1. Continuum Solvation Models in Gaussian 03
Dr. Ivan Rostov
Australian National University,
Canberra

2. Outline Types of solvent effects and solvent models
Overview of solvation continuum models available in Gaussian 03.
Summary of Gaussian keywords
Applications
Recommendations
In my talk I am going to give you a brief introduction to the theory of solvation continuum models available in Gaussian 03. I give you examples of keywords to setup Gaussian solvation calculations and demonstrate their efficiency of the continuum approach on a few examples. At the end of the talk I give you some recommendations which might be useful for Gaussian users, who just about to start calculations using continuum solvation models. Hopefully, they will be of help to minimize your computation costs.

3. Solvent Effects
Nicolai Alexandrovich Menshutkin, Z. Physik. Chem. 1890, 5, 589
NH3 CH3Cl NH3CH3+ Cl-
The fact that solvent may affect the properties of chemical substances has been known for centuries. However, it was only in the second half of 19th century, with rise of the atomistic theory of matter, when people started to understand that the solvent effects is not a magic but can be explained solely by science. In 1890, the head of recently born Russian Chemical Society Nikolai Menshutkin published a paper on the effect of polarity of solvent on the rate of what we know now as Menshutkin reaction. Nowadays, it is common name for the reaction of methylation of tertiary amines to quaternary ammonium salt by alkyl halide. In simple case we have neutral ammonia and methyl chloride on input and ions of methylammonium chloride salt on output. Menshutkin found in his experiment that the rate and endothermithicity, or exothermicity of reaction changes with the polarity of the solvent. As found, the problem can be brought to taking the proper accounting of physical interactions between solute and solvent molecules. This discovery was giving a sign that the electrostatic forces induced between solute and solvent molecules play the major role behind the solvent effects.

4. Solvent Effects The solvent environment influences all of these:
Structure
Energies
Reaction and activation energies
Bond energies
Spectra
Rotational (Microwave)
Vibrational (IR, Raman)
Electronic (UV, visible)
To the present day, it was found that the solvent environment influences structure, energies, spectra and other properties of solute. Therefore, they must be taken into account in Computational Chemistry when we modelling reaction in realistic environment.

5. 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
The major approaches in Computational Chemistry in treating of solvent effects are:
supermolecule, continuum models, Molecular Mechanics, and recently appeared various hybrid constructions.
In the supermolecule approach one places some number of solvent molecules together with solute in the one QM calculation. While, in many cases, it can give some insights on solvent effects even with limited number of solvent molecules, the quantitative results require the very large of number of solvent molecules to be included brining the computational costs beyond the present day limits.
Molecular Mechanics methods due to the simplicity of the atom-atomic force field allows us take quite a reasonable number of solvent molecules into consideration at cheap price. However, the simplicity of the MM approach does not allow the MM methods to get an adequate description of many processes, such as bond breaking in chemical reaction, for example. Regarding of the solvent effects, the accounting for the mutual polarization of solute and solvent molecules requires a considerable complication of the MM theory rising considerably the cost of such calculations.
The hybrid QM/MM methods is quite a fresh branch on the tree of Computational Chemistry. It is a promising approach. However, QM/MM calculations are not easy to setup and they are costly.
Now we come to continuum solvation models. To the surprise of many sceptical opponents, the combination of QM methods with continuum solvation theory proven to be a successful. Surely, it has limitation on area of applicability, but where it works it allows us to get an estimate of solvent effects at quite a cheap price. The cheap price is achieved by exclusion of information on explicit configuration of solvent molecules. Solvent is described as a uniform medium characterized by some macroscopic properties.
(Add pictures) Talk small add some subbullet

6. Solvation Process 2) Turning on dispersion and repulsion forces
3) Turning on electrostatic forces
1) Creation of cavity
For easy understanding of the solvation process and separation of effects of different nature, it is convinient in the continuum theory to split the solvation process in three imaginary steps: 1) creation of the cavity , 2) turning on dispersion-repulsion forces and, then 3) electrostatic forces. Dispersion-repulsion forces and cavitation contribution to the energy normally comes with opposite signs, therefore, reducing the total contribution. In many cases, specifically for the case of charged or highly polar solutes, electrostatic forces play the dominant role. Additionally, during the chemical reaction, cavitation and repulsion forces do not change much, and therefore, if we are concerned with the effect of solvent on reaction, they may be neglected.

7. 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
As I just told, solvent in the continuum model described in terms of the macroscopic properties. To count electrostatic effect, solvent is described as dielectric medium characterized in most cases, by a single property, which its dielectric constant. As it can be derived from the electrostatic, the polarization of solvent can be expressed in terms of the surface charge density on the cavity surface. Having the surface charge calculated we can calculate the electric field in the cavity and its effect on solute. If the surface charge on the cavity surface is calculated. Cavitation and Dispersion-Repulsion contribution does not affect the QM part of calculation and are calculated separately afterwards, or ignored. Both these contributions calculated using the atomic accessible surface areas (ASAs) and basic formulas derived from a general theory of liquids

8. The electrostatic problem
Poisson equations
with boundary conditions
on S:
Solution is calculated as

9. Born Model A single charge inside a spherical cavity
No constructing of the cavity surface elements, because the Poisson equation is solved analytically

10. 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).

11. 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).

