Transcript Incorporation of Zeolites into Solid State Devices

Comparative Study of Three Methods of
Calculating Atomic Charge in a Molecule
Wanda Lew
Sharam Emami
Heather Harding
Shungo Miyabe
San Francisco State University
Tomekia Simeon
Jackson State University
Source of Wisdom: Sergio Aragon
January 16, 2004
Why is assigning charges to various atoms
of a molecule of interest?
Assigning charge to various atoms allows:
• Prediction of reactive sites in a molecule
• Charge distribution determines all molecular
properties
Andrew S. Ichimura
SFSU presentation 9/26/03
Why isn’t there just one best method that everyone
uses to calculate atomic charge?
• No concensus on what criteria to use to judge
a.
b.
which method is better i.e.
Do we arbitrarily say that if a method is basis set
independent it is “better”?*
Or is the better method one that’s able to
account for anticipated changes in charge
distribution after various perturbations to the
molecule such as:
● varying dihedral angles* in a molecule
We Decided to Examine Three Methods for
Assigning Charges to Atoms in a Molecule
• Population Analysis (R.S. Mulliken, 1955)
• Atoms in Molecule (R.W.F. Bader, 1965)
• Electrostatic Potential (Merz-Sing-Kollman)
What is Population Analysis?
•
•
This method was proposed by R.S. Mulliken
Sample Molecule:
A-B
To assign charge on atom A, uses a molecular orbital
function represented by a linear combination of the atomic
orbitals
YMO=CAYA + CBYB
N=N(CA 2 + 2CACBSAB+ CB 2 )
Mulliken Charge on Atom A would be:
QA=N(CA2 + CACBSAB)
• Weaknesses:
a. Divides overlap term symmetrically
b. Atomic orbital term CA2 assigned to atom even if the
charge on that atom is polarized/diffuse enough to bleed
some e- density into neighboring atom
Electrostatic Potential
• Ability to compute the degree to which a
positive or negative test charge is
attracted to or repelled by the molecule
that is being represented by the multipole
expansion.
• ESP is directly calculated from the electron
density using a many electron
wavefunction and point charges of the
nuclei.
• Electrostatic potential is both a
molecular property and a spatial
property.
• It depends on what charges
exist in the molecule and how
they there are distributed.
• The electrostatic potential
created by a system of charges
at a particular point in space, (x,
y, z), is equal to the change in
potential energy that occurs
when a +1 ion is introduced at
this point.
It also depends on what point
•
(x, y, z) we choose to investigate. If we select a point where the +1
charge is attracted by the molecule, the potential will be negative at this
point.
•
On the other hand, if we select a point where the +1 charge is repelled,
the potential will be positive.
AIM
• Let (r) be the electron density
• Gradient of (r) is a vector that points in the direction of
maximum increase in the density. One makes an
infinitesimal step in this direction and then recalculates
the gradient to obtain the new direction. By continued
repetition of this process, one traces out a trajectory of
(r).
AIM (cont.)
• A gradient vector map generated for ethene:
• Since the density exhibits a maximum at the position of
each nucleus, sets of trajectories terminate at each
nucleus. The nuclei are the attractors of the gradient
vector field of the electron density.
AIM (cont.)
• The molecule is disjointly and exhaustively partitioned into basins, a
basin being the region of space traversed by the trajectories
terminating at a given nucleus or attractor.
