Transcript "Everything You Always Wanted to Know about Computational

"Everything You Always Wanted to Know about Computational
Chemistry, But Were Afraid Would Be Answered by 27 Pages of
Integrals in a Nomenclature That You've Never Seen Before."
or
“How to Understand MO Calculations, for the
Theoretically-Challenged."
web.utk.edu/~bartmess/comptalk.html
John Bartmess
Dept. of Chemistry
University of Tennessee
Theoretical Chemistry
Molecular Orbital (MO) Calculations
Quantum Mechanics Calculations
Computational Chemistry
"In theory, there is no difference
between theory and practice.
In practice, there is."
- Jan L. A. van de Snepscheut
(computer scientist)
But often attributed to Yogi Berra
"Man's gotta know his limitations"
- Dirty Harry Callahan (John Milius)
Goal of this Talk:
-To give you an understanding of the basics of
computational work in the literature
-Information on which methods are really good, and
which are either inappropriate or flat-out garbage
for a given problem
- The Alphabet Soup of Computation
Goals of Computational Chemistry:
Gas-phase molecules (molecules in solution take extra work,
and involve major approximations)
Geometries:
Closed shell (= octets around all heavy (non-H) atoms):
well-met even at low level calculations
Open shell (= radicals, sextet cations):
problematic, but solvable with knowledge
Energies:
relative versus absolute
accuracy and precision
Other Quantities:
Dipole Moments
Orbital energies and occupations
(eigenvalues and eigenvectors)
Charge distributions (atomic and orbital)
Mulliken populations (atomic charges)
Spin matrices, total spin states
Bond orders
Ionization energy & electron affinity
(vertical and adiabatic): Koopmans Physica 1934 1, 104)
Polarizabilities, hyperpolarizability
Vibrational frequencies/force constants (intensities)
Rotational constants/moments of inertia
Entropy, Heat capacity, Partition functions
Zero point energies
Units
Bohr - One atomic unit of distance = 0.5292 Angstrom (archaic now)
Hartree - One atomic unit of energy = 2 x IE(H.)
2625.500 kJ/mol
627.5095 kcal/mol
27.2114 eV
219474.6 cm-1
Energetic Data (ab initio)
- absolute energy, as negative value:
cleavage of all bonds to form free atoms, then ionization of atoms
to bare ionic nuclei plus free electrons at infinite distance (E = 0)
benzene: -231.820 hartrees = -145,469 kcal/mol
- atomization energy to atoms:
benzene -2.1099 hartrees (-1324 kcal/mol); expt: -1323 kcal/mol
- heat of formation
semi-empirical: close (± 2 kcal/mol, average organics)
ab initio: usually too unstable, unless very high level calculation
(variational principle)
Practicalities
speed ("cost" to computationalists): scales as as a high
power of the number of electrons (typically n4 to n8)
known failure modes of method (certain structures
known to be wrong energy or geometry)
cost of hardware
3.3GHz duo hex-core processor PC, 12 GB RAM,
1 TB hard drive :
$3000 (Feb 2012)
: 100x speed of a 1969 Cray I ($30M in current $)
: 330,000x speed of Osborne (1979; $6K current)
10,000,000x media storage
200,000,000x RAM
= 3 x1020 better, at ½ cost
cost of software
Gaussian 03 $1500 (site license)
MOPAC (QCPE $400?)
MNDO: free
Linux (Red Hat or Fedora) for ab initio
Hierarchy of 4 Methods
- Molecular Mechanics:
Not a quantum mechanical method.
- Empirical: Hückel, Extended Hückel
- Semi-empirical
archaic: INDO, PPP, CNDO/n, MINDO/n
current: MNDO, AM1, PM3
- ab initio
e.g. Gaussian, GAMES, MOLPRO (programs)
Hartree/Fock
Electron Correlation
Configuration Interaction
Extrapolation
Density Functional Theory
Input
name, method, time limits
charge, multiplicity
geometry:
- Cartesian coordinates
- Z matrix, or internal coordinates:
bond lengths
planar angles
dihedral (torsional) angles
connectivity
sometimes called “Natural Coordinates”
Semi-empirical input
AM1 precise
acetone
O
C 1.22 1
C 1.54 1 120. 1
C 1.53 1 120. 1
H 1.11 1 110. 1
H 1.11 1 110. 1
H 1.11 1 110. 1
H 1.11 1 110. 1
H 1.11 1 110. 1
H 1.11 1 110. 1
00000000000
180.
180.
60.
-60.
180.
60.
-60.