12. 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)
UA0: Use the United Atom Topological Model applied on atomic radii of the UFF force field.
UAHF: Use the United Atom Topological Model applied on radii optimized for the HF/6-31G(d) level of theory. These are the recommended radii for for the calculation of ΔGsolvation via the SCFVAC PCM keyword.
UAKS: Use the United Atom Topological Model applied on radii optimized for the PBE0/6-31G(d) level of theory.
UFF: Use radii from the UFF force field. Hydrogens have individual spheres (explicit hydrogens).
PAULING: Use the Pauling (actually Merz-Kollman) atomic radii (explicit hydrogens).
BONDI: Use the Bondi's atomic radii (explicit hydrogens).

13. 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.
(C5NH12+)
It is useful to check the surface created by Gaussian before going in furhter calculations.

14. 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.

15. 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

16. Integral Equation Formalism PCM (IEFPCM)
Default in Gaussian 03
Less sensitive to diffuse solute charge distributions
PCM + careful outlying charge corrections => IEFPCM

17. 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
COSMO RS (COSMO Realistic Solvation) calculate the thermodynamic data from molecular surface polarity distributions resulting from COSMO calculations of the individual compounds in the mixture.

18. Isodensity PCM (IPCM) and Self-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
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).

19. Gaussian 03 Keyword Examples
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)
Emphasise read thing

20. Sample input for PCM calculations
PCM solvation is requested. Solvent is Water. Additional PCM specific keywords are provided
%chk=pip-pcm
#P HF/6-31g(d) SCRF(PCM,Solvent=Water,Read) test
Piperidinium cation
1 1 N C C C C C H H H H H H H H H H H H
PCMDOC
ITERATIVE
GEOMVIEW
25 solvent are hardwired. Alternatively, the dielctric constant eps and solvent radius can be set up manually.
PCM specific keywords

21. Sample output SCF Done: E(RHF) = -250.669391936 A.U. after 6 cycles
Convg = D V/T =
S**2 =
Variational PCM results
=======================
<psi(f)| H |psi(f)> (a.u.) =
<psi(f)|H+V(f)/2|psi(f)> (a.u.) =
Total free energy in solution:
with all non electrostatic terms (a.u.) =
(Polarized solute)-Solvent (kcal/mol) =
Cavitation energy (kcal/mol) =
Dispersion energy (kcal/mol) =
Repulsion energy (kcal/mol) =
Total non electrostatic (kcal/mol) =

22. Applications

23. Piperedin cation (C5NH12+), free energy of hydration
QM: HF/6-31G(d)
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
SP timing: sec., Opt 2-3 min. using Itanium2 CPU
Non-electrostatic: +4.3 kcal/mol
PCM cavity was constructed of 1006 tesserae
Dipole, IPCM and SCIPCM results includes electrostatic effects only, sum of non-electrostatic is kcal/mol (PCM).

24. ET system Donor = 4-Biphenyl Acceptor = 2-Naphthyl e- D-SA → DSA-
Spacer: 5-a-androstane
First, DSA structure in its neutral state (to avoid biasing) was optimized in vacuo.

25. Method to solve surface charges
ET system
D-SA → DSA-
D: 4-Biphenyl
A: 2-Naphthyl
S:5-a-androstane
87 atoms in total,
5158 tesserae created
ET system
ROHF/6-31G(d,p) SP SCRF(IEFPCM, Solvent=THF)
Method to solve surface charges
Memory,Mb
CPUs
Time, min.
Matrix inversion
(default)
240 1
92.5
640 32
800 31
1600 30 4 22
Iterative 64 28 29 27
400
17.5

26. Method to solve surface charges
ET system
D-SA → DSA-
D: 4-Biphenyl
A: 2-Naphthyl
S:5-a-androstane
87 atoms in total,
5158 tesserae created
ROHF/6-31G(d,p) SP SCRF(СPCM, Solvent=THF)
Method to solve surface charges
Memory,Mb
CPUs
Time, min.
Matrix inversion
(default)
240 1 29
640
800 28
1600 4 19
Iterative 64 16
5.75

27. ET system
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
DG = -7.7 kcal/mol (IEFPCM)
DG = -9.6 kcal/mol (СPCM)
DG = -2.7 kcal/mol (СPCM, optimization, 78 hrs.)
DG = -5±1 kcal/mol (Experiment)
using guess=alter option and altering order of HOMO and LUMO
ET molecules without cavity.
Blue structure is the precursor, 4-biphenyl is planar
Red structure is successor, 4-biphenyl dihedral angle is 42.9º

28. Menshutkin reaction What is DG and DG≠ for the reaction?
NH3 CH3Cl NH3CH3+ Cl-
What is DG and DG≠ for the reaction?
What is the nature of the transition state?
How does solvent change the result?
Methylation of tetriary amines to quaternary ammonium salt by reaction with an alkyl halide

29. Menshutkin reaction DG≠ DG Model Gas 43.7 120.0 Onsager 18.2 10.0
NH3 CH3Cl NH3CH3+ Cl-
Model
DG≠ DG
Gas
43.7
120.0
Onsager
18.2
10.0
24.2
-21.0
CPCM
24.8
-21.5
Experiment – for CH3I ?
110
Solution 24
-30
Energies in kcal/mol
Methylation of tetriary amines to quaternary ammonium salt by reaction with an alkyl halide

30. 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

31. 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!