

ondy

nam

ics

(QH

D)

Hie

rarc

hyof

equa

tions

for

quan

tum

desc

ript

ions

ofbo

thel

ectr

ons

and

nucl

ei

Con

verg

ence

toex

actr

esul

t;qu

antu

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fect

sca

ptur

edw

ithm

inim

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mbe

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sica

l-lik

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les

Hig

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mpl

icat

edcl

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esan

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ear

equa

tions

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t-tim

ean

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alita

tive

long

-tim

ede

scri

ptio

nof

quan

tum

effe

cts

Few

est-

switc

hes

surf

ace

hopp

ing

(FSS

H)

Mos

tpop

ular

surf

ace-

hopp

ing

algo

rith

mm

inim

izin

gth

enu

mbe

rof

hops

Sim

ple,

effic

ient

;str

ong

elec

tron

-nuc

lear

corr

elat

ions

capt

ured

;lea

dsto

ther

mod

ynam

iceq

uilib

rium

Ad

hoc

and

over

cohe

rent

;no

supe

rexc

hang

e;tr

ivia

lcr

ossi

ngpr

oble

min

exte

nded

syst

ems

Mos

tcom

mon

met

hod;

corr

ectio

ns/m

odifi

catio

nsca

nbe

intr

oduc

edas

need

ed

Flex

ible

surf

ace

hopp

ing

(FSH

)FS

SHw

ithse

lf-ad

just

edsy

stem

size

for

surf

ace

hopp

ing

Sam

eas

FSSH

butt

rivi

alcr

ossi

ngpr

oble

mal

soso

lved

Req

uire

spa

ram

eter

toen

larg

eor

shri

nksy

stem

size

FSSH

for

exte

nded

syst

ems

Self-

cons

iste

ntfe

wes

t-sw

itche

ssu

rfac

eho

ppin

g(S

C-F

SSH

)

FSSH

with

self-

cons

iste

ntsu

rfac

e-ho

ppin

gpr

obab

ilitie

sSa

me

asFS

SHbu

ttri

vial

cros

sing

prob

lem

also

solv

edO

verc

oher

ent

Par

amet

er-f

ree

FSSH

for

exte

nded

syst

ems

ifw

ave-

func

tion

evol

utio

nis

accu

rate

lykn

own

Glo

balfl

uxsu

rfac

eho

ppin

g(G

FSH

)FS

SHge

nera

lized

whi

lem

inim

izin

gnu

mbe

rof

hops

Sam

eas

FSSH

buta

lso

supe

rexc

hang

ede

scri

bed

and

triv

ialc

ross

ing

prob

lem

solv

ed

Ove

rcoh

eren

tR

epla

cem

entf

orFS

SH

Seco

nd-q

uant

ized

surf

ace

hopp

ing

(SQ

UA

SH)

FSSH

gene

raliz

edto

enta

ngle

dtr

ajec

tori

esQ

uant

umef

fect

sca

ptur

ed;

sim

ple

impl

emen

tatio

nB

ecom

esex

pens

ive

ifm

any

traj

ecto

ries

are

enta

ngle

d;re

quir

esen

ergy

part

ition

sche

me

FSSH

with

quan

tum

effe

cts

(Con

tinue

d)


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Tab

le1

(Con

tinu

ed)

Met

hod

Des

crip

tion

Adv

anta

ges

Wea

knes

ses

Sugg

este

dap

plic

atio

nsSt

ocha

stic

mea

nfie

ld(S

MF)

Stoc

hast

icm

odifi

catio

nof

the

Schr

odin

ger

equa

tion

that

inco

rpor

ates

quan

tum

deco

here

nce

and

bran

chin

g

Dec

oher

ence

rigo

rous

lyin

clud

ed;a

dho

cbr

anch

ing

elim

inat

ed;h

opre

ject

ion

muc

hle

sspr

onou

nced

Req

uire

sde

cohe

renc

etim

epa

ram

eter

;pot

entia

lene

rgy

surf

ace

fluct

uate

sev

ery

time

step

DIS

Hba

sed

onw

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insignificant, the Ehrenfest approach is sufficient. At the Ehrenfest level, NAMD is independentof the chosen electronic basis. The adiabatic representation is equivalent to spatial and plane-wavegrids (79, 95) or a localized atomic basis (96). When electron-nuclear correlations are important,nuclear trajectories branch depending on the electronic state. Then, trajectory SH needs to beadopted (21, 33, 91).

Instead of the Schrodinger representation, correlated electron-nuclear dynamics can also bestudied within the Heisenberg representation. By treating quantum mechanically not only the elec-tron creation and annihilation operators, but also the nuclear position and momentum variables,one can achieve the time derivative of the expectation value for any system observable of interestfrom the Heisenberg equation. In this QHD method, there exists an interesting phenomenon: Theoriginal operators become coupled to higher-order operators, resulting in a hierarchy of equations(34, 35, 97–99). Different levels of approximations to the quantum dynamics are achieved throughtermination of the chain with a closure that expresses the expectation values of the higher-orderoperators in terms of products of the expectations of the lower-order operators. In particular, itwas found that the first-order QHD coincides with the Ehrenfest theory (35). Simple extensions tohigher-order QHD can efficiently represent quantum nuclear effects, such as phonon zero-pointenergy, tunneling, and loss of coherence in the electronic subsystem caused by phonons.

2.2.2. Fewest-switches surface hopping, self-consistent fewest-switches surface hopping,and adaptive flexible surface hopping. Among all SH strategies, Tully’s (21) FSSH is the mostwidely used approach. It minimizes the number of surface hops by prescribing an SH probabilitybased on population fluxes, rather than the populations themselves. The NACs are used, alongwith the wave function amplitudes, to determine the FSSH probabilities. The time-dependentprobability of hopping between states i and j within a time step �t reads (21)

gi j (t, �t) = max{

0, − bi j �taii (t)

}, (7)

where

bi j = −2Re(a∗i j di j · R), (8)

ai j = c i c ∗j . (9)

A ground state nuclear trajectory can be used to sample initial conditions to create ensembleaverages for the excited state dynamics.

SH studies on weakly interacting or large-scale systems severely suffer from the trivial crossingproblem, arising from the high density of adiabatic PESs (38–41). Around the trivial crossingpoint, the NAC becomes a delta function, and FSSH probabilities cannot be computed accu-rately in numerical simulations with a finite time step. The SC-FSSH technique (42) providesa straightforward solution to the problem by introducing a self-consistency test to the standardFSSH procedure. The sum of all FSSH probabilities from the active state i to other states j satisfies(42)

gtot = aii (t) − aii (t + �t)aii (t)

. (10)

If we calculate the energy differences between the active adiabatic state i and all other adiabaticstates, and find the adiabatic state k that gives the smallest energy difference, we identify the mainsource of the trivial crossing. Then, we can correct the error by computing the SH probability


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corresponding to the trivial crossing, gik, using the simple expression

gik = gto t −∑j �=k

gi j . (11)

With the Holstein Hamiltonian as an example, SC-FSSH allows us to reduce the simulation time10,000-fold to achieve the FSSH accuracy already in a five-state system (42).