1
21
1213
1421
1421
1421
1321
1321
1321
%mem=256MB
%nosave
# g3mp2b3 Opt=Maxcyc=100
Me2C(.)CH2NH3+
+1
N
C
C
C
C
H
H
H
H
H
H
H
H
H
H
H
2
1
2
3
3
4
4
4
5
5
5
2
2
1
1
1
1.5283
1.5050
1.5022
1.4956
1.1100
1.1100
1.1077
1.1104
1.1108
1.1085
1.1190
1.1192
1.0250
1.0245
1.0246
1
2
2
3
3
3
3
3
3
1
1
2
2
2
115.9692
115.2106
124.5590
110.6428
110.6213
112.2541
111.0735
111.3159
111.9526
105.8385
105.6916
110.0652
112.2413
112.1792
1 182.2808
1 2.8544
2 60.1046
2 -239.9345
2 180.0153
2 61.1423
2 -239.8219
2 180.4718
3 122.4183
3 -122.5352
3 179.7632
14 119.2315
14 -119.2190
Common to all:
- Input of starting geometry
- Trial orbital set (Extended Hückel)
- Self Consistent Field (modify orbitals to reflect
reality)
- Geometry Optimization (modify nuclear geometry
to find minimum energy)
Method of Steepest Descent
– derivatives of E vs. geom.
Problems
Local minima: benzene with 1 H inside
= +156 kcal/mol above reality
Oscillation
- Final output:
Total energy, other properties
Vibrational Frequencies,
other Statistical Mechanics properties
Global vs. local minima:
anti vs gauche butane
Benzene, with H in center: ΔfH = 131 vs. 19.4 kcal/mol normal
Negative freq
↓
←1/2hυ
Thermochemistry (non-0K)
From statistical mechanics:
Etot = E0 + Etrans + Erot + Evib + Eelec
mass
geometry (moments of inertia)
vibrational frequencies
orbital energies
allow calculation of:
zero point energy = h/2·
E0 = E0 + ZPE
heat capacity: E298 H298 (=E298 + RT)
entropies:
S298 G298
Frequencies
- Scaling: 0.896 HF/6-31G*
0.96 B3LYP
- Harmonic approximation (parabola),
yet real ones anharmonic
-Lowest ones (<300 cm-1) most important to
stat. mech. entropy, yet worst known
Internal rotors, free vs. hindered
Ring breathing modes
Heats of Formation
Absolute:
ΔfHo(molecule) =
E0 (molecule)
-  E0(atoms)
+  ΔfHoexptl(atoms)
Relative:
A + B = C + D
EA
EB
EC
ED
ΔfH(A) = EA+ EB - EC – ED
+ ΔfH(C) + ΔfH(D) - ΔfH(B)
EXACT THEORY:
the Schrödinger Equation
H(Ψ) = E·Ψ
where Ψ is a "full molecule" wave function.
H = Hamiltonian function
(general case: Hermetian operator)
E = eigenvalue
H = T (kinetic part) + V (potential part)
M
M M
H = - h2/82  MA-12A +   e2ZAZBrAB-1
A=1
N
A=1 B>A
NM
N N
- h2/(8m)  i2 - 2ZArAi-1 + e2rij-1
i=1
i=1 A=1
i=1 j>i
Hamiltonian divides up into:
1. Kinetic energy of nuclei
2. Nuclear-nuclear repulsion
3. Kinetic energy of electrons
4. Nuclear-electron attraction
5. Electron-electron repulsion
Born-Oppenheimer approximation:
Nuclei don’t move, on electron motion timeframe
1. = 0
2. Static calculation: Coulomb’s Law
MORE APPROXIMATIONS:
1. Ψ = ψ1 . ψ2 . ψ3 ....,
where ψi are one electron molecular orbitals.
Separate the Schrödinger equation: H(ψi) = Ei· ψi
2 = probability of electron position
All physical observables relate to 2, because
 has imaginary parts.
Normalized:
aa* = 1
Orthogonal:
ab = 0
no overlap
<a|a*> = 1
<a|b> = 0
1 electron orbitals so far
Spin:  and 
= spatial·
Pauli Principle:
 is antisymmetric wrt exchange of 2 electrons
(1,2) = -(2,1)
If every electron has its own , “unrestricted”
If paired s, “restricted” (faster calculation)
2. Represent each ψi as a Linear Combination of
Atomic Orbitals (LCAO):
ψi = ci,1· φ1 + ci,2· φ2 + .....
where φj are basis orbitals (usually atomic)
3. Variational Principle:
For any approximate (one e-) ψi, Ei from the Schrödinger
Equation is greater than the true Ei for the exact ψi. Thus ψi
and cij are varied so as to minimize Ei, or δEi/δci,j = 0.
The true value of the variational principle is
that one knows when the calculation is getting
closer to reality, because the energy is going
down. There are other methods, such as Density
Functional Theory, or certain types of electron
Correlation, that are not variational.
