continuum solvation models in gaussian 03 (2)
DESCRIPTION
Solvatation modelTRANSCRIPT
CONTINUUM SOLVATION MODELS IN GAUSSIAN 03
Dr. Ivan RostovAustralian National University,Canberra
E-mail: [email protected]
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
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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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