Because an electron is delocalized over a finite space, and electron-phonon interactions aregenerally local (100–102), only a limited number of nuclear degrees of freedom are stronglycoupled to the electron dynamics. Thereby, one can treat a small portion of the nuclei surroundingthe electron in an SH manner and the rest of the nuclei simply at the MD level (43). As both thecentral position and extension of the electron may change in time, this should be done in aflexible way by adding and/or removing neighboring nuclear degrees of freedom to/from the SHsubsystem at any time step. In this aspect, the problematic trivial crossings are avoided becauseall adiabatic states are spatially close. The computational cost is also largely reduced because onlya very small Hamiltonian matrix is diagonalized to get all important PESs. A flexible time-steptechnique, which ensures the smoothness of all time-dependent adiabatic states, enables us todescribe SH accurately with a relative large time step. This FSH algorithm (43, 44) based on aminimum subsystem implementing SH and a maximum time step for SH dynamics can recoverall charge transport regimes described by existing theories (103–105) and can be easily extendedto more complex Hamiltonians.

2.2.3. Global flux surface hopping and second-quantized surface hopping. Superexchangeis a class of dynamical processes (106) in which two electronic states are coupled indirectly throughan intermediate state, typically with higher energy. Common to nanoscale systems, Auger-typeelectron-hole energy exchange and multi-exciton (ME) generation and annihilation (107–109) aremultiparticle reactions, which also proceed with intermediate states. Transitions into high-energyintermediate states violate energy conservation and are forbidden in SH. Because FSSH allowstransitions only between states that are directly coupled, it mistreats quantum processes involvingthe superexchange mechanism. GFSH solves this problem while remaining close to FSSH in otherinstances. Rather than using the FSSH state-to-state flux given by Equation 7, the GFSH method(45) considers the gross population flow between states. The SH probabilities are expressed as

gi j = �a j j

aii

�aii∑k �akk

(if �aii < 0, �a j j > 0, and �akk < 0). (12)

No other type of state switching is allowed. Similar to FSSH, GFSH uses a flux of populationsrather than their absolute values, and therefore, it also minimizes the number of hops. Just likeFSSH, GFSH fulfills the internal consistency: The changes in the state populations according tothe SH rules (Equations 7 and 12) agree with the changes produced by solving the Schrodingerequation. Numerical calculation shows that GFSH captures the superexchange mechanism andAuger-type population transfer. GFSH can replace FSSH, although further tests are needed(45).

The problem of superexchange can be related to the quality of the nuclear wave-functionrepresentation in the approximate semiclassical schemes. In particular, FSSH utilizes a set ofuncorrelated trajectories to describe a nuclear wave packet. The approximation breaks downwhen nuclear quantum effects become important. The SQUASH method has been developedto overcome this limitation of the FSSH method (46). The approach is based on two key ideas.First, one describes dynamics in terms of coupled N-particle states that entangle N semiclassical


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trajectories. In contrast, the standard FSSH formulation uses only one-particle states, each ofwhich is associated with an independent trajectory. Second, SQUASH allows energy exchange viaentangled trajectories. This is achieved by imposing energy conservation on a set of N coupledtrajectories, rather than on each individual trajectory. The resulting SQUASH technique achieveshigh accuracy as demonstrated on a three-state model of superexchange. The energy exchange inthe set of entangled trajectories provides a natural mechanism for tunneling and superexchange,and can be used to capture decoherence effects.

2.2.4. Stochastic mean-field, decoherence-induced surface-hopping, and coherencepenalty functional theories. The SMF method (50) to NAMD bridges the gap between mixedquantum-classical and fully quantum descriptions. With the presence of additional terms in theSchrodinger equation that result from the system-environment interaction, SMF accounts for thequantum features of the environment with the Lindblad approach (110). In the simplest form,the quantum environment, such as a set of harmonic oscillators linearly coupled to the system,is described by Markovian diffusion terms in the Schrodinger equation (50). The SMF methodsimultaneously resolves the two major drawbacks of NAMD: Decoherence effects within the quan-tum subsystem due to interactions with the environment are rigorously included, and branching ofNAMD trajectories is achieved. Decoherence provides the physical mechanism for the trajectorybranching. Hop rejection due to violation of energy conservation disappears in the SMF approach.

The quantum mechanical wave packet of the whole system, including both electrons and nu-clei, splits into uncorrelated branches and loses coherence over time. The resulting decoherencecan be viewed as an environment-induced destruction of superpositioned quantum states of themicroscopic system (111, 112). Drawing from the methodology of stochastic Schrodinger andmaster equations (113–115), the DISH method (51) was proposed. By combining the computa-tional simplicity of quantum-classical NAMD with a formal treatment of quantum decoherence,DISH provides a straightforward and physically justified trajectory SH scheme, in which quantumtransitions between surfaces occur only during decoherence events. The transition probabilitiesare computed according to the standard quantum mechanical rules. On one hand, DISH can beviewed as an SH approach to quantum dynamics in dissipative environments. And, on the otherhand, DISH unifies decoherence and nonadiabatic transitions, providing a nonphenomenologi-cal account of quantum transitions in condensed-phase systems. DISH extends the feasibility ofquantum-classical simulations to large quantum systems in macroscopic environments.

The CPF method (52) is another approach to incorporate decoherence effects into NAMDsimulations. The method is based on a simple idea of dynamically penalizing the development ofcoherences during the evolution of quantum degrees of freedom. The methodology is formulatedon the grounds of the Ehrenfest method for semiclassical dynamics. Decoherence effects areintroduced via an additional term in the classically mapped Hamiltonian, thus preserving theoverall Hamiltonian structure of the EOM. The CPF is analogous to XC functionals in DFT.It provides an effective way of introducing dynamical correlation effects, such as decoherence,on top of the Ehrenfest approach. The CPF methodology has a certain relation to QHD, andthe method can be enhanced by allowing some of the variables entering the penalty functional todepend on time. A simple form for the penalty functional has been proposed, and good resultshave been demonstrated (52). The dependence of the penalty functional on coherences can berather arbitrary, in principle, and other functional forms may prove more accurate, more general,or both. It is straightforward to combine the CPF scheme with FSSH and related approachesdiscussed above, in which SH probabilities can include decoherence effects through the modifiedtime-dependent Schrodinger equation.


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2.3. User-Friendly Implementation: The PYXAID Program

The PYXAID (PYthon eXtension for Ab Initio Dynamics) program has been developed as an open-source, flexible, and computationally efficient implementation of the NAMD methodology in theframework of KS DFT for large-scale condensed matter systems (93, 116). It carries out a numberof basic and more advanced functionalities, including standard FSSH, the decoherence correctionsvia DISH, the use of ME basis configurations of the TDKS equations, and the direct simulationof photoexcitation via explicit light-matter interaction. Advanced integration techniques withTrotter factorization (117) of the evolution operator for solving the time-dependent Schrodingerequation lead to a significant speedup of the calculations and provide more stable solutions. TheCPA approximation (93) achieves additional and considerable computational savings and makes itpossible to study photoinduced dynamics at the ab initio level in systems comprising hundreds ofatoms and involving thousands of electronic states. The first PYXAID paper describes the CPA forFSSH and DISH (93). The software is interfaced with QUANTUM ESPRESSO (118), which isused as an efficient driver for ab initio electronic structure and MD calculations. The key featuresof the PYXAID program have been demonstrated by studying the electron-nuclear dynamicsin a variety of systems. PYXAID is organized as a Python extension module and can be easilycombined with other Python-driven modules, enhancing user-friendliness and flexibility of thesoftware. In addition to QUANTUM ESPRESSO, PYXAID has been interfaced with VASP andsemiempirical electronic structure codes. The source and additional information are available onthe PYXAID website (http://gdriv.es/pyxaid). The program is released under the GNU GeneralPublic License.