4. Self Consistent Field (SCF) approximation.
“Three Body Problem”
ψi is calculated for one given electron interacting
with the field of the nuclei plus an average
smeared-out charge distribution of all other
electrons. This ψi is then used as part of the
average distribution as the next electron's ψi is
found, and so on. After successive iterations
result in an energy change of less than a given
amount (ca. 1 cal), the Self Consistent Field is
said to have converged, and that set of ψis is used
as a valid wave function.
5. Hartree-Fock Limit.
- Approximations 2 and 4 (LCAO and SCF) lead to Eo
always too high.
- If a small number of terms [limited number of
basis orbitals] is used in (2), then the ψi will not be
as good as with a larger number of terms.
- As a sufficiently large number of terms (j>20, typically)
is used, E approaches the "Hartree-Fock limit".
This Hartree-Fock limit still is only 90-95% of the way
to the true energy, since the SCF approximation ignores :
(1) "electron correlation", or the fact that the
other electrons are not a statistical average, but
moving, when calculating the SCF.
(2) "configuration interaction" or "CI", because
empty orbitals mix into filled MOs.
(3) relativistic speed of the core electrons, which can
still contribute a 0.1% error in total energy (especially
important for atoms low in the Periodic Table)
RHF (Restricted Hartree-Fock)
Every spatial orbital has an exactly equal orbital, i.e. every spin up
electron has a spatially equivalent spin down electron. This
generally implies a closed-shell wavefunction, though restricted
open-shell SCF can be done.
UHF (Unrestricted Hartree-Fock) Every spin-orbital has different
spatial forms. Drawback: time, spin contamination.
spin-contamination: calculations with UHF wavefunctions that are
not eigenfunctions of spin, and are contaminated by states of higher
spin multiplicity (which usually raises the energy).
ECP = Effective Core Potential. The core electrons have been
replaced by an effective potential. Saves computational expense.
May sacrifice some accuracy, but can include some relativistic
effects for heavy elements.
isodesmic: a chemical reaction that conserves types of chemical
bond.
MeO- + EtOH → MeOH + EtOisogyric: a chemical reaction that conserves net spin.
Lower-level calculations of such relative energetics can be as
accurate as much higher(slower) ones of absolute energetics
Koopman's Theorem:
IE = energy of the HOMO (Highest Occupied Molecular Orbital).
This is a vertical IE, not adiabatic.
Errors from no e- correlation plus geometry relaxation tend to cancel
for IEs.
EA = energy of the LUMO (Lowest Unoccupied Molecular Orbital).
These errors compound for trying to approximate EA
______________
______________
------------------------ 0 E
______________ LUMO
↑↓______ HOMO
_____
↑↓ _____
_____
MERP (Minimum Energy Reaction Path) or
IRC (Intrinsic Reaction Coordinate):
An optimized reaction path that is followed downhill, starting from a
transition state, to approximate the course (mechanism) of an elementary
reaction step.
(Ignores tunneling, contribution of vibrationally excited modes/partition
function, etc.)
Transition States: saddle points (one negative frequency),
sometimes found as minima. Search routines exist.
scaling: Multiplying calculated results by an empirical fudge
factor in the hope of getting a more accurate prediction. Very
often done for vibrational frequencies computed at the HF/6-31G*
level, for which the accepted scaling factor is 0.893.
Molecular Mechanics Methods
"Balls and Springs"
MM2 - Allinger Force Field version 2
MM3 MMX - PCModel
Sybyl Amber CHARMn All ΔfH ca.±1 kcal/mol
μD ±0.1
Limit: only parameterized functional groups
Advantage: fast, up to proteins
Empirical Methods
Hückel Calculation
Many integrals pre-calculated or
equated to measured data
Pros:
orbital symmetry
resonance energy
back of envelope
Cons:
flat geometry, π orbitals only
polar bonds poor
EHT - Extended Hückel Theory (Roald Hoffman)
Hückel with sigma bonds as well
Ignores e- e- repulsion
Uses expt’l IEs for certain integrals
Pros:
Ethane rotational barrier
Woodward-Hoffman rules
includes AO overlap terms
Frontier orbitals
All elements
Cons:
valence only (not hypervalents)
geometry poor (Me-Me = 1.92Å)
partial charges high
singlet & triplet same (no e- spin)
Used as first guess for higher level methods
Semi-Empirical Methods
Approximation: many computationally expensive (= slow)
integrals replaced by adjustable parameters, determined by
fitting experimental atomic and molecular data.
Non-nearest-neighbor interactions neglected
Different choices of parameterization lead to different
specific theories (e.g., MNDO, AM1, PM3).
