CONTINUUM SOLVATION MODELS IN GAUSSIAN 03

Dr. Ivan RostovAustralian National University,Canberra

E-mail: Ivan.Rostov@anu.edu.au

OUTLINE

Types of solvent effects and solvent models

Overview of solvation continuum models available in Gaussian 03.

Summary of Gaussian keywords Applications Recommendations

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SOLVENT EFFECTS

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Nicolai Alexandrovich Menshutkin, Z. Physik. Chem. 1890, 5, 589

NH3 CH3Cl NH3CH3+

Cl-

SOLVENT EFFECTS

The solvent environment influences all of these: Structure Energies

Reaction and activation energiesBond energies

SpectraRotational (Microwave)Vibrational (IR, Raman)Electronic (UV, visible)

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METHODS FOR TREATMENT OF SOLVATION

Supermolecule Solute and some number of solvent molecules are

included in one large QM calculation

Molecular Mechanics Force Fields Simple classical force fields allows us to include a large

number of solvent molecules

Continuum models Explicit consideration of solvent molecules is neglected Solvent effects are described in terms of macroscopic

properties of the chosen solvent (e, <Rsolvent>)

Hybrid/mixed: Supermolecule + Continuum model QM + MM QM + MM + Continuum model

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SOLVATION PROCESS

... elecrepdispcavsolv UUUU

1) Creation of cavity 3) Turning on electrostatic forces

elecrep.-disp.iNiN FF

2) Turning on dispersion and repulsion forces

rep.-disp.iNF

BASICS OF THE CONTINUUM MODEL THEORY

Solvent is described in terms of macroscopic properties

Solvent is dielectric medium (uniform, normally), characterized by the dielectric constant e0

Polarization of solvent is expressed in terms of the surface charge density on the cavity surface

Polarization produces the electric field in the cavity making an effect on solute

Dispersion-Repulsion and Cavitation are added separately, or ignored

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THE ELECTROSTATIC PROBLEM

= 1= 1

= = 00

SS= 1= 1

= = 00

SS

Solution is calculated as

rr

rr

rr

rrr

)()(

)( 23 SV

dd

0

42

e

i

V

V

r

r

Poisson equations

with boundary conditions on S:

nn

outin

outin

BORN MODEL

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A single charge inside a spherical cavity No constructing of the cavity surface elements,

because the Poisson equation is solved analytically

R

QU solv

2

0

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ONSAGER MODEL Spherical cavity Dipolar reaction field No constructing of the cavity surface elements,

because the Poisson equation is solved analytically

Keywords in Gaussian: SCRF(Dipole,A0=value,Dielectric=value)

Area of applicability: Solute shape is close to spherical Solute is polar (m >> 0)

References L. Onsager, J. Am. Chem. Soc. 58, 1486 (1936). M. Wong, M. Frisch, K. Wiberg, J. Am. Chem. Soc. 113,

4476 (1991).

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1

0

03

2

RHE

μ

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POLARIZED CONTINUUM MODEL (PCM) Realistic molecular shape of the cavity

(interlocking spheres around each atom or group, or isodensity surface)

Induced surface charges represent solvent polarization

Includes free energy contributions from forming the cavity and dispersion-repulsion

Comes in number of “flavours”: IEFPCM, CPCM, DPCM, IPCM, or SCIPCM

Keywords in Gaussian: SCRF(Solvent=, PCM specific options)

References: E. Canses, B. Mennucci, J. Tomasi, J. Chem Phys. 107,

3032 (1997). J. Tomasi, M. Persico, Chem. Rev. 94,2027 (1994). J. Tomasi, B. Mennucci, R. Camm, Chem. Rev. 105, 2999

(2005). 11

PCM, THE CAVITY CONSTRUCTION

Interlocking spheres around atomic groups This is default in Gaussian 03 A choice of united atoms radii set, RADII=UAO (default),

UAHF, UAKS, or UFF Interlocking spheres around each atom

Radii=Pauling (or Bondi) Requires the scaling factor ALPHA by which the sphere

radius is multiplied. The default value is 1.0 though should be 1.2

A number of keywords is provided to add extraspheres when necessary

A number of keyword is provided to govern the size and number of surface elements (tesserae)

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PCM, THE CAVITY VIEW Keyword: GeomView Creates files in GeomView format to visualize the

cavity construction and the charge distribution on the cavity: tesserae.off charge.off

Files are readable by GeomView, JavaView and other visualization software.