3. INORGANIC INTERFACES

Inorganic materials (e.g., colloidal QDs, noble metal nanoparticles, and TiO2) exhibit high chargecarrier conductivity and excellent photostability. Photoinduced electron transfer at the interfacesbetween these inorganic components is essential for various photovoltaic and photocatalytic appli-cations. Electron transfer occurs by two basic mechanisms (61): Adiabatic electron transfer resultsfrom a vibrational motion driving the electronic subsystem over a transition state, and nonadiabaticelectron transfer occurs by a quantum transition between electron donor and acceptor states. Adi-abatic electron transfer relies on strong donor-acceptor coupling, whereas nonadiabatic electrontransfer operates in the weak-coupling regime. The nonadiabatic electron transfer rate is enhancedby the high density of acceptor states. The adiabatic and nonadiabatic mechanisms are describedby different mathematical expressions [e.g., an Arrhenius expression and Fermi’s golden rule (55),respectively]. The complex interplay of donor-acceptor and electron-phonon interactions createsa broad spectrum of electron injection scenarios. This section describes recent atomistic studieson real-time photoinduced electron transfer at interfaces of bulk and nanoscale TiO2 with semi-conducting and metallic nanoparticles. We analyze in detail why hot electrons can be extractedefficiently from PbSe QDs into TiO2, how TiO2 dimensionality determines the mechanism ofelectron transfer from CdSe QDs, and why charge separation can be achieved instantaneously atthe interface between a gold particle and TiO2.

3.1. Extraction of Hot Electrons from a PbSe Quantum Dot into a TiO2 Slab

In recent years, QDs have been extensively employed as chromophores for TiO2 sensitizationproducing quantum dot–sensitized solar cells (QDSCs) (119). QDs are excellent light absorbersdue to their large intrinsic dipole moments, high extinction coefficients, and good photostability.


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They have size-dependent band gaps and thus can be easily tuned to absorb light at any wave-length of the solar spectrum. QDs provide opportunities for increasing solar cell voltage by rapidextraction of hot charge carriers and enhancing current using the additional energy available at theblue end of the solar spectrum via the generation of multiple electron-hole pairs (120). Because ofthese advantages, QDSCs become promising candidates to harvest sunlight for solar-to-electricalenergy conservation.

Photoinduced electron transfer is key for QDSC efficiency. As a representative example, thenanoscale system comprising a PbSe QD adsorbed on a rutile TiO2 (111) surface has beeninvestigated (61). In line with recent time-resolved experiments (19, 20), the computational resultdirectly mimics the observation that the ultrafast interfacial electron transfer in the PbSe-TiO2

system successfully competes with energy losses due to electron-phonon relaxation inside thePbSe subsystem. The electron transfer is found to proceed primarily by the adiabatic mechanism(see Supplemental Figure 1; follow the Supplemental Material link from the Annual Reviewshome page at http://www.annualreviews.org) because of the strong coupling between PbSe andTiO2. Owing to the large size and high rigidity of QDs, the electron donor density is spreadover the whole QD, whereas the acceptor density is distributed nearly uniformly across the TiO2

slab. The optical phonons available in the PbSe-TiO2 system are of the same order of magnitudeof thermal energies because QDs comprise heavy elements. These vibrations, in particular polarPb-Se and Ti-O stretches, promote electron transfer because they can rapidly shift the electronicdensity between the donor and acceptor species. Low-frequency modes of TiO2 and PbSe surfacescreate an inhomogeneous distribution of initial conditions for electron transfer. The nonadiabatictransfer component is nearly an order of magnitude slower than the adiabatic electron transfer.

3.2. Minimizing Electron-Hole Recombination on TiO2Sensitized with PbSe Quantum Dots

Despite the rapid interfacial charge separation, the final yields of the light-induced processes inQDSCs are limited by electron-hole recombination that also occurs at the interface. Minimizingcharge recombination can largely enhance the photon-to-electron conversion efficiency.

Ab initio NAMD has been combined with analytic theory to investigate charge recombination atthe PbSe QD-TiO2 interface (62). The time-domain atomistic simulation directly mimics the laserexperiment (20) and generates important details of the recombination mechanism. The simulationsindicate that the recombination is largely promoted by a high-frequency optical Raman-activemode of TiO2. Lower-frequency optical modes contribute to a lesser extent. The elastic electron-phonon scattering takes 40 fs, which is an order of magnitude shorter than the picosecond timescaleof inelastic scattering. The simulated electron-hole recombination timescale agrees well withthe experimental observation (20). The donor and acceptor states are strongly localized on thecorresponding materials. This contrasts with the photoinduced charge separation in the samesystem, which starts from a QD state that is delocalized onto TiO2 and which is significantly fasterthan the charge recombination. Counter to expectations, the PbSe-TiO2 bonding strengthens atan elevated temperature because thermal fluctuations create additional bonding opportunities.

An analytic theory extends the simulation results to larger QDs and longer QD-TiO2 bridges.It shows that the electron-hole recombination rate can be suppressed exponentially by increasingeither the ligand bridge length or the QD size (see Supplemental Figure 2). Changes in bothdonor-acceptor coupling and the energy gap lead to exponential dependence, with the couplingproviding a more significant contribution. By varying the QD size and/or ligands, one can reducecharge losses while still maintaining efficient charge separation, providing design principles foroptimizing solar cells.


Supplemental Material

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http://www.annualreviews.org

http://www.annualreviews.org/doi/suppl/10.1146/annurev-physchem-040214-121359


3.3. Dimensionality of TiO2 Determines Photoinduced ElectronTransfer Mechanism from CdSe Quantum Dots

The dependence of electron transfer efficiency on the system properties is very different for the adi-abatic and nonadiabatic electron transfer mechanisms. The adiabatic mechanism requires strongdonor-acceptor coupling, and therefore, it is quite sensitive to the binding mode, and the presenceand length of a bridge. In contrast, the nonadiabatic mechanism operates if the donor-acceptorcoupling is weak and requires a high density of acceptor states and the availability of phononmodes to accommodate changes in the electronic energy during nonadiabatic transitions. As aresult, the efficiency of nonadiabatic electron transfer depends on the photoexcitation energy andacceptor size. Highly ordered 1D nanostructures (e.g., nanotubes, nanowires, and nanorods) haverecently received considerable attention as solar materials (121–123). They provide a significantimprovement in the charge transport and photoconversion efficiency compared to 0D QDs. Thephotoinjection mechanism of electrons across QD-TiO2 interfaces may vary with the shape of thesemiconductor nanostructure.

The role of TiO2 dimensionality on the mechanism of photoinduced interfacial electron trans-fer from CdSe QDs into nanoscale TiO2 has been studied (63). A quasi-0D TiO2 QD and 1DTiO2 nanobelt have been considered. As shown in Supplemental Figure 3, the adiabatic mech-anism operates in the TiO2 QD system because of the strong chemical binding between CdSeand TiO2, arising from unsaturated chemical bonds on the QD surface. The density of acceptorstates in the TiO2 QD is low, inhibiting the nonadiabatic mechanism. In contrast, the injectioninto a TiO2 nanobelt is nonadiabatic because the donor-acceptor coupling is weak, the acceptorstate density is high, and multiple phonons can accommodate changes in the electronic energy.The CdSe adsorbant breaks the symmetry of delocalized band-type states of the TiO2 nanobelt,creating localized acceptor states. It also relaxes donor-acceptor and nonadiabatic coupling se-lection rules and generates more electron transfer channels. Both mechanisms can give efficientand ultrafast injection. However, the fundamental principles leading to efficient charge separationstrongly depend on the type of nanoscale material.