Archaic:
CNDO - Complete Neglect of Differential Overlap
PPP - Pariser-Parr-Pople
INDO/1 - Intermediate NDO
MINDO/3 – Modified Intermediate Neglect..
MNDO: Minimal Neglect of Differential Overlap
Atoms: H, Li-F, Al-Cl, Cr, Zn, Ge, Br, Sn, I, Hg, Pb
Basis: 32 molecule parameterization
Developed by M.J.S. Dewar
Problems (geometries):
-O-O- bond ~0.17Å short
C-O-C angle 9o large
amides pyramidal
Aniline, nitrobenzene: NH2, NO2 group perpendicular
to ring, due to nuclear repulsion
MNDO
Problems (energies):
no H-bonds, no H2O dimer
S, Cl, & Br Ionization Energies high
activation barriers high
bond dissociation enthalpies too weak
conjugation too stable
3-center B bonds too stable
no Van der Waals attraction:
Sterically crowded hydrocarbons too unstable
(Me4C: -24. kcal/mol, exp -40.3 kcal/mol)
N-O bonds poorly parameterized - heats way off
(MeNO2: calc ΔfH = +5.1, exp -17.9 kcal/mol)
4 membered rings too stable
(cyclobutane: -11.9, exp +6.8 kcal/mol)
(cubane: + 108 , exp 148.7 kcal/mol)
Underestimates polarizability interactions
(aliphatic alcohol acidities all the same)
hypervalent unstable
3rd,4th row elements: only low valent cases have good
absolute heats though relative heats of same
oxidation state okay
AM1 - Austin Model 1 (Dewar)
Atoms: H, Li, B - F, Al - Cl, Zn, Ge, Br, I, Hg
Basis: 100 molecule parameterization
Pros:
H-bond energies, lengths better
proton affinities good
better activation barriers
Heat of Formation 40% better
2-Cl-THP axial (anomeric effect)
Aniline, nitrobenzene now planar
AM1: Problems:
poor on hypervalent compounds (none in parameterization set)
conjugate interactions low
-CH2- ΔfH ~ 0.2 kcal/mole low each
Heat of Hydrogenation low
bond dissociation enthalpies too weak
activation enthalpies high
-NO2 energies high
-O-O- bond ~ 0.17Å short
H-bond angles, H2O H-bond geometry wrong
C-C-O-H gauche in ethanol
proton transfer barrier high
PM3 – Parameterized Model 3 (Stewart: student of Dewar’s)
Program: MOPAC
Atoms: H, Li, Be, C-F, Mg-Cl, Zn-Br, Cd-I, Hg-Bi
Basis: 657 molecule parameterization
Pros:
hypervalent included in parameterization set
ΔfH 40% better
-NO2 better
ground state geometries better
H2O H-bonds: lengths & angles
PM3: Cons:
partial charges on N unreliable
bond dissociation enthalpies low
amides pyramidal, barrier low
no barrier to formamide rotation
spurious minima
D2d symmetry for CBr4
IEs poor
proton transfer barrier high
wrong glucose geometry:
H-bonds 0.1A short
C-C-O-H gauche in ethanol
Van der Waals attraction high/H-H core repulsion low
(MeNO2: calc -15.9, exp -17.9 kcal/mol)
(cyclobutane: -3.8, exp +6.8 kcal/mol)
(cubane:
114, exp 148.7 kcal/mol)
(Me4C:
-35.8, exp -40.3 kcal/mol)
(MeOH..-OMe: bond strength 19, exp 28.8 kcal/mol
Hypervalents good energy
Ab initio Methods
Hartree-Fock methods
Basis Set: math functions that describle orbitals
STO (Slater-Type Orbital) Minimal Basis Set
Basis function with an exponential radial function, i.e., e –αr
or
a fit to such a function using other functions, such as Gaussians: e-ar2
(Gaussians are computationally faster)
STO-3G “stodgy” (1969, Pople)
is a MBS that uses 3 Gaussians to fit an exponential.
Exponentials are better basis functions than Gaussians, but are
expensive computationally.
Split Valence: a basis set that is more than minimal for the valence
orbitals. Much better for polar bonds than MBS.
DZ (Double-Zeta): A basis set for which there are twice as many basis
functions as are minimally necessary. "Zeta" (Greek letter ζ) is the usual
name for the exponent that characterizes a Gaussian function.