• An atom is defined as the union of an attractor and its basin
Comparison of 3 Ways to Calculate Charge on
Atom in a Molecule (MUL, AIM, ESP) Using 7
Different Molecules
a. Molecules Studied:
Urea, Proprionitrile, 1,2-difluoroethane, Glycine, Serine,
Propylaldehyde, propane, propanol
b. Calculation Methods Used:
Hartree-Fock (HF)
Density Functional (DFT, specifically B3LYP)
c. Criteria used to evaluate quality of method:
i. independence of basis set (STO-3g, 321g, 631g, 6311g,
6311g*, 6311g**)
ii. How charge on atom changes with change in dihedral
angles
Andrew S. Ichimura
SFSU presentation 9/26/03
Basis Set Dependence of MUL, AIM and ESP –HF Method
Urea Mulliken Charge w ith Hartree-Fock Method at
Optimal Geometry
1
1.5
1
hfsto3g
Charge
0.5
hf321g
0
-0.5 0
1
2
3
4
5
6
7
8
4
hf631g
9
Atom Number
Urea ESP Charge w ith Hartree-Fock Method at
Optim al Geom etry
Urea AIM Charge with Hartree-Fock Method
at Optimal Geometry
1.5
2.5
hfsto3g
Charge
0.5
hf321g
0
2
hfsto3g
1.5
Charge
1
-0.5
6
Urea
-1
5
3
7
hf6311g
-1.5
2
8
hf321g
1
0.5
0
1
2
3
4
5
6
7
8
9
hf631g
0
hf6311g -0.5
-1
hf631g
0
1
2
3
4
5
6
-1
-1.5
-1.5
Atom Number
Atom Number
7
8
9
hf6311g
Basis Set Dependence MUL, AIM and ESP -- DFT Methods
0.8
Urea Mulliken Charge with DFT Method at
Optimal Geometry
1
Charge
0.6
0.4
blypsto3g
0.2
blyp631g
2
7
4
0
-0.2 0
1
2
3
4
5
6
7
8
9
-0.4
8
blyp6311g++
-0.8
-1
Urea AIM Charge with DFT Method at
Optimal Geometry
Urea ESP Charge w ith DFT Method at Optim al
Geom etry
2.5
1
blypsto3g
2
0.5
blyp631g
1.5
blyp6311g
0
-0.5 0
1
2
3
4
5
6
7
8
9
blyp6311g+
blyp6311g++
-1
blyp6311g++dp
-1.5
Atom Number
Charge
Charge
1.5
6
Urea
blyp6311g++dp
Atom Number
3
blyp6311g
blyp6311g+
-0.6
5
blypsto3g
blyp631g
1
blyp6311g
0.5
blyp6311g+
0
-0.5 0
1
2
3
4
5
6
8
9
blyp6311g++
blyp6311g++dp
-1
-1.5
7
Atom Number
Dihedral Angle Dependence of MUL, AIM and ESP with HF
Methods
1
Urea Mulliken Charge (HF6311g) w ith Varying
Dihedral
1.5
Charge
0
45
0.5
0
-0.5 0
2
8
1
1
2
3
4
5
6
7
8
9
4
90
135
6
3
7
5
Urea
-1
-1.5
Atom Number
Urea AIM Charge (HF 6311g) with Varied
Dihedral Angle
Urea ESP Charge (HF6311g) with Varied
Dihedral Angle
Charge
1.5
1
0.5
0
-0.5 0
-1
-1.5
2
1.5
0
45
1
2 3
4
5
6 7
8
9
90
135
1
0
45
0.5
0
-0.5
0
1
2
3
4
5
6
-1
-1.5
Atom Number
Atom Num ber
7
8
9
90
135
Dihedral Angle Dependence of MUL, AIM and ESP
with DFT Methods
Urea Mulliken (BLYP6311g) with Varied
Dihedral Angles
1
Charge
0.5
0
45
0
0
1
2
3
4
5
6
7
8
9
-0.5
90
135
Urea AIM Charges (BLYP6311g) with Varied
Dihedral Angles
-1
Atom Number
2
1.5
