CONTINUUM SOLVATION MODELS IN
GAUSSIAN 03
Dr. Ivan Rostov
Australian 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

2
SOLVENT EFFECTS
Nicolai Alexandrovich Menshutkin, Z. Physik. Chem. 1890, 5, 589
NH3
CH3Cl
NH3CH3+
Cl-
3
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)
4
METHODS FOR TREATMENT OF
SOLVATION

Supermolecule


Molecular Mechanics Force Fields



Solute and some number of solvent molecules are included in one
large QM calculation
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
5
SOLVATION PROCESS
 disp.-rep.
FiN
1) Creation of cavity 2) Turning on
dispersion and
repulsion forces
 disp.-rep.  elec
FiN
 FiN
3) Turning on
electrostatic forces
U solv  U cav  U disp.- rep.  U elec.
6
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
7
THE ELECTROSTATIC PROBLEM
Poisson equations
r  Vi 
- 4
 2  
r  Ve 
 0
with boundary conditions
on S:
in  out
in

 e out
e= 1
n
S
n
e= e0
Solution is calculated as
 (r)   d r
3
V
 (r)
r - r
  d r
2
S
 (r)
r - r
8
BORN MODEL


A single charge inside a spherical cavity
No constructing of the cavity surface elements, because
the Poisson equation is solved analytically

1  Q2
U solv  -1 - 
 e0  R
9
ONSAGER MODEL




Spherical cavity
μ2 e 0 -1
E  H- 3

R 2e 0  1
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).
10
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



Interlocking spheres around each atom




This is default in Gaussian 03
A choice of united atoms radii set, RADII=UAO (default), UAHF, UAKS,
or UFF
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)
12
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+)
13
PCM, METHODS OF SOLVING OF THE SCRF
PROBLEM TO CALCULATE SURFACE CHARGES
 3


1

1
2




 r    d r
 r   2 r 
 d r
 Iterative



n
(
r
)
r
r

n
(
r
)
r
r
V

S
 Keyword: ITERATIVE
q
 Solves the PCM electrostatic problem
 r   i
Si
through a linear scaling iterative
method using a Jacobi-like scheme
 Advantageous when memory is
limited.
1
 r  
f0

Inversion



Keyword: INVERSION
ˆ -1 (r, r ' )Vˆ (r, r' )  (r )



r

D
Solve the PCM electrostatic problem to
calculate polarization charges through
the inversion matrix D with dimension
of NtesxNtes
Gaussian 03 uses Inversion by default.
14
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
15
INTEGRAL EQUATION FORMALISM PCM
(IEFPCM)
Default in Gaussian 03
 Less sensitive to diffuse solute charge
distributions
 PCM + careful outlying charge corrections =>
IEFPCM

16
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

17
ISODENSITY PCM (IPCM) AND
SELF-CONSISTENT ISODENSITY PCM (SCIPCM)

Cavity formed using gas-phase static electronic isodensity
surface (IPCM)





Self-Consistent Isodensity (SCIPCM)



Less arbitrary than spheres on atoms
Cavity changes with electron density and environment
The default density value is 0.0004
only single point calculations
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).
18
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)
19
SAMPLE INPUT FOR PCM CALCULATIONS
%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
1
2
3
1
4
1
1
2
2
3
3
4
4
5
5
6
6
1.50977268
1.52365511
1.53136665
1.50978576
1.53134037
1.00969298
1.01028619
1.08151743
1.08069845
1.08732966
1.08342937
1.08661607
1.08269752
1.08069728
1.08151732
1.08732304
1.08344075
PCMDOC
ITERATIVE
GEOMVIEW
1
2
2
3
5
5
1
1
2
2
3
3
1
1
4
4
109.63925419
111.56508108
113.42079276
110.99585756
109.64667654
109.06107319
106.09798567
107.09512052
109.45874935
107.81444282
109.70973952
109.4557835
107.09836585
106.09918524
110.31444998
110.90163383
1
3
2
6
6
5
5
1
1
2
2
2
2
3
3
PCM solvation is
requested. Solvent is
Water. Additional PCM
specific keywords are
provided
-55.04631728
57.07092348
54.90811126
-179.99768911
64.67690355
-64.03241054
179.68520816
67.33780856
-177.04873713
-66.50424273
176.38517116
-179.68240007
64.03563496
66.98445589
-175.10999479
PCM specific keywords
20
SAMPLE OUTPUT
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
--------------------------------------------------------------
21
APPLICATIONS
22
+
(C5NH12 ),
PIPEREDIN CATION
FREE ENERGY OF HYDRATION
QM: HF/6-31G(d)
Method
PCM cavity was
constructed of
1006 tesserae
Gsolv, 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
Dipole, IPCM and SCIPCM results includes electrostatic effects only, sum of
non-electrostatic is + 4.3 kcal/mol (PCM).
23
ET SYSTEM
Donor = 4-Biphenyl
e-
Acceptor = 2-Naphthyl
D-SA → DSA-
Spacer: 5-a-androstane
24
ET SYSTEM
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(IEFPCM, Solvent=THF)
Method to solve
surface charges
Matrix inversion
(default)
Iterative
Memory,M
b
CPUs
Time,
min.
240
1
92.5
640
1
32
800
1
31
1600
1
30
1600
4
22
64
1
28
640
1
29
800
1
27
1600
1
29
400
4
17.5
25
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
Matrix inversion
(default)
Iterative
Memory,M
b
CPUs
Time,
min.
240
1
29
640
1
29
800
1
28
1600
1
28
1600
4
19
64
1
16
640
1
16
800
1
16
1600
1
16
800
4
5.75
26
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
• G = -7.7 kcal/mol (IEFPCM)
using guess=alter option
and altering order of HOMO
and LUMO
• 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 planar
Red structure is successor, 4-biphenyl dihedral angle is 42.9º
27
MENSHUTKIN REACTION
NH3



CH3Cl
NH3CH3+
Cl-
What is G and G≠ for the reaction?
What is the nature of the transition state?
How does solvent change the result?
28
MENSHUTKIN REACTION
NH3
Cl-
NH3CH3+
CH3Cl
Model
G≠
G
Gas
43.7
120.0
Onsager
18.2
10.0
DPCM@Onsager
24.2
-21.0
CPCM
24.8
-21.5
Gas
?
110
Solution
24
-30
Experiment – for CH3I
Energies in kcal/mol
29
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
30
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!
31