(Dunning, 1970)
TZ: (triple zeta)
3-21G Basis set:
3 Gaussian function primitives for core electrons
Split Valence:
2 Gaussians with linked coefficients for inner valence electrons
1 Gaussian for each outer valence electron
- Polar bonds better described than minimal basis set
- Atoms: H – Xe
6-31G Basis set:
6 Gaussian functions for core
3 Gaussian (linked coefficients) for inner valence electrons
1 Gaussian for each outer
- Atoms: H - Ar
6-31G* = 6-31G(d)
6-31G plus a set of polarizing d-functions (6D) added to heavy atoms
- most popular, widely used/validated
- Atoms: H - Ar
- Polarization functions help to account for the fact that atoms
within molecules are not spherical. Even better for polar bonds.
6-31+G
diffuse (large) s orbitals added (in essence opposite of *)
- negative ions bound
- slower
6-31+G* = 6-31+G(d) - Augmented 6-31G*
6-31++G* = 6-31++G(d) - Augmented 6-31+G
set of diffuse s-functions added to H, too
6-31+G* = 6-31+G(d,p)6-31++G* = 6-31++G(d,p)-
cc-pVDZ - Correlation Consistent, polarized Valence Double Zeta
Basis:
correlation consistent basis set
Valence Double Zeta
set of polarizing d-functions (5D) added to heavy atoms
Pros:
use with correlated methods
series converges exponentially to complete basis set limit
Atoms:
H-Ne, B-Ne, Al-Ar
cc-pVDZ+ - Augmented cc-pVDZ
Basis: add diffuse functions
Atoms:
H, C-F, Si-Cl
cc-pVDZ++
cc-pVTZ - Correlation Consistent Valence, polarized Triple Zeta
Post-Hartree-Fock Methods
Electron Correlation:
Explicitly considering the effect of the interactions of specific electron
pairs, rather than the effect each electron feels from the average of all
the other electrons. (the latter is the SCF approximation).
Large correlation effects occur for:
- electron rich systems
- transition states
- "unusual” coordination numbers
- no unique Lewis structure
- conjugated multiple bonds
- radicals and biradicals
MP2 - 2nd Order Møller Plesset ( = Many Body Perturbation Theory)
Basis: Taylor Series expansion, truncated at 2nd order
Pros:
dynamic correlation for Van der Waals forces:
CH4 - CH4 binding
π-π stacking interaction
bond breaking consistent with diradical formation
(without correlation, heterolytic cleavage is seen)
anomeric effect
Cons:
not variational (MP3, MP4, etc.)
transition metals not parametrized
overbinds CO2, PO
free radicals too stable
O3 frequencies way off
bonds too long
scales as n5 (slow)
CI (Configuration Interaction)
The simplest variational approach to incorporate dynamic electron
correlation. Combination of the Hartree-Fock configuration plus many
other configurations of electrons in excited states
MRCI (Multi-Reference Configuration Interaction)
CISD (Configuration Interaction, Singles and Doubles substitution only)
Comparable to MP2.
QCISD(T) Quadratic Configuration Interaction, all Single and
double excitations and perturbative inclusion of Triple excitations.
Scales as n7.
MCSCF (MultiConfiguration Self-Consistent Field)
CASSCF (Complete Active Space Self-Consistent Field
CC (Coupled Cluster)
CCD (Coupled Cluster, Doubles only.)
CCSD (Coupled Cluster, Singles and Doubles only.)
CCSD(T) (Coupled Cluster, Singles and Doubles
with Triples treated approximately.)
CCSDT (Coupled Cluster, Singles, Doubles and Triples)
Extrapolation (to complete basis set (CBS)) methods
G1, G2, G3 (Pople: Nobel 1998) (Gaussian 1(2,3,4) theory):
empirical algorithm to extrapolate to complete basis set and full
correlation from combination of lower level calculations:
G2:
HF/6-31G(d) frequencies;
MP2/6-311G(dp) geometries;
single point energies of
MP4SDTQ w/ 6-311G**,
6-311+G**
6-311G**(2df)
QCISD(T)/6-311G**.
Practical up to ~7 heavy atoms.
Cons: Cl, F BDE's poor
ΔfH ±1.93 kcal/mol
Atoms: H-Ca,Ga-Br
G3 (Gaussian 3 "slightly empirical" theory) extension of G2,
adding systematic correction for each paired e- (3.3 milliHa = 2
kcal/mol) & each unpaired e- (3.1 milliHa).
ΔfH ±1.45 kcal/mol
Atoms: H-Ar
G3(MP2)
G3(MP2)/B3LYP (Geometries and Frequencies at DFT B3LYP)
CBS-xxx (Peterson)
CBS-QCI (Complete Basis Set Quadratic Configuration
Interaction)
alternative extrapolation algorithm to complete basis set.
W1/W2 (Martin)
Density Functional Theory - DFT
ab initio electronic method from solid state physics. Tries to
find best approximate “functional” to calculate energy from edensity. Static correlation built in. Not variational. Believed
to be size consistent.