Urea ESP Charge (BLYP6311g) with Varied
Dihedral Angles
Charge
0
0.5
45
0
-0.5
90
0
1
2
3
4
5
6
-1
-1.5
Atom Number
7
8
9
135
Charge
1.5
1
0
1
0.5
45
0
90
-0.5
0
1
2
3
4
5
6
-1
-1.5
Atom Number
7
8
9
135
Basis Set Dependence of MUL, AIM and ESP with HF
Methods
Propionitrile Mulliken Charge via HartreeFock Method at Optimal Geometry
1
0.4
2
0.2
hfsto3g
8
Charge
0
-0.2
0
2
4
6
8
10
7
hf321g
-0.4
hf631g
-0.6
hf6311g
Proprionitrile
Atom Number
Proprionitrile ESP Charge via Hartree-Fock
Method at Optimal Geometry
1
0.4
0.5
hfsto3g
Charge
0.2
hf321g
0
2
4
6
8
10
hf631g
Charge
0.6
0
Propioniltrile AIM Charge via Hartree-Fock
Method at Optimal Geometry
hfsto3g
hf321g
0
0
1
2
3
4
5
6
Atom Number
-1.5
8
9
hf6311g
hf6311g
-0.6
7
hf631g
-0.5
-1
-0.4
5
4
9
-0.8
-0.2
3
6
Atom Number
Basis Set Dependence of MUL, AIM and ESP with
DFT Methods
Proprionitrile Mulliken Charge via DFT
Method at Optimal Geometry
0.4
blypsto3g
0.2
Charge
blyp631g
0
-0.2
0
1
2
3
4
5
6
7
8
9
10
blyp6311g
blyp6311g+
-0.4
-0.6
Propionitrile ESP Charge via DFT Method at
Optimal Geometry
0.6
blypsto3g
0.4
blypsto3g
0.5
blyp631g
Charge
Atom Number
blyp6311g
0
-0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
blyp6311g+
-0.5
blyp631g
0.2
Charge
1
blyp6311g++d
p
-0.8
blyp6311g
0
-0.2
Proprionitrile AIM Charges via DFT Method
at Optimal Geometry
blyp6311g++
0
2
4
6
8
10
blyp6311g+
blyp6311g++
-0.4
blyp6311g++dp
-0.6
Atom Number
blyp6311g++
-1
blyp6311g++dp
-1.5
Atom Number
Dihedral Angle Dependence of Charges on Atoms in
Proprionitrile Using MUL, AIM and ESP with HF Methods
Proprionitrile Mulliken Charges via HartreeFock Method at Varying Dihedral Angles
0.3
0.2
15 Degrees
Charge
0.1
0
-0.1 0
2
4
6
8
60 Degrees
10
-0.2
105 Degrees
-0.3
150 Degrees
-0.4
Propionitrile AIM Charges via Hartree-Fock
Method at Varying Dihedral Angles
195 Degrees
-0.5
1
-0.6
Atom Number
0.6
Charge
0
0
2
4
6
-0.5
0.4
0.2
0
-0.2
Charge
0.5
Proprionitrile ESP Charges via Hartree-Fock
Method at Varying Dihedral Angles
0
2
4
6
-0.4
-0.6
Atom Number
8
10
15
Degrees
60
Degrees
105
Degrees
150
Degrees
195
Degrees
-1
-1.5
Atom Number
8
10
15
Degrees
60
Degrees
105
Degrees
150
Degrees
195
Degrees
Dihedral Angle Dependence of Charges on Atoms
in Proprionitrile Using MUL, AIM and ESP with
DFT Methods
Proprionitrile Mulliken Charges via DFT
Method at Varying Dihedral Angle
0.3
15 Degrees
0
-0.1 0
-0.2
2
4
6
8
10
60 Degree
105 degree
-0.3
150 degree
-0.4
-0.5
195 degree
-0.6
Atom Number
Proprionitrile ESP Charges via DFT Method
at Varying Dihedral Angle
0.4
15
Degrees
60 Degree