3.4. Instantaneous Charge Separation on a TiO2 SurfaceSensitized with Plasmonic Nanoparticles

Solar cells based on semiconductor sensitization with metal nanoparticles have also attractedsignificant attention because of the unique electronic and optical properties of metallic clusters(124). The exciting optical physics of metal nanoparticles arises from the resonant interactionof conduction band electrons and the electromagnetic field (125). The collective excitations,usually known as plasmons, are responsible for the specific light extinction and high local fields.In addition, the prominent catalytic properties of gold nanoparticles on well-ordered metal oxidesubstrates stimulate extensive research activities. These systems combine the light-harvestingability of semiconductor nanocrystals with the catalytic activity of small metal particles, showinggreat promise in photocatalysis, such as light-driven hydrogen production (126).

An Au20 nanoparticle absorbed on a TiO2 surface has been carefully studied (64). The in-teraction between gold and TiO2 is noncovalent at both low and room temperatures. Ab initiosimulations show that the photogenerated plasmon-like state is highly delocalized onto TiO2 (i.e.,it is shared by the whole system) (see Figure 3). Because of this, the interfacial charge separationoccurs instantaneously upon photoexcitation of the plasmon band with a high probability (<50%),bypassing the intermediate step of electron-hole thermalization inside the Au20 nanoparticle. Inthe remaining 50% of the scenarios, the plasmon excitation generates electron-hole pairs in gold,



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a Plasmon b TiO2 acceptor c Fermi energystate

Figure 3Charge densities of (a) a plasmon state, (b) a TiO2 acceptor state, and (c) the Fermi energy state of theAu20-TiO2 system. The excited state is delocalized significantly onto TiO2, leading to instantaneous chargeseparation upon photoexcitation at the plasmon energy. Entropy drives the electron into the TiO2 bulk,exemplified by the TiO2 acceptor state. Following electron-vibrational relaxation, the electron canrecombine with the hole, residing in the Fermi energy state, on a picosecond timescale. Figure adapted withpermission from Reference 64. Copyright 2014 American Chemical Society.

and the electron is transferred to the TiO2 surface on a sub-100-fs timescale. Electron-phononenergy relaxation paralleling electron injection is somewhat slower. Driven by entropy due to thehigh density of bulk TiO2 states, the electron overcomes the Coulombic electron-hole attractionand delocalizes further into TiO2 bulk. Structural defects in the TiO2 surface can trap the injectedelectron near the gold nanoparticle, leading to a picosecond timescale of electron-hole recom-bination. Electrons that have diffused into bulk TiO2 can find their way back to the surface andrecombine with the hole on a much longer timescale.

The electron injection occurs primarily by the nonadiabatic mechanism due to a relatively weakdonor-acceptor coupling and a high density of TiO2 acceptor states. The recombination proceedsexclusively by the nonadiabatic mechanism because of the large energy gap between the initialand final states in this case. The obtained electron transfer and recombination timescales showexcellent agreement with the time-resolved experimental data (17). The strong optical responseof the surface plasmon, rapid charge separation, and a significantly slower electron-hole recom-bination provide the fundamental basis for utilization of plasmon-sensitized TiO2 as an excellentphotovoltaic material and a visible-light photocatalyst.

4. ORGANIC/INORGANIC HYBRIDS

Organic/inorganic nanocomposites find multiple applications in photovoltaic, photocatalytic, andtransport devices. Similar to metal nanocrystals, graphene has no band gap and exhibits ultrahighcharge mobility (127, 128). Efficient photoinduced charge separation needs to compete withenergy losses due to rapid electron-hole annihilation inside metallic graphene. In contrast, bulksemiconductors, QDs, molecules, and polymers possess band gaps; thus charge recombinationcan be restrained. Besides electricity, solar energy can be converted to chemical energy, forinstance, by water splitting assisted by inorganic photocatalysts. In this section, we describe recentwork concerning graphene-TiO2, QD-molecule, QD-polymer, and GaN-H2O interfaces. Weshow that both electron and energy transfer from graphene to the TiO2 surface are consistently


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faster than energy relaxation and that defects are essential rather than detrimental for fast electrontransfer from QDs to molecules. We rationalize a counterintuitive result that, along an insulatingbridge, can enhance photoinduced charge separation. We also introduce a new type of electrontransfer mechanism, Auger-assisted electron transfer, that eliminates the electron transfer ratereduction in the Marcus inverted regime. Because Auger-type processes are generic to nanoscalematerials, Auger-assisted electron transfer should be very common in these systems. We findthat 1D poly(3-hexylthiophene) (P3HT) behaves as a 0D molecule, whereas a 0D QD acts asa 3D bulk material in the P3HT/QD interaction region. The inverted dimensionally restoressymmetric electron-hole dynamics, creating favorable conditions for current generation in solarcells. Finally, we discuss photocatalytic water oxidation on a semiconductor surface and formulatea set of design rules for improving water splitting.

4.1. Efficient Photoinduced Charge Separation Acrossthe Graphene-TiO2 Interface

Many experimental efforts are currently focusing on the synthesis of hybrid graphene-TiO2

nanocomposites for photovoltaic and photocatalytic applications (129, 130). Graphene’s advan-tages include a high surface area for interfacial contact, excellent charge conductivity, and out-standing mechanical properties. Graphene can harvest a larger fraction of the solar spectrum thancan many other nanostructured materials. The obtained electrons can produce electricity or drivea water-splitting reaction to generate hydrogen. However, because graphene is a metal, the pho-togenerated electrons and holes may rapidly relax through the continuous manifold of states andannihilate. Therefore, one wonders whether graphene can be used at all as a chromophore forsolar power conversion.

A representative hybrid graphene-TiO2 system has been constructed (65). At ambient tem-peratures, the interfacial oxygen atoms disrupt the π-electron system of graphene. This makesgraphene locally semiconducting and strengthens graphene-TiO2 bonding. The electron and en-ergy transfer in graphene-TiO2 composites can proceed in both directions, depending on theenergy of the excited electron. Once the electron relaxes to the bottom of the TiO2 conductionband, it can move back onto graphene, as graphene has energy levels within the TiO2 band gap.The back-transfer process competes with the electron delocalization into bulk TiO2 that is drivenby entropy, related to the TiO2 DOS.

The timescales for the photoinduced interfacial electron transfer, energy relaxation, andenergy transfer can be obtained using NAMD. It has been established that the photoinducedelectron transfer occurs faster than the electron-phonon energy relaxation (i.e., charge separationis efficient in the presence of electron-phonon relaxation). The ultrafast electron injection occursbecause of the strong donor-acceptor coupling, favoring the photoexcitation of states that aredelocalized significantly between the two subsystems (see Supplemental Figure 4a). Injection ispromoted by both out-of-plane graphene motions, which modulate the graphene-TiO2 distanceand interaction, and high-frequency carbon bond stretching and bending vibrations, whichgenerate large nonadiabatic coupling. The subsequent evolution occurs by rapid nonadiabatictransitions down the manifold of delocalized states, resulting in simultaneous electron transfer,energy transfer, and electron-vibrational energy relaxation. The simulation shows that bothelectron transfer and energy transfer from graphene to the TiO2 surface are consistentlyfaster than the relaxation, regardless of the excitation energy (see Supplemental Figure 4b,c),rationalizing the high direct light-to-current conversion efficiencies of graphene-TiO2 solarcells reported experimentally (131). Thereby, graphene-TiO2 composites can form the basis forphotovoltaic and photocatalytic devices.