SVWN
LYP
P86
B88
BP - Becke-Perdew
BLYP - Becke Lee-Yang-Parr
GGA91
B3LYP (most commonly used one!)
B3P86
Scales as n5 or less.
Houk et al. J. Phys. Chem. A 2003 107, 11445.
"Benchmarking Computational Methods.."
AIM (Atoms In Molecule) An analysis method based upon the shape
of the total electron density; used to define bonds, atoms, etc. Atomic
charges computed using this theory are probably the most justifiable
theoretically, but are often quite different from those from older
analyses, such as Mulliken populations. The latter uses LCAO
coefficients, and overestimates charge separation.
Books:
Tim Clark, "Molecular Orbital Calculations."
No math! Written in English! Deals with actual input to the programs.
Highly recommended, if currently dated (1985).
Szabo and Ostlund, "Modern Quantum Chemistry," MacMillan 1982.
Good explanations between the 42 pages of integrals.
For Michael Dewar's (somewhat biased, but amusing) history of MO
Calculations: J. Molec. Struc. 100 (1983) 41.
Solvation
COSMO (Conductor-Like Screening Model) implicit solvation model.
Considers macroscopic dielectric continuum around solvent
accessible surface of solute.
TIP3P Molecular Mechanics model of water with charge, Van der
Waals, and angle terms.
Timings (Different Methods)
(2.8 GHz PC)
Gaussian 98, benzene starting at 1.40Å hexagon, units of seconds
no freqs with freqs
E
ΔfH
exptl:
19.8
AM1
1.5
3.1
22.0
STO-3G
4.9
8.6
-227.8914
HF/6-31G
8.1
9.4
-230.6245
1234.
HF/6-31G*
17.4
116
-230.7031
HF/6-31+G*
61
321
-230.7111
MP2/6-31G*
71
752
-231.4872
MP2/6-31+G* 161
1747
-231.5020
G2
4231
-231.7815
23.6
G3
2702
-232.0522
20.4
G2(MP2)
1278
-231.7708
24.8
G3(MP2)
681
704
-231.8297
18.6
G3(MP2)B3
685
-231.8406
18.4
B3LYP/6-31G*
132
-232.2486
MNDO on a 8088 PC: 1100 sec.
Timing: size (cation, 2007)
G3(MP2), all anti conformation
molecule
#eminutes
MeOH
14
2.
EtOH
20
18.
nPrOH
26
64.
nBuOH
32
195.
nPnOH
38
569.
nHxOH
44
736.
nHpOH
50
1734.
(72 min 2012)
- scales as n7, n = # valence e- more elaborate geometry
optimizations take longer
Conformations:
nHxO4 rotatable bonds: anti, +gauche(g), -gauche(f)
ΔfH
agfg
-61.75 aagg
-64.14 ggag
aggf
-61.95 gffg
-64.22 gfag
aagf
-62.33 aaga
-64.25 gafa
agfa
-62.67 agaa
-64.25 gfgg
agff
-63.04 aaaa
-64.55 gfga
gggf
-63.19 gfgf
-64.61 gfff
agag
-63.28 gfaf
-64.83 gaaa
agaf
-63.30 gaga
-65.48 ggga
gagf
-63.54 ggaf
-65.50 gagg
aggg
-63.59 gaag
-65.51 ggff
gafg
-63.77 gaff
-65.58 ggaa
agga
-63.84 gaaf
-65.62 gffa
aaag
-63.98 gggg
-65.74 ggfa
ggfg
weighted average: -66.24
-65.76
-65.77
-65.78
-65.87
-65.91
-65.91
-66.06
-66.08
-66.17
-66.28
-66.29
-66.46
-66.58
-66.59
Cations [G3(MP2)]
Me2CHCH2NH2+.
Me2C(.)CH2NH3+
ΔfH298
178.41±0.41
168.49±0.41
S
E0
ΔfG298
84.12 186.24 213.00
90.02 176.02 201.33
CH3CHO+.
CH2=CHOH+.
198.27±0.20
184.13±0.20
61.88 201.14 206.57
62.61 186.80 192.21
NH4+
NH3
PA:
152.67±0.10
-10.00±0.10
203.0
44.35 155.37 165.90
48.08 -8.32 -3.54
22.3
H2NNH2+.
211.64±0.20
59.10 214.81 226.29
H2NNH2
27.82±0.20
58.70 31.04 42.59
Neutral pyramidal: θ = 106.5º, ion θ = 157º
Relaxation Energy of cation ca. 17 kcal/mol
%mem=256MB
%rwf=a,1900MB,b,1900MB,c,1900MB,d,1900MB,e,1900MB,f,1900MB,g,1900MB,h,-1
%nosave
-------------------# g3mp2 maxdisk=15GB
-------------------H2O
--Symbolic Z-matrix:
Charge = 0 Multiplicity = 1
H
O
1
0.95
H
2
0.95
1
107.