Charge
0.2
0
0
2
4
6
-0.2
-0.4
-0.6
Atom Num ber
8
10
105
degree
150
degree
195
degree
Proprionitrile AIM Charges via DFT Methods
at Varying Dihedral Angle
0.8
0.6
0.4
0.2
0
-0.2 0
-0.4
-0.6
-0.8
-1
Charge
Charge
0.2
0.1
2
4
6
Atom Number
8
10
15
Degrees
60
Degree
105
degree
150
degree
195
degree
Glycine
6
9
8
3
10
7
1
5
2
4
Basis Set Dependence of Charges on Atoms
in Glycine Using a Mulliken Population
Analysis
1
0.8
0.6
0.4
0.2
HF321
charge
HF631
HF6311
0
1
2
3
4
5
6
7
8
9
10
DFT631
DFT6311++d
DFT6311++dp
-0.2
-0.4
-0.6
-0.8
-1
atom
Basis Set Dependence of Charges on
Atoms in Glycine Using AIM
1.2
0.7
HF321
charge
HF631
0.2
HF6311
DFT631
DFT6311++d
1
2
3
4
5
6
-0.3
-0.8
-1.3
atom
7
8
9
10
DFT6311++dp
Basis Set Dependence of Charges on
Atoms in Glycine Using ESP
1.5
1
0.5
HF321
charge
HF631
HF6311
0
1
2
3
4
5
6
7
8
9
10
DFT631
DFT6311++d
DFT6311++dp
-0.5
-1
-1.5
atom
Glycine – Different Dihedral Angles
Optimized
45º
90º
Dihedral Angle Dependence of Charges
on Atoms in Glycine Using MUL with DFT
0.6
0.4
0.2
0
charge
1
2
3
4
5
6
7
8
9
10
optimized
45 dihedral
90 dihedral
-0.2
-0.4
-0.6
-0.8
atom
Dihedral Angle dependence of Charges
on Atoms in Glycine Using AIM with DFT
1.5
1
charge
0.5
optimized
0
45 dihedral
1
2
3
4
5
6
-0.5
-1
-1.5
atom
7
8
9
10
90 dihedral
Dihedral Angle dependence of Charges
on Atoms in Glycine Using ESP with DFT
1.5
1
charge
0.5
optimized
0
45 dihedral
1
2
3
4
5
6
-0.5
-1
-1.5
atom
7
8
9
10
90 dihedral
Basis Set Dependence of Charges on Atoms
in Serine Using MUL, AIM and ESP with
Hartree-Fock Methods
Atom ic charge using Hartree-Fock and Mulliken m ethod for serine as a
function of basis set
1.2
HF STO-3G MUL
1
HF 321-G MUL
0.8
HF 6311-G d MUL
atomic charge
0.6
0.4
0.2
0
-0.2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
-0.4
-0.6
-0.8
-1
Atom ic charge using Hartree-Fock and AIM for serine as a function of basis set
Atomic charge using Hartree-Fock and ESP method for serine as a function of basis set
1.5
2
HF 6311-G d ESP
HF 6311-G d AIM
atomic charge
0.5
0.5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
0
1
-0.5
-0.5
-1
-1
-1.5
HF 321-G ESP
1
HF 321-G AIM
1
atomic charge
HF STO-3G ESP
HF STO-3G AIM
1.5
-1.5
2
3
4
5
6
7
8
9
10
11
12
13
14
Basis Set Dependence of Charges on Atoms
in Serine Using MUL, AIM and ESP with
Density Functional Theory Methods
Atom ic charge using DFT and AIM m ethod for serine as a function of basis set
2
DFT STO-3G AIM
DFT 321-G AIM
1.5
DFT 6311-G d AIM
atomic charge
1
Atom ic charge using DFT and Mulliken m ethod for serine as a function of basis