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4.2. Defects Are Needed for Fast Photoinduced ElectronTransfer from a Quantum Dot to a Molecule

The surfaces of most optically active QDs are metal rich because metal atoms can successfullyreconstruct nanocrystal surfaces, eliminating unsaturated chemical bonds and other defects (132).As a result, QD surfaces are missing the complementary elements, for instance, sulfur atoms inCdS QDs. Sulfur vacancies create states below the conduction band (133). Defects are considereddetrimental in many applications. For instance, they lead to QD blinking due to charge trappingand rapid electron-phonon energy losses due to decreased electronic energy gaps and increasedelectron-phonon coupling. Surface defects can have a positive effect on the photoinduced chargeseparation, thereby improving solar energy conversion efficiencies (66).

Electron transfer from a PbS QD to the rhodamine B molecule and subsequent electronreturn from rhodamine B to the QD has been investigated in detail (66). Both charge separationand recombination are nonadiabatic processes, driven by nuclear vibrational motions. Thenonadiabatic electron-phonon coupling is created predominantly by motions of the moleculebecause it comprises lighter atoms and is more labile than the QD. In contrast, the donor-acceptorcoupling between the QD and molecule arises from the QD because its wave function is moredelocalized and leaks onto the adsorbed molecular species, generating the required overlapbetween the donor and acceptor wave functions. Although the donor-acceptor energy gap issmaller for the recombination, the NAMD simulation supports the experimental observation(134) that charge separation is faster than recombination, rationalizing this fact by a twice-stronger nonadiabatic coupling for the forward than the backward electron transfer reaction.The computed electron-hole recombination timescale obtained for the system without defectsagrees very well with experiment (134). However, the charge separation timescale is notablyoverestimated. Repeating the simulation by including a sulfur vacancy has improved agreementbetween theory and experiment. The missing sulfur creates unsaturated chemical bonds on leadatoms, which form the PbS conduction band. As a result, the QD lowest unoccupied molecularorbital (LUMO) is lowered in energy, decreasing the donor-acceptor energy gap. In addition,the unsaturated bonds extend the LUMO density onto the adsorbed molecule, increasingthe donor-acceptor coupling. The combination of a decreased energy gap and an increasednonadiabatic coupling accelerates the charge separation (see Figure 4). The counterintuitiveconclusion that defects are helpful rather than harmful to sunlight harvesting and utilizationbrings a novel perspective to QD synthesis for photovoltaic and photocatalytic applications.

4.3. An Insulating Bridge Greatly Enhances Photoinduced ElectronTransfer in Quantum Dot–Fullerene Nanocomposites

Bang & Kamat (135) prepared fullerene-QD solar cells by placing a blend of CdSe QDs andC60 on an optically transparent electrode. By functionalizing C60 with a thiol compound, theycovalently linked it to the QD and investigated the photoinduced electron transfer from the QDto C60 using time-resolved transient absorption spectroscopy. The covalent linking provided asignificant improvement in the charge separation and photoconversion efficiency compared withthe previous work utilizing a mechanical blend.

To rationalize the experimental findings, investigators have used NAMD combined withTDDFT to characterize photoinduced electron transfer in two kinds of architectures, includinga mechanical mixture of C60 and CdSe QD, as well as covalently linked composites (67). Thecalculations demonstrated that a covalent bridge connecting the QD to C60 is particularlyimportant to ensure ultrafast transmission of the excited electron from the QD photon harvesterto the C60 electron acceptor (see Supplemental Figure 5). Despite the close proximity of the



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LUMO

LUMO

Defect

1 ps

3.4 ps

Cl–+

10.4 ps

HOMO

Figure 4Energy levels and timescales involved in charge separation and recombination processes in the PbS quantumdot (QD)–rhodamine B (RhB) system. The geometries of the QD and RhB are shown next to theircorresponding levels. Figure adapted with permission from Reference 66. Copyright 2013 AmericanChemical Society. Abbreviations: HOMO, highest occupied molecular orbital; LUMO, lowest unoccupiedmolecular orbital.

donor and acceptor species provided by direct van der Waals contact, it leads to a notably weakerQD-C60 interaction than a lengthy and insulating molecular bridge. Additionally, it was foundthat the electron transfer rate in a nonbonded mixture can be tuned by C60 doping with lithium.The calculated electron transfer times are in good agreement with experiment (135). The electrontransfer rate in the QD-bridge-C60 system is enhanced owing to the following three factors.(a) Most importantly, the bridge increases the nonadiabatic coupling by providing high-frequencyvibrational modes. The electron-vibrational interaction is critical to the electron transfer becausesignificant amounts of the electronic energy have to be deposited into vibrational modes.(b) By allowing the QD wave function to extend onto the bridge and effectively increasing theQD size, the bridge lowers the QD band gap and consequently the donor-acceptor energy gap.(c) Long-range correlations between the atomic motions of the donor and acceptor speciescreated by the bridge decrease the phonon-induced pure-dephasing rate and prolong quantumcoherence during the nonadiabatic transition. This study highlights an often-overlooked designprinciple for enhancing photoinduced charge separation in nanoscale light-harvesting materials.

4.4. Auger-Assisted Electron Transfer from PhotoexcitedQuantum Dots to Molecular Acceptors

Traditionally in chemistry, electron transfer processes are understood in terms of the Marcustheory (136). Because of strong electron-nuclear interaction in molecules, intermolecular electrontransfer is accompanied by a large rearrangement of the nuclear configuration. The Marcus theorydescribes the well-known dependence of the electron transfer rate on the donor-acceptor energygap, including the normal, barrierless, and inverted regimes. In bulk inorganic semiconductors,electron transfer requires little change in nuclear configuration due to weak electron-phononcoupling (137), and charge carriers are regarded as quasi-free particles. Both electron-hole and


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electron-phonon interactions in nanoscale materials fall between those in molecules and bulk. Thechoice of an appropriate model for describing photoinduced electron transfer on the nanoscaleremains an area of active research.

Because of quantum confinement, semiconductor QDs exhibit atomic-like discrete electroniclevels and corresponding excitonic transitions that can be widely tuned by QD size (138). Suchsize-dependent energetics provides an ideal platform for testing theoretical models for describingelectron transfer from excitonic nanomaterials. With regard to this aspect, photoinduced electrontransfer from CdS, CdSe, and CdTe QDs to three molecular acceptors, anthraquinone, methylviologen, and methylene blue, has been systematically studied (68). The observed electron trans-fer rates increase with decreasing QD size, regardless of QD compositions and acceptor redoxpotentials, showing a lack of the Marcus inverted regime over a broad range of donor-acceptorenergy gaps, from 0 to 1.3 eV (see Supplemental Figure 6). The unexpected driving force de-pendence has been accounted for by the recently proposed Auger-assisted electron transfer model(68), in which the electron transfer is coupled to the excitation of the hole, circumventing theunfavorable Franck-Condon overlap in the Marcus inverted regime. This model is supported bycomputational studies on a realistic QD-acceptor complex.

The photoinduced electron transfer from QDs is fundamentally different from those in molec-ular chromophores and bulk semiconductors. Supplemental Figure 6 shows the time evolution ofthe energies of various parts of the system along a representative trajectory. The energy lost by theelectron during the transfer is gained at the initial stage exclusively by the hole rather than by thephonons, confirming the proposed Auger-assisted electron transfer mechanism. Because Auger-type processes occur in most nanomaterials exhibiting quantum confinement, the Auger-assistedelectron transfer model proposed for CdX QDs should be generally applicable to exciton disso-ciation in other nanomaterials, including nanotubes, nanowires, quantum wells, and graphene.