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(C5NH12+)

PCM, METHODS OF SOLVING OF THE SCRF PROBLEM TO CALCULATE SURFACE CHARGES

Iterative Keyword: ITERATIVE Solves the PCM electrostatic

problem through a linear scaling iterative method using a Jacobi-like scheme

Advantageous when memory is limited.

Inversion Keyword: INVERSION Solve the PCM electrostatic

problem to calculate polarization charges through the inversion matrix D with dimension of NtesxNtes

Gaussian 03 uses Inversion by default.

rr

rrrrr

rrrrr

2

1

)(

1

)(

1 23

0 SV nd

nd

f

i

i

S

q

r

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)()(ˆ)'(ˆ 1 rr'r,rr,r VD

DIELECTRIC PCM

The original version of PCM Electrostatics directly from the cavity model Charges produces by discontinuity in the

electric field across the boundary created by the cavity

Very sensitive to solute charge outside the cavity

Only single point calculations No longer recommended

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INTEGRAL EQUATION FORMALISM PCM (IEFPCM)

Default in Gaussian 03 Less sensitive to diffuse solute charge

distributions PCM + careful outlying charge

corrections => IEFPCM

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CPCM (COSMO) Uses the assumption that the cavity

surface to be conductor-like This assumption simplifies the solution of

Poisson equation and calculation of the surface charges

Results can be outputted in COSMO RS format

Not recommended for solvents with low polarity

It is more efficient in iterative regime

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ISODENSITY PCM (IPCM) ANDSELF-CONSISTENT ISODENSITY PCM (SCIPCM)

Cavity formed using gas-phase static electronic isodensity surface (IPCM) Less arbitrary than spheres on atoms Cavity changes with electron density and environment The default density value is 0.0004 only single point calculations

Self-Consistent Isodensity (SCIPCM) iterations are folded in SCF issues regarding scaling of charges still remain

References J. Foresman, T.Keith, K. Wiberg, J. Snoonian, M. Frisch,

J. Phys. Chem. 100,16098 (1996).

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GAUSSIAN 03 KEYWORD EXAMPLES

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SCRF(Dipole,A0=5.5,eps=78.39)

SCRF(IEFPCM) is the same as SCRF(PCM), or just SCRF

SCRF(CPCM,Solvent=THF,Read)

SCRF(IPCM)

SCRF(SCIPCM)

SAMPLE INPUT FOR PCM CALCULATIONS

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%chk=pip-pcm#P HF/6-31g(d) SCRF(PCM,Solvent=Water,Read) test

Piperidinium cation

1 1 N C 1 1.50977268 C 2 1.52365511 1 109.63925419 C 3 1.53136665 2 111.56508108 1 -55.04631728 C 1 1.50978576 2 113.42079276 3 57.07092348 C 4 1.53134037 3 110.99585756 2 54.90811126 H 1 1.00969298 5 109.64667654 6 -179.99768911 H 1 1.01028619 5 109.06107319 6 64.67690355 H 2 1.08151743 1 106.09798567 5 -64.03241054 H 2 1.08069845 1 107.09512052 5 179.68520816 H 3 1.08732966 2 109.45874935 1 67.33780856 H 3 1.08342937 2 107.81444282 1 -177.04873713 H 4 1.08661607 3 109.70973952 2 -66.50424273 H 4 1.08269752 3 109.4557835 2 176.38517116 H 5 1.08069728 1 107.09836585 2 -179.68240007 H 5 1.08151732 1 106.09918524 2 64.03563496 H 6 1.08732304 4 110.31444998 3 66.98445589 H 6 1.08344075 4 110.90163383 3 -175.10999479

PCMDOCITERATIVEGEOMVIEW

PCM solvation is requested. Solvent is

Water. Additional PCM specific keywords are

provided

PCM specific keywords

SAMPLE OUTPUT

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SCF Done: E(RHF) = -250.669391936 A.U. after 6 cycles Convg = 0.7269D-05 -V/T = 2.0012 S**2 = 0.0000 -------------------------------------------------------------- Variational PCM results ======================= <psi(f)| H |psi(f)> (a.u.) = -250.570493 <psi(f)|H+V(f)/2|psi(f)> (a.u.) = -250.669392 Total free energy in solution: with all non electrostatic terms (a.u.) = -250.662541 -------------------------------------------------------------- (Polarized solute)-Solvent (kcal/mol) = -62.06 -------------------------------------------------------------- Cavitation energy (kcal/mol) = 16.10 Dispersion energy (kcal/mol) = -12.61 Repulsion energy (kcal/mol) = 0.81 Total non electrostatic (kcal/mol) = 4.30 --------------------------------------------------------------