set
1
DFT STO-3G MUL
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
-0.5
DFT 321-G MUL
0.8
-1
DFT 6311-G d MUL
0.6
-1.5
0.4
0.2
0
-0.2
Atomic charge using DFT and ESP method for serine as a function of basis set
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1
DFT STO-3G ESP
-0.4
DFT 321-G ESP
DFT 6311-G d ESP
-0.6
0.5
-0.8
-1
atomic charge
atomic charge
0.5
0
1
-0.5
-1
-1.5
2
3
4
5
6
7
8
9
10
11
12
13
14
Comparison of methods using 6311-G d
basis set using DFT and HF
Atomic charge of serine using AIM with DFT and HF
2
1.5
HF 6311-G d AIM
DFT 6311-G d AIM
atomic charge
1
0.5
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
-0.5
-1
-1.5
Atomic charge of serine using ESP with DFT and HF
1
HF 6311-G d ESP
DFT 6311-G d ESP
atomic charge
0.5
0
1
-0.5
-1
-1.5
2
3
4
5
6
7
8
9
10
11
12
13
14
Basis Set Dependence of Charges on Atoms
in Propyl Aldehyde Using MUL, AIM and ESP
with Hartree-Fock Methods at theta~2.318
Atom ic charge using Hartree-Fock and Mulliken m ethod for propyl aldehyde
as a function of basis set
1
2
3
4
5
6
7
8
9
10
0.4
atomic charge
0.2
0
-0.2
-0.4
HF STO-3G MUL
HF 321-G MUL
-0.6
HF 6311-G d MUL
-0.8
Atomic charge using Hartree-Fock and ESP method for propyl
aldehyde as a function of basis set
Atomic charge using Hartree-Fock and AIM method for propyl
aldehyde as a function of basis set
0.4
0.2
0.2
0.1
-0.2
0
1
2
3
4
5
6
7
8
-0.4
-0.6
-0.8
-1
-1.2
-1.4
HF STO-3G AIM
HF 321-G AIM
9
atomic charge
atomic charge
0
-0.1
1
2
3
4
5
6
7
-0.2
-0.3
HF STO-3G ESP
HF 321-G ESP
-0.4
HF 6311-G d AIM
-0.5
-0.6
HF 6311-G d ESP
8
9
Comparison of Mulliken and AIM
using HF and DFT methods
Mulliken vs. AIM for propyl aldehyde
1.5
1
0.5
E HF 321-G MUL
E HF 6311-G d MUL
E B3LYP 6311-G d MUL
0
1
-0.5
-1
-1.5
2
3
4
5
6
7
8
9
10
E HF 321-G AIM
E HF 6311-G d AIM
E B3LYP 6311-G d AIM
Basis Set Dependence of Charges on Atoms
in Propyl Aldehyde Using MUL, AIM and ESP
with Density Functional Theory Methods
Atom ic charge using DFT and AIM m ethod for propyl aldehyde as a function of
basis set
1
0.5
atomic charge
Atomic charge using DFT and Mulliken method for propyl aldehyde as
a function of basis set
0.3
0
1
2
3
4
5
6
7
8
9
10
-0.5
B3LYP STO-3G AIM
B3LYP 321-G AIM
0.2
-1
B3LYP 6311-G d AIM
0.1
-0.1
1
2
3
4
5
6
7
8
9
10
Atom ic charge using DFT and ESP m ethod for propyl aldehyde as a function of basis
set
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
B3LYP STO-3G
MUL
B3LYP 321-G MUL
1
0.5
B3LYP 6311-G d
MUL
atomic charge
atomic charge
-1.5
0
0
1
2
3
4
5
6
7
8
9