4.5. Inverted Dimensionality Restores Electron-Hole Symmetryin a Quantum Dot–Polymer Hybrid

Hybrid photovoltaic cells based on inorganic QDs and polymers possess significant potential forlow-cost and scalable solar power conversion. Polymers harvest solar light and donate electronsin organic solar cells. Polymer-based solar cells offer the advantages of solution processing andstraightforward chemical synthesis. At the same time, Coulomb interactions between charge car-riers are strong because of low dielectric constants, giving rise to strongly bound electron-holepairs rather than to free charge carriers (139). This drawback significantly reduces the powerconversion efficiency of polymer-based solar cells.

Compared to fullerenes, which are used as electron acceptors in traditional organic solar cells,colloidal QDs exhibit better morphological stability and higher electron mobilities. In addition,QDs improve light harvesting because of their large absorption cross sections, easily tunableover the entire solar spectrum. The electron-phonon relaxation dynamics in QDs have attractedintense attention. Hot-carrier generation and carrier multiplication provide opportunities toimprove the conversion efficiencies of QDSCs by reducing the loss of high-energy carriers.Using the advantages of both organic polymer and inorganic QD materials provides new ways toenhance solar cell performance.

NAMD combined with TDDFT has been employed to investigate the photoinduced electronand hole dynamics in a heterojunction formed by P3HT and a CdS QD. QDs are viewed as quasi-0D materials, whereas polymers are 1D. Simple models predict discrete energy levels in QDs andcontinuous bands in polymers. However, the atomistic calculations present a different picture.Generally, QDs exhibit discrete levels only close to the band gap. Indeed, Figure 5 shows that



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0.87 eV

1.41 eV

e

h

a

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S (1

/eV

)Energy (eV)

Holes Electrons

b

25

50

0–2 –1 0 2 31

P3HT

CdS

Figure 5(a) Projected density of states (DOS) of the poly(3-hexylthiophene) (P3HT)-CdS quantum dot (QD) system.The QD has a much larger DOS than P3HT does. (Inset) The offset energy between the donor and acceptororbitals for the electron (e) and hole (h) transfer. (b) Charge densities of the donor and acceptor orbitals forthe electron and hole transfer. The electron donor state is significantly delocalized between P3HT and theQD. Similarity, the hole donor state is also shared by the QD and P3HT. The acceptor states are localizedin both cases. The vertical arrows between panels a and b relate the donor and acceptor orbital densities tothe energies.

the CdS QD LUMO is separated from LUMO + 1 by approximately 0.5 eV. At higher energiesrelevant for the charge separation dynamics, the QD spectrum is continuous. The polymer indeedexhibits a band-like electronic structure. At the same time, the DOS of the polymer is much lowerthan that of the QD. In the local interaction QD-P3HT region involved in the photoinducedcharge separation, and at the relevant energy range, P3HT behaves as a molecule, while the QD isnearly bulk-like. The inversion of the dimensionally, relative to the common expectation, helps tobalance the electron and hole injection rates. Such balance is essential for a solar device; otherwise,one of the charges will present a bottleneck to the photoinduced dynamics. The driving force forthe hole transfer from the QD to P3HT is larger, but the density of P3HT acceptor states is small(Figure 5). In comparison, the driving force for the electron transfer from P3HT to the QD issmall, but the density of QD acceptor states is large. The leveling of the two factors produceselectron and hole injection times on a timescale of several hundred femtoseconds, in agreementwith experiment (140).

4.6. Positive Charge Dynamics During Photocatalytic WaterSplitting on a GaN(10-10) Surface

Photocatalytic water splitting is a promising avenue to sustainable, clean energy and fuel pro-duction. Since the discovery of water splitting on TiO2 electrodes by Fujishima & Honda (141),significant progress has been made in the experimental characterization and preparation of various


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Thermal activation>1 ns Hole relaxation

~50 fs

h+h+h+ h+h+h+

h+h+h+

h+h+h+

ba

h+h+h+

N-H deprotonation>1 ps

>50 ps

Hole migration~50 fs

Proton transfer~1.5 ps

~0.5 ps

O-Hdeprotonation:water splitting

Photoexcitation

Figure 6(a) Electron spin density of the photogenerated hole in the GaN-water system at 0.22 eV below the valence band edge. The blackparallelogram indicates the simulation cell. (b) Kinetic scheme of the hole and proton migration processes involved in the initial stagesof photocatalytic water oxidation. Figure adapted with permission from Reference 70. Copyright 2013 American Chemical Society.

photocatalytic materials, as well as in the theoretical description of the underlying processes andtheir mechanisms (142, 143). Nonetheless, the fundamental understanding is far from complete.One of the manifestations of the lack of comprehensive knowledge is a relatively small quantumyield of this reaction achieved with the currently available materials. The search for efficient andcheap catalytic materials has led scientists to explore a large variety of semiconductor photo-catalysts. In recent studies, Domen and colleagues (144) have shown that GaN can be used forwater splitting under ultraviolet light irradiation, although with a relatively small yield. The yieldincreases in a GaN:ZnO solid solution and especially in the presence of a cocatalyst.

A comprehensive kinetic model of the processes taking place during the initial stages of thephotoinduced water oxidation reaction on the GaN(10-10) surface has been constructed basedon NAMD calculations (see Figure 6) (70). The quantum dynamics of hole relaxation, mediatedby coupling to nuclear vibrations, the hole transfer from GaN to water, and the ensuing proton-transfer events have been characterized. The calculations show that the hole loses its excess energywithin 100 fs and localizes primarily on the nitrogen atoms of the GaN surface, initiating a sequenceof proton-transfer events from the surface N-H group to the nearby OH groups and bulk watermolecules. During the energy relaxation, the hole transiently populates the oxygen species, makingwater oxidation possible from both kinetic and thermodynamics points of view. The relaxationkinetics of the hole determines its dwelling time on the surface hydroxyl groups. This time isapproximately 50 fs and is too short in general to initiate the nuclear rearrangements required forthe water oxidation reaction, contributing to the low efficiency of water splitting on pure GaN.This atomistic study strongly indicates that an efficient material for water oxidation should favorhole localization on surface hydroxyl groups. Lacking in pure GaN, this feature can be achievedwith composite materials, such as oxide cocatalysts, oxinitride substrates, and their chemicallymodified derivatives.

In the absence of a hole, water molecules are completely dissociated, occupying all availablegallium and nitrogen surface sites. The situation is qualitatively different for the charged surface, inwhich some protons dissociate from surface N-H groups and migrate near the surface. The result


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is a hydroxonium cation and a free, uncapped nitrogen site. The proton moves further betweenthe hydroxonium and the adjacent chemisorbed hydroxyl groups or, with a smaller probability,diffuses into bulk water. The free energy barriers for the proton transfer along the GaN surface arecalculated to be 2.16 and 0.64 kcal/mol, depending on the direction of the proton transfer amongthe asymmetric surface sites. The characteristic time of the proton-transfer reaction starting fromthe most stable configuration of the charged surface is estimated to be 1.6 ps. Both the freeenergy barriers and the transfer rates are in good agreement with the available experimental andtheoretical studies (144).

5. ORGANIC SYSTEMS

Organic systems, including small molecules and polymers, exhibit both advantages and disadvan-tages compared to inorganic compounds. Organic molecules are extremely diverse, providing anessentially unlimited availability of raw materials. They are mechanically flexible and lightweight.They can be mass produced at a low cost. At the same time, electrons and holes are strongly boundinside organic matter, making photoinduced charge separation challenging. The opposite process,the radiative recombination of injected charges, occurs more readily, giving rise to light-emittingdiodes. Electron-phonon interaction is also strong in organic materials, generating polarons withlarge effective masses and low mobilities. Charge and exciton dynamics at organic interfaces areof great importance for solar energy and electronics applications. In the following, we present acomprehensive kinetics at a pentacene-C60 interface, exhibiting a fundamentally interesting andpractically important phenomenon known as singlet fission (SF). SF allows one to convert onephoton into two electron-hole pairs, thereby increasing the photoinduced current. We also ana-lyze the origin of significant asymmetry between electron and hole transfer in a polymer-carbonnanotube (CNT) composite and propose how this asymmetry can be utilized to tune photovoltaicperformance.

