Tutorial IV: TDDFT, solvation and QM/MM

Q-Chem User Workshop, Denver March 21, 2015

1 / 23

Time-dependent density functional theory

Implicit solvation

QM/MM

2 / 23

CIS

Configuration interaction singles:

3 / 23

TDDFT

I Time-dependent density functional theory (TDDFT)computes the poles in the response of the ground stateenergy to a time-varying applied electric field.

I These poles correspond to excitation energies.I Its computation cost is roughly that of CIS, O(N2), but

includes correlation.I Dreuw and Head-Gordon, Chem Rev. 105, 4009 (2005).

4 / 23

TDDFT Performance

I Pure (BLYP, PBE) and conventional hybrid functionals(B3LYP, PBE0): TDDFT performs well for low-lyingvalence transitions, and less well for Rydberg andcharge-transfer states.

I Long-range corrected functionals (ωB97X-D, LC-ωPBE,LC-ωPBEh, BNL, CAM-B3LYP): Can help improvedescription of Rydberg and charges transfer states.

I Meta functionals: M06-2X might perform reasonablywell.

I Isegawa, Peverati, and Truhlar, J. Chem. Phys. 137,244104 (2012).

5 / 23

Spin-Flip DFT

I Based on a high-spin reference and is able to modelradicals, diradicals and systems with stretched bonds.

I Shao, Head-Gordon, and Krylov, 118, 4807 (2003).Bernard, Shao, and Krylov, 136, 204, 103 (2012).

6 / 23

TDDFT setup

7 / 23

TDDFT output

8 / 23

Formaldehyde MOs

9 / 23

Exercise 4.1

I Optimize ground-state geometry of formaldehyde withB3LYP/6-31G*

I Compute vertical TDDFT/TDA and full TDDFT excitationenergies with B3LYP/6-31G*

I Hint: Full TDDFT requires “RPA TRUE”I Compute vertical TDDFT/TDA and full TDDFT excitation

energies with ωB97X-D/6-31G*.

10 / 23

Results

TDDFT and TDDFT/TDA vertical excitation energies forformaldehyde at ground-state B3LYP/6-31G* geometry.

State B3LYP ωB97X-DTDA TDDFT TDA TDDFT

1 4.1096 4.0889 4.1072 4.07932 9.1450 9.0975 9.3622 9.27713 9.2598 9.1802 9.6512 9.60094 10.1910 9.8036 10.4136 9.9362

In actual calculations, triple-ζ or larger basis might be needed.

11 / 23

Time-dependent density functional theory

Implicit solvation

QM/MM

12 / 23

Implicit solvation models

Q-CHEM supports several advanced implicit solvation modelsI PCMI COSMOI SM8I SM12, SM12MK, SM12CHELPGI Prof. John Herbert’s webinar:

https://www.youtube.com/watch?v=rsWdDwXzaQY

13 / 23

PCM model

SWIG-PCM model yields continuous potential energy surface.

Lange & Herbert, JCP 133, 244111 (2010); JPCL 1, 556 (2010).

14 / 23

Input setup

15 / 23

PCM results

16 / 23

SM8 results

17 / 23

Exercise 4.2

I Use B3LYP/6-31G* geometry for formaldehyde

I Compute PCM solvation free energy

I Compute SM8 solvation free energy

18 / 23

Time-dependent density functional theory

Implicit solvation

QM/MM

19 / 23

Effective Fragment Potential

I Fully ab initio:NO empirical parameters.

I 4 components of interactionenergy: electrostatics,polarization, dispersion, andexchange-repulsion.

I Electronic embedding.I Polarizable solute.

I Gordon, Fedorov, Pruitt, and Slipchenko, Chem Rev, 112,632 (2012).

I Ghosh, Kosenkov, Vanovschi, Flick, Kaliman, Shao,Gilbert, Krylov, and Slipchenko, JCC, 34, 1060 (2013).

20 / 23

EFP benchmark

I Ghosh, Roy, Seidel, Winter, Bradforth, and Krylov,JPCB 116, 7269 (2012).

21 / 23

EFP calculation setup

22 / 23

Exercise 4.3

I Add an EFP water next to formaldehydeI Compute TDDFT/TDA vertical excitation

energies using B3LYP/6-31G*I Compare energies to gas-phase

23 / 23