-0.5
B3LYP STO-3G ESP
B3LYP 321-G ESP
-1
-1.5
B3LYP 6311-G d ESP
10
Basis Set Dependence of Charges on Atoms
in Propyl Aldehyde Using MUL, AIM and ESP
with Hartree-Fock Methods at theta~127.46
Atom ic charge using Hartree-Fock am d AIM m ethod for propyl aldehyde
(127.46) as a function of basis set
1.5
1
atomic charge
Atomic charge using Hartree-Fock and Mulliken method for propyl
aldehyde (127.46) as a function of basis set
0
1
2
3
4
5
6
7
-0.5
0.4
-1
0.2
-1.5
8
9
10
HF STO-3G AIM
HF 321-G AIM
HF 6311-G d AIM
0
1
2
3
4
5
6
7
8
9
10
-0.2
-0.4
Atom ic charge using DFT and ESP m ethod for propyl aldehyde (127.46) as a
function of basis set
HF STO-G MUL
0.5
HF 321-G MUL
-0.6
-0.8
0.4
HF 6311-G d MUL
0.3
atomic charge
atomic charge
0.6
0.5
0.2
0.1
0
-0.1
1
2
3
4
5
6
7
8
9
10
-0.2
-0.3
-0.4
-0.5
B3LYP STO-3G ESP
B3LYP 321-G ESP
B3LYP 6311-G d ESP
Basis Set Dependence of Charges on Atoms
in Propyl Aldehyde Using MUL, AIM and ESP
with DFT Methods at theta~127.46
Atom ic charge using DFT and AIM m ethod for propyl aldehyde (127.46) as a
function of basis set
1.5
atomic charge
1
0.5
0
1
2
3
4
5
6
7
-0.5
8
9
10
B3LYP STO-3G AIM
B3LYP 321-G AIM
-1
B3LYP 6311-G d AIM
-1.5
Atom ic charge using DFT and ESP m ethod for propyl aldehyde (127.46) as a
function of basis set
0.5
0.4
atomic charge
0.3
0.2
0.1
0
-0.1
1
2
3
4
5
6
7
8
9
10
-0.2
-0.3
-0.4
-0.5
B3LYP STO-3G ESP
B3LYP 321-G ESP
B3LYP 6311-G d ESP
Comparison of Charges on Atoms in Propyl
Aldehyde Using MUL and AIM as a function
rotating carbonyl group
Charges on Atoms in Propyl Aldehyde Using
MUL and AIM with HF and DFT Methods as a
function of rotating carbonyl group
AIM atomic charges as a function of dihedral angle of the carbonyl
group
1
2
3
4
5
6
7
8
9
10
1.5
1
0.5
0
-0.5
-1
-1.5
Mulliken charges as a function of dihedral angle of carbonyl group
1
2
3
4
5
6
7
8
9
10
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
E HF 321-G =-2.318
E HF 6311-G d =-2.318
E B3LYP 6311-G d =-2.318
E HF 321-G =-127.875
E HF 6311-G d =-127.875
E B3LYP 6311-G d =-127.875
Comparison of single and double
bonded propyl aldehyde!
Comparison of HF and DFT using Mulliken Method for
propyl aldehyde with single and double bonds
Mulliken vs. AIM vs. ESP for prop// di=0.000
1
2
3
4
5
6
7
8
1
0.8
0.6
0.5
0
MUL1
AIM1
-0.5
-1
ESP1
atomic charge
0.4
0.2
-0.2
-0.4
-0.6
-0.8
-1.5
321-G MUL HF/
0
-1
1
2
3
4
5
6
7
8
9
10
321-G MUL DFT/
321-G MUL HF//
Comparison of charges using Mulliken and
AIM with HF and DFT @ dihedral angle =
127.46
Mulliken vs. AIM for butylaldehyde @ 127.46