Job cpu time: 0 days 0 hours 0 minutes 44.6 seconds.
Exact polarizability:
2.778
0.000
6.679
0.000
0.000
4.808
Approx polarizability:
2.363
0.000
5.340
0.000
0.000
4.005
Full mass-weighted force constant matrix:
Low frequencies --0.0010
0.0017
0.0021
7.3489
8.3093
9.9159
Low frequencies --- 1826.5724 4070.4025 4188.6410
Harmonic frequencies (cm**-1), IR intensities (KM/Mole),
Raman scattering activities (A**4/AMU), Raman depolarization ratios,
reduced masses (AMU), force constants (mDyne/A) and normal coordinates:
1
2
3
A1
A1
B2
Frequencies -- 1826.5724
4070.4025
4188.6410
Red. masses -1.0823
1.0455
1.0828
Frc consts -2.1275
10.2061
11.1935
IR Inten
-107.2699
18.2084
58.1069
Raman Activ -5.7238
75.5382
39.0879
Depolar
-0.5300
0.1830
0.7500
Atom AN
X
Y
Z
X
Y
Z
X
Y
Z
1
1
0.00
0.43
0.56
0.00
0.58 -0.40
0.00 -0.56
0.43
2
8
0.00
0.00 -0.07
0.00
0.00
0.05
0.00
0.07
0.00
3
1
0.00 -0.43
0.56
0.00 -0.58 -0.40
0.00 -0.56 -0.43
E (Thermal)
CV
S
TOTAL
16.196
5.985
Job cpu time: 0 days 0 hours 0 minutes 28.5 seconds.
Job cpu time: 0 days 0 hours 0 minutes 50.6 seconds.
Time for triples=
0.30 seconds.
Job cpu time: 0 days 0 hours 0 minutes 14.8 seconds.
44.987
Population analysis using the SCF density.
**********************************************************************
Orbital Symmetries:
Occupied (A1) (A1)
Virtual
(A1) (B2)
(A1) (A2)
(B1) (A2)
(A1) (B2)
The electronic state is
Alpha occ. eigenvalues
Alpha virt. eigenvalues
Alpha virt. eigenvalues
Alpha virt. eigenvalues
Alpha virt. eigenvalues
Alpha virt. eigenvalues
Alpha virt. eigenvalues
Alpha virt. eigenvalues
Alpha virt. eigenvalues
Alpha virt. eigenvalues
Alpha virt. eigenvalues
(B2) (A1) (B1)
(A1) (B1) (A1)
(B1) (A1) (B2)
(A1) (B2) (A1)
(A1) (B1) (B1)
1-A1.
-- -20.56872
-0.04343
-0.25723
-0.78527
-1.17607
-2.04137
-2.75287
-4.20632
-5.57238
-6.15622
-7.82945
(B2)
(B2)
(A1)
(A1)
(B2)
(B1)
(B2)
(B2)
-1.34865
0.07176
0.31315
0.83837
1.26297
2.05832
3.17403
4.44500
5.67011
7.41580
7.84240
(A1)
(A1)
(A2)
(A1)
(B2)
(B2)
(B2)
(B1)
-0.71169
0.23737
0.32565
0.91676
1.49508
2.16884
3.92773
4.57676
5.83662
7.44458
8.06737
(A1)
(A1)
(B1)
(A2)
-0.58430
0.24590
0.66568
1.05684
1.59397
2.42432
3.96741
5.44010
5.91657
7.46822
51.59303
-0.51016
0.24670
0.71047
1.08545
1.65944
2.51212
3.98654
5.51822
6.05253
7.56939
Condensed to atoms (all electrons):
1
2
3
1 H
0.484816
0.269298 -0.009496
2 O
0.269298
7.972169
0.269298
3 H
-0.009496
0.269298
0.484816
Total atomic charges:
1
1 H
0.255382
2 O
-0.510764
3 H
0.255382
Sum of Mulliken charges=
0.00000
Atomic charges with hydrogens summed into heavy
atoms:
1
1 H
0.000000
2 O
0.000000
3 H
0.000000
Sum of Mulliken charges=
0.00000
Electronic spatial extent (au): <R**2>=
19.6152
Charge=
0.0000 electrons
Dipole moment (Debye):
X=
0.0000
Y=
0.0000
Z=
-2.0828 Tot=
2.0828