5.1. Singlet Fission and Charge Transfer at the Pentacene-C60 Interface

The generation of two electron-hole pairs per single absorbed photon is known in organic systemsas SF (145–147). SF is interesting from a fundamental point of view because simple selection rulesforbid the excitation of two electrons by one photon. SF holds promise for the development of so-lar cells with enhanced photon-to-electron yields, and therefore, it is of substantial applied interestas well. The efficiency of photovoltaic devices based on this principle is determined by complexdynamics involving key electronic states coupled to particular nuclear motions. Extensive exper-imental and theoretical studies are dedicated to this topic, generating multiple opinions on thenature of such states and motions, their properties, and mechanisms of the competing processes,including electron-phonon relaxation, SF, and charge separation (145, 146). Using NAMD, onecan identify the most important steps involved in SF and subsequent charge separation, and builda comprehensive kinetic scheme that is consistent with the existing experimental and theoret-ical results. The model helps to resolve controversies regarding the nature and importance ofintermediate states, energy-level alignment, SF mechanism, and timescales of quantum dynamics.

A minimalistic atomistic model has been constructed to describe a pentacene/C60 interface (71).The simulation has demonstrated that SF competes with the traditional photoinduced electrontransfer between pentacene and C60 layers. Efficient SF relies on the presence of intermediatedark states. These configurations can be viewed as either independent states or components of theME and triplet pair (TT) states arising due to electron correlation. Several pentacene-pentaceneand pentacene-fullerene charge transfer states should be taken into account, including the lowest-energy charge transfer state (CT0) and excited charge transfer states (CT1 and CT2). Having


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e–

a

e–

hv

Ener

gy

~1.8 ps ~2.8 ps

~1.7 ps

~240 fs

~300 fs

DiffusionS1

CT1

+ ME

CT0

CT2

Tx2 Tx2'

b

~38 fs

Figure 7(a) A simulated pentacene-C60 interface and (b) comprehensive kinetic scheme of the singlet fission andcharge transfer processes at the interface. Figure adapted from Reference 71. Copyright 2014 AmericanChemical Society. Abbreviations: CT, charge transfer; ME, multi-exciton.

ME and charge transfer character, these states play critical roles in the dynamics and should beconsidered explicitly when explaining the entire process from photoexcitation to the final chargeseparation.

The relative energies of the states involved in the photoinduced dynamics should be carefullyaligned with respect to each other. Assigning the energy of the CT0 state at approximately 0.5 eVaccording to experiment (148) produces a consistent quantum dynamical scheme. An interestingway of controlling the SF efficiency can be suggested based on the energy alignment. If CT2 isdesigned to have energy larger than that of the TT state, triplet production can be maximized.After dissociation of the TT state, each triplet can access states of the CT0 type, provided thattheir energy is lower than the energy of the TT state. Then, the generation of two electron-holepairs will be maximized. The S1 and ME states involved in the SF process are rather weakly cou-pled. Direct nonadiabatic transitions between these states are suppressed, although not forbidden.Because the S1 and TT states are also weakly coupled, the triplet production originates only fromthe ME state, which is populated during photoexcitation (see Figure 7). Generally, photoexci-tation creates a superposition of the S1 and ME configurations. To maximize the SF yield, oneshould design systems and utilize photoexcitation conditions under which the contribution of theME configurations is maximized. One can also consider designing electromagnetic fields to di-rectionally pump S1 into the ME or TT state. The reported analysis enhances our understandingof the complex quantum dynamics in nanoscale materials capable of the SF and charge transferprocesses.

5.2. Asymmetric Electron and Hole Transfer at a P3HT–CarbonNanotube Heterojunction

Bulk heterojunction organic photovoltaics have been demonstrated as low-cost alternatives tosilicon-based solar cells, offering a long-term solution for clean, renewable energy (149). Toachieve high photon-to-charge conversion efficiency, the electron-hole pair generated by pho-ton absorption in organic photovoltaic systems must overcome the Coulomb attraction, whichoften results in voltage loss. The low dielectric constant of organic conjugated materials resultsin significant Coulomb interactions between charge carriers and gives rise to a strongly boundelectron-hole pair, rather than to free charge carriers.


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By applying the unique methodologies combining TDDFT and NAMD, one can investigatethe photoinduced electron and hole dynamics and energy relaxation across an interface formedby P3HT and a single-walled CNT (72). As shown in Supplemental Figure 7, photoexcitationof the polymer leads to a 100-fs electron transfer, in agreement with experiment (150), followedby an energy loss of 0.6 eV within 0.5 ps. Photoexcitation of the CNT leads to hole transfer,which requires nearly 2 ps, but loses only 0.3 eV of energy. The electron transfer is an orderof magnitude faster than the hole transfer, establishing that the electron and hole dynamics arehighly asymmetric in CNT/P3HT composite materials. The strong disparity arises from thedifferences in the localization of the photoexcited donor states, the densities of the acceptorstates, the strength of the donor-acceptor interaction, and the phonon modes involved. The hole-vibrational relaxation is promoted primarily by the high-frequency C–C stretching modes, withthe electron relaxation additionally involving low-frequency CNT and P3HT motions. Used asa chromophore, P3HT produces faster charge separation but leads to larger energy losses andcannot harvest light in the red region of the solar spectrum. In contrast, CNT absorbs a broaderrange of photons, and reduces energy losses, but gives less efficient charge separation.

The complementary properties of P3HT and CNT can be utilized to improve the performanceof solar cells by simultaneously optimizing light harvesting, charge separation, and energy relax-ation, which affect photovoltaic yield, current, and voltage. By increasing the CNT concentration,one can harvest a broader range of the solar spectrum and reduce energy and voltage losses. Byincreasing the P3HT concentration, one achieves better charge separation and higher currents.The reported simulations provide a comprehensive description of the charge and energy transferdynamics in the hybrid nanoscale material and suggest novel design principles for photovoltaicand photocatalytic devices.

6. CONCLUSIONS AND OUTLOOK

The amount of solar energy reaching the Earth’s surface is approximately 7,000 times morethan our current global consumption, and thereby solar energy conversion is currently the mostpromising tool to solve the energy problem. If we could use a larger fraction of the solar energy,we could reduce our dependence on fossil fuels. A massive array of materials has been designedand applied in photovoltaic and photocatalytic devices. Because of the substantial difference in theorigin and nature of the explored materials, ab initio atomistic simulations are especially valuablefor investigating the charge and exciton dynamics at photovoltaic and photocatalytic interfaces.

The combination of TDDFT and NAMD has provided a unique, practical, and universal the-oretical tool to study various nonequilibrium processes in a broad spectrum of systems. Abovewe summarize recent efforts in both methodological developments and realistic applications. Thetimescales for electron and energy transfer, thermal relaxation, and charge recombination in sys-tems consisting of two complementary inorganic or organic materials have been obtained andcompared extensively with experimental observations. The branching between the alternative dy-namical processes governs the global efficiency of various devices and determines efficiency bottle-necks. Thorough understanding of the mechanisms underlying each dynamical channel providesuseful guidelines for improving the performance of devices for solar energy conversion. The issuesand processes occurring at photovoltaic and photocatalytic interfaces bear close resemblance tothose encountered in electronic, spintronic, and other types of transport processes.