1
2
3
4
5
6
7
8
9
10
11
12
13
1.5
1
0.5
M1
M2
0
M3
AIM1
AIM2
-0.5
-1
-1.5
AIM3
Comparison of Mulliken and AIM for Butyl
Aldehyde using HF and DFT @ dihedral
angle ~0.000
MUL VS AIM FOR BUTYL @0.065
1
2
3
4
5
6
7
8
9
10
11
12
13
1.5
1
0.5
M1
M2
0
M3
AIM1
AIM2
-0.5
-1
-1.5
AIM3
Comparison of charge as a function of
dihedral angle for butyl aldehyde using HF
and DFT with AIM and MUL
Charge as a function of dihedral angle using HF and DFT
with Mulliken
0.3
0.2
atomic charge
0.1
0
1
-0.1
2
3
4
5
6
7
8
9
10
11
12
13
6311-Gd HF MUL
127.46
6311-G d DFT MUL
127.46
6311-G d HF MUL
~0.00
6311-G d DFT MUL
~0.00
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
Charge as a function of dihedral angle for 6311-G d using HF
and DFT with AIM
1.5
6311-G d HF AIM 127.46
6311-G d DFT AIM 127.46
1
atomic charge
6311-G d HF AIM ~0.00
0.5
6311-G d DFT AIM ~0.00
0
1
-0.5
-1
-1.5
2
3
4
5
6
7
8
9
10
11
12
13
Propane
Mulliken Charges via HF, Post HF
and DFT Methods
Propane Mulliken Charges
1
Charge
0.5
B3LYP/6-31gd
0
-0.5
C1
C2
C3
H4
H5
H6
H7
-1.5
Atom Number
1
Charge
0.5
0
-0.5
B3LYP/6-311gd
C1
C2 C3
H4
H5
H6 H7
H8
H9 H10 H11
MP2/6-311gd
HF/6-311gd
-1
-1.5
-2
Atom Number
H9 H10 H11
MP2/6-31gd
HF/6-31gd
-1
Propane Mulliken Charges
(Basis Set 6-311gd)
H8
Propane
Electrostatic Charges via HF, Post HF and
DFT Methods
Propane Electrostatic Charges
(Basis Set 6-31gd)
1.5
Charge
1
B3LYP/6-31g
0.5
MP2/6-31g
0
-0.5
C1
C2
C3
H4
H5
H6
H7
H8
-1
Atom Num ber
Propane Electrostatic Charges
(Basis Set 6-311gd)
1.5
Charge
1
0.5
B3LYP/6-311gd
0
-0.5
MP2/6-311gd
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
-1
-1.5
Atom Number
HF/6-311gd
H9
H10
H11
HF/6-31g
Atoms in Molecules via HF, Post HF
and DFT Methods
Atoms in Molecules Charges
(Basis Set 6-31gd)
Charge
0.3
0.2
B3LYP/6-31g
0.1
MP2/6-31g
HF/6-31g
0
-0.1
C1
C2
C3
H4
H5
H6
H7
H8
H9
H10
H11
Atom Num ber
Atoms in Molecules Charges
(Basis Set 6-311gd)
Charge
0.2
0.15
0.1
B3LYP/6-311gd
MP2/6-311gd
0.05
HF/6-311gd
0
-0.05
C1
C2
C3
H4
H5
H6
H7
-0.1
Atom Number
H8
H9
H10
H11
Conformational Dependence
of Charge
(Basis Set 6-31gd)
Charge
Charge
Type
Analysis
Propane
H5
0.202
0.079
0.013
0.4
H6
0.207
0.077
0.016
0.2
0
H7
0.213
0.101
0.022
0.182
H6
-0.02
H7
H8-0.004 H9
H9
0.21
-0.007
0.021
-0.6
-0.8
H10
0.177
-0.012
0.004
-1
H11
0.202
0.06
0.033
0.372
Atom
Number0.406
0.504
-0.2
-0.4
C1
C2
H4 H8
C3
H12
H5
A HF/6-31g
H10
H11
E HF/6-31g
M HF/6-31gd
Charge Type Analysis Propane
0.4
0.2
Charge
0
-0.2
C1
C2
C3
H4
H5
H6
H7
H8
H9
H10
H11
A HF/6-311gd
E HF/6-311gd
-0.4
M HF/6-311gd
-0.6