Quadrupole moment (Debye-Ang):
XX=
-7.5928
YY=
-4.2259
ZZ=
-6.2360
XY=
0.0000
XZ=
0.0000
YZ=
0.0000
Octapole moment (Debye-Ang**2):
XXX=
0.0000 YYY=
0.0000 ZZZ=
-1.3274 XYY=
0.0000
XXY=
0.0000 XXZ=
-0.3419 XZZ=
0.0000 YZZ=
0.0000
YYZ=
-1.4746 XYZ=
0.0000
Hexadecapole moment (Debye-Ang**3):
XXXX=
-6.6121 YYYY=
-5.9400 ZZZZ=
-7.2496 XXXY=
0.0000
XXXZ=
0.0000 YYYX=
0.0000 YYYZ=
0.0000 ZZZX=
0.0000
ZZZY=
0.0000 XXYY=
-2.4331 XXZZ=
-2.3735 YYZZ=
-1.8084
XXYZ=
0.0000 YYXZ=
0.0000 ZZXY=
0.0000
N-N= 9.088303640043D+00 E-N=-1.987824085983D+02 KE= 7.594119614980D+01
Symmetry A1
KE= 6.791617182163D+01
Symmetry A2
KE= 1.406616952546D-34
Symmetry B1
KE= 4.473677327000D+00
Symmetry B2
KE= 3.551347001170D+00
1\1\GINC-THERMO\SP\RMP2-FC\GTMP2Large\H2O1\JB\14-Nov-2001\0\\#N GEOM=A
LLCHECK GUESS=TCHECK MP2/GTMP2LARGE\\H2O\\0,1\H,-0.070384131,0.,-0.897
2787415\O,-0.0958886836,0.,0.0709538934\H,0.8374935995,0.,0.3296475945
\\Version=x86-Linux-G98RevA.7\State=1-A1\HF=-76.0558204\MP2=-76.314758
5\RMSD=9.212e-09\PG=C02V [C2(O1),SGV(H2)]\\@
PICNIC:
A SNACK IN THE GRASS.
Temperature=
298.150000 Pressure=
1.000000
E(ZPE)=
0.020515 E(Thermal)=
0.023350
E(QCISD(T))=
-76.207892 E(Empiric)=
-0.037116
DE(MP2)=
-0.117911
G3MP2(0 K)=
-76.342404 G3MP2 Energy=
-76.339568
G3MP2 Enthalpy=
-76.338624 G3MP2 Free Energy=
-76.360001
1\1\GINC-THERMO\Mixed\G3MP2\G3MP2\H2O1\JB\14-Nov-2001\0\\# G3MP2 MAXDI
SK=15GB\\H2O\\0,1\H,-0.070384131,0.,-0.8972787415\O,-0.0958886836,0.,0
.0709538934\H,0.8374935995,0.,0.3296475945\\Version=x86-Linux-G98RevA.
7\State=1-A1\MP2/6-31G(d)=-76.1968478\QCISD(T)/6-31G(d)=-76.2078917\MP
2/GTMP2Large=-76.3147585\G3MP2=-76.3424035\FreqCoord=-0.1507632936,0.,
-1.6611179585,-0.1742115986,0.,0.1289098018,1.5444560828,0.,0.62983954
4\PG=C02V [C2(O1),SGV(H2)]\NImag=0\\0.05943423,0.,0.00000270,0.0086474
6,0.,0.61314791,-0.06074901,0.,-0.01968431,0.62304397,0.,-0.00000333,0
.,0.,0.00000666,0.05298665,0.,-0.59899355,0.12003565,0.,0.69644113,0.0
0131478,0.,0.01103685,-0.56229497,0.,-0.17302230,0.56098019,0.,0.00000
064,0.,0.,-0.00000333,0.,0.,0.00000270,-0.06163412,0.,-0.01415436,-0.1
0035133,0.,-0.09744759,0.16198545,0.,0.11160194\\0.00000116,0.,-0.0000
0451,-0.00000580,0.,0.00000429,0.00000465,0.,0.00000021\\\@
Job cpu time: 0 days 0 hours 0 minutes 18.3 seconds.
File lengths (MBytes): RWF= 263 Int=
Normal termination of Gaussian 98.
# g3mp2 maxdisk=15GB
0 D2E=
0 Chk=
3 Scr=
H2O
0 1
H
O
H
1
2
.9686
.9686
1
103.9822
_dHf(298)= -57.41+/-0.02
S= 44.99
Time:
2.6 min. Polarizability =
E0= -56.72
1.23 Ang^3
dGf(298)=
-54.20
1
Bottom line:
Molecular Mechanics: proteins/DNA above oligimer
(>10)
Semi-empirical: front end for ab initio
Ab initio: at least MP2
Gn up to 20 heavies
DFT: most common these days (speed), but
hard to find “best” functionals,
sometimes strange errors