An atomistic simulation of nonequilibrium processes in molecular, nanoscale, and condensedmatter systems relies on an accurate description of the electronic structure and a reliable rep-resentation of the electron-vibrational dynamics. These needs motivate further developments inthe field. More robust and simultaneously efficient XC DFT functionals are required for the



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proper description of long-range electron transfer, multiply excited states, bond breaking, andother situations that take the system far from the ground state equilibrium. To perform large-scale simulations, the computational cost for electronic structure calculations should be reduced.Significant efforts are devoted to the density-functional tight-binding (DFTB) method (151),which parameterizes the key DFT quantities, such as pseudo-atomic orbitals, matrix elements,and short-range repulsions. DFTB can significantly reduce the computational complexity, whilemaintaining reasonable accuracy (152). Implementing time-dependent DFTB can greatly extendthe scope of NAMD applications. Most NAMD applications still neglect decoherence (47–49) andother quantum nuclear effects, which are important for many dynamical processes and deserveserious consideration. With rare exceptions, semiclassical NAMD algorithms capable of capturingthese effects have been applied only to model or small systems. Further simplifying approxima-tions and implementations of such schemes are clearly needed. NAMD simulations performedexplicitly in the time domain can be coupled to kinetic descriptions to explore longer timescales.NAMD techniques have clearly demonstrated the ability to resolve a wide range of problems andquestions arising in systems perturbed far from equilibrium. As demonstrated in this review, inparticular, they satisfy the impending demand of mechanism exploration and material design formore efficient utilization of solar energy.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings thatmight be perceived as affecting the objectivity of this review.

ACKNOWLEDGMENTS

The authors are indebted to many experimentalist and theoretician colleagues for fruitful and il-luminating discussions. Many thanks go to the past and current group members, including AlexeyAkimov, Amanda Neukirch, Vitaly Chaban, Heather Jaeger, and Hyeon-Deuk Kim. R.L. is grate-ful to the SIRG Program 11/SIRG/E2172 of the Science Foundation Ireland. The research wassupported by the US National Science Foundation, grant CHE-1300118, and the US Departmentof Energy, grant DE-SC0006527.

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PC66-FrontMatter ARI 4 March 2015 12:22

Annual Review ofPhysical Chemistry

Volume 66, 2015Contents

Molecules in Motion: Chemical Reaction and Allied Dynamics inSolution and ElsewhereJames T. Hynes � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Crystal Structure and PredictionTejender S. Thakur, Ritesh Dubey, and Gautam R. Desiraju � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �21

Reaction Dynamics in Astrochemistry: Low-Temperature Pathways toPolycyclic Aromatic Hydrocarbons in the Interstellar MediumRalf I. Kaiser, Dorian S.N. Parker, and Alexander M. Mebel � � � � � � � � � � � � � � � � � � � � � � � � � � � � �43

Coherence in Energy Transfer and PhotosynthesisAurelia Chenu and Gregory D. Scholes � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �69

Ultrafast Dynamics of Electrons in AmmoniaPeter Vohringer � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �97

Dynamics of Bimolecular Reactions in SolutionAndrew J. Orr-Ewing � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 119

The Statistical Mechanics of Dynamic Pathways to Self-AssemblyStephen Whitelam and Robert L. Jack � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 143

Reaction Dynamics at Liquid InterfacesIlan Benjamin � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 165

Quantitative Sum-Frequency Generation Vibrational Spectroscopy ofMolecular Surfaces and Interfaces: Lineshape, Polarization,and OrientationHong-Fei Wang, Luis Velarde, Wei Gan, and Li Fu � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 189

Mechanisms of Virus AssemblyJason D. Perlmutter and Michael F. Hagan � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 217

Cold and Controlled Molecular Beams: Production and ApplicationsJustin Jankunas and Andreas Osterwalder � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 241

Spintronics and Chirality: Spin Selectivity in Electron TransportThrough Chiral MoleculesRon Naaman and David H. Waldeck � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 263

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DFT: A Theory Full of Holes?Aurora Pribram-Jones, David A. Gross, and Kieron Burke � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 283

Theoretical Description of Structural and Electronic Properties ofOrganic Photovoltaic MaterialsAndriy Zhugayevych and Sergei Tretiak � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 305

Advanced Physical Chemistry of Carbon NanotubesJun Li and Gaind P. Pandey � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 331

Site-Specific Infrared Probes of ProteinsJianqiang Ma, Ileana M. Pazos, Wenkai Zhang, Robert M. Culik, and Feng Gai � � � � � 357

Biomolecular Damage Induced by Ionizing Radiation: The Direct andIndirect Effects of Low-Energy Electrons on DNAElahe Alizadeh, Thomas M. Orlando, and Leon Sanche � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 379

The Dynamics of Molecular Interactions and Chemical Reactions atMetal Surfaces: Testing the Foundations of TheoryKai Golibrzuch, Nils Bartels, Daniel J. Auerbach, and Alec M. Wodtke � � � � � � � � � � � � � � � � 399

Molecular Force Spectroscopy on CellsBaoyu Liu, Wei Chen, and Cheng Zhu � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 427

Mass Spectrometry of Protein Complexes: From Originsto ApplicationsShahid Mehmood, Timothy M. Allison, and Carol V. Robinson � � � � � � � � � � � � � � � � � � � � � � � � � � 453

Low-Temperature Kinetics and Dynamics with Coulomb CrystalsBrianna R. Heazlewood and Timothy P. Softley � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 475

Early Events of DNA PhotodamageWolfgang J. Schreier, Peter Gilch, and Wolfgang Zinth � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 497

Physical Chemistry of Nanomedicine: Understanding the ComplexBehaviors of Nanoparticles in VivoLucas A. Lane, Ximei Qian, Andrew M. Smith, and Shuming Nie � � � � � � � � � � � � � � � � � � � � � 521

Time-Domain Ab Initio Modeling of Photoinduced Dynamics atNanoscale InterfacesLinjun Wang, Run Long, and Oleg V. Prezhdo � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 549

Toward Design Rules of Directional Janus Colloidal AssemblyJie Zhang, Erik Luijten, and Steve Granick � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 581

Charge Transfer–Mediated Singlet FissionN. Monahan and X.-Y. Zhu � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 601

Upconversion of Rare Earth NanomaterialsLing-Dong Sun, Hao Dong, Pei-Zhi Zhang, and Chun-Hua Yan � � � � � � � � � � � � � � � � � � � � � � 619

vi Contents

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Computational Studies of Protein Aggregation: Methods andApplicationsAlex Morriss-Andrews and Joan-Emma Shea � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 643

Experimental Implementations of Two-Dimensional FourierTransform Electronic SpectroscopyFranklin D. Fuller and Jennifer P. Ogilvie � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 667

Electron Transfer Mechanisms of DNA Repair by PhotolyaseDongping Zhong � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 691

Vibrational Energy Transport in Molecules Studied byRelaxation-Assisted Two-Dimensional Infrared SpectroscopyNatalia I. Rubtsova and Igor V. Rubtsov � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 717

Indexes

Cumulative Index of Contributing Authors, Volumes 62–66 � � � � � � � � � � � � � � � � � � � � � � � � � � � 739

Cumulative Index of Article Titles, Volumes 62–66 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 743

Errata

An online log of corrections to Annual Review of Physical Chemistry articles may befound at http://www.annualreviews.org/errata/physchem

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