APPLICATIONS

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PIPEREDIN CATION (C5NH12+),

FREE ENERGY OF HYDRATION

Method DGsolv, kcal/mol

SP SCRF(Dipole,A0=5.5) -30.6

SP SCRF(PCM) -56.0

SP SCRF(CPCM) -56.1

SP SCRF(IPCM) -59.4

SP SCRF(SCIPCM) -60.9

Opt SCRF(PCM) -56.3

Opt SCRF(CPCM) -56.4

Opt SCRF(SCIPCM) -61.1

Experiment -60.0

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PCM cavity was constructed of 1006 tesserae

Dipole, IPCM and SCIPCM results includes electrostatic effects only, sum of non-electrostatic is + 4.3 kcal/mol (PCM).

QM: HF/6-31G(d)

ET SYSTEM

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Donor = 4-Biphenyl Acceptor = 2-Naphthyl

Spacer: 5-a-androstane

e-

D-SA → DSA-

ET SYSTEM

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ET system

Method to solve surface charges

Memory,Mb

CPUs Time, min.

Matrix inversion(default)

240 1 92.5

640 1 32

800 1 31

1600 1 30

1600 4 22

Iterative

64 1 28

640 1 29

800 1 27

1600 1 29

400 4 17.5

ROHF/6-31G(d,p) SP SCRF(IEFPCM, Solvent=THF)

D-SA → DSA-

D: 4-BiphenylA: 2-NaphthylS:5-a-androstane87 atoms in total,5158 tesserae created

ET SYSTEM

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Method to solve surface charges

Memory,Mb

CPUs Time, min.

Matrix inversion(default)

240 1 29

640 1 29

800 1 28

1600 1 28

1600 4 19

Iterative

64 1 16

640 1 16

800 1 16

1600 1 16

800 4 5.75

ROHF/6-31G(d,p) SP SCRF(СPCM, Solvent=THF)

D-SA → DSA-

D: 4-BiphenylA: 2-NaphthylS:5-a-androstane87 atoms in total,5158 tesserae created

ET SYSTEM

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• In vacuo ROHF and UHF calculations fails to produce the precursor state. Altering of MOs does not help.

• Polarization field of solvent makes it possible to obtain solution (with solvent polarization effects included!) for both precursor and successor states

• G = -7.7 kcal/mol (IEFPCM)

• G = -9.6 kcal/mol (СPCM)

• G = -2.7 kcal/mol (СPCM, optimization, 78 hrs.)

• G = -5±1 kcal/mol (Experiment)

Blue structure is the precursor, 4-biphenyl is planarRed structure is successor, 4-biphenyl dihedral angle is 42.9º

using guess=alter option and altering order of HOMO and LUMO

MENSHUTKIN REACTION

What is DG and DG≠ for the reaction? What is the nature of the transition state? How does solvent change the result?

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NH3 CH3Cl NH3CH3+

Cl-

MENSHUTKIN REACTION

Model DG≠ DGGas 43.7 120.0

Onsager 18.2 10.0

DPCM@Onsager 24.2 -21.0

CPCM 24.8 -21.5

Experiment – for CH3I

Gas ? 110

Solution 24 -30Energies in kcal/mol

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NH3 CH3Cl NH3CH3+ Cl-

MENSHUTKIN REACTION: TRANSITION STATE

Model C-N C-Cl H-N-C Cl-C-H

Gas 1.765 2.571 110.6 78.7

Onsager 2.273 2.250 112.6 94.2

CPCM 2.145 2.249 110.3 92.6

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RECOMMENDATIONS

Preliminary in vacuo calculations (geometry and wavefunction guess)

In many cases SP SCRF after Optimization in vacuo is enough

IEFPCM ( It is the default method in G03) When memory is limited, or the system is large, the

Iterative algorithm is faster and less demanding than Inversion

When time is crucial, CPCM is recommended under some conditions: polar solvent; keyword Iterative!

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