-0.8
-1
Atom Number
Conformational Dependence of Charge
(Basis Set 6-311gd)
CTA
CTA
0.4
E MP2/6-31gd
M MP2/6-31gd
-0.8
-1
-0.2
E MP2/6-311gd
M MP2/6-311gd
-0.6
-0.8
-1
Atom Number
CTA
CTA
0.4
0.4
0.2
0.2
0
0
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
A B3LYP/6-31g
E B3LYP/6-31g
M B3LYP/6-31gd
-0.4
Charge
Charge
A MP2/6-311gd
-0.4
Atom Number
-0.2
H11
H9 H10 H11
H10
H8
H9
H7
H8
H6
H7
H5
H6
H4
H5
C3
H4
C2
C3
C1
0
C2
A MP2/6-31gd
C1
0
-0.2
-0.4
-0.6
0.2
Charge
Charge
0.4
0.2
-0.2
C1
C2
C3
H4
H5
H6
H7
Atom Number
H10
H11
-0.6
A B3LYP/6-311gd
-1
-0.8
H9
-0.4
-0.8
-0.6
H8
E B3LYP/6-311gd
-1.2
M B3LYP/6-311gd
Atom Number
Propanol
Mulliken Charges via
HF, Post HF and DFT Methods
Mullikan Charges
1.5
Charge
1
0.5
0
-0.5
B3LYP/6-31gd
C1
C2
C3
H4
H5
H6
H7
H8
H9 H10 O11 H12
MP2/6-31gd
-1
HF/6-31gd
-1.5
-2
-2.5
Atom Number
Mullikan Charges
1.5
1
Charge
0.5
B3LYP/6-311gd
0
-0.5
C1
C2
C3
H4
H5
H6
H7
-1
H8
H9
H10
O11
H12
MP2/6-311gd
HF/6-311gd
-1.5
-2
-2.5
Atom
Propanol’s Electrostatic
Charges via HF, Post HF and
DFT Methods
2
1
0
-1
-2
-3
C1
C2
C3
H4
H5
H6
H7
H8
H9
H10
O11
B3LYP/631gd
MP2/631gd
HF/631gd
H12
Atom Number
ESP Charges Propanol (Basis Set 6-311gd)
2
1
Charge
Charge
Electrostatic Charges Propanol (Basis Set 6-31gd)
0
-1
C1
C2
C3
H4
H5
H6
H7
-2
-3
Atom Number
H8
H9
H10 O11 H12
B3LYP/6-311gd
MP2/6-311gd
HF/6-311gd
Propanol’s Atoms in Molecules Charges
via HF, Post HF and DFT Methods
Atoms in Molecules Charges Propanol (Basis Set 6-31gd)
Charge
4
2
B3LYP/6-31gd
0
MP2/6-31gd
HF/6-31gd
-2
C1
C2
C3
H4
H5
H6
H7
H8
H9
H10 O11
H12
-4
Atom Number
Atoms in Molecules Charges Propanol (Basis Set 6-311gd)
Charge
2
0
-2
C1
C2
C3
H4
H5
H6
H7
H8
H9
H10
O11
H12
B3LYP/6-311gd
MP2/6-311gd
HF/6-311gd
-4
Atom Number
A Comparsion of Propanol at Varying Dihedral Angles
Conformational Dependence of Charge
(Basis Set 6-311gd)
Charge Type Analysis forPropanol Dihedral Angle HF/6311gd
Charge Type Analysis Propanol
2
2
1.5
1
0.5
A HF/6-311gd
0
C1
-1
C2
C3
H4
H5
H6
H7
H8
H9
H10 O11 H12
E HF/6-311gd
M HF/6-311gd
Charge
Charge
1
-2
0
AIM
C1
-0.5
-1
-1.5
C2
C3
H4
H5
H6
H7
H8
H9 H10 O11 H12
ESP
Mulliken
-2
-2.5
-3
-3
Atom Num ber
Atom Number
Charge Type Analysis for Propanol Dihedral Angle
MP2/6-311gd
Charge Type Analysis Propanol
2
2
1
H8
H9
H10 O11 H12
E MP2/6-311gd
M MP2/6-311gd
-2
AIM
0
-1
ESP
Mulliken
-2
-3
-3
Atom Num ber
Atom Number
Charge Type Analysis Propanol
Charge Type Analysis for Propanol
Dihedral Angle B3LYP/6-311gd
1.5
1
2
0.5
12
H
M B3LYP/6-311gd
1
Charge
-1.5
10
O
11
9
-1
H
7
8
H
H
H
5
6
H
H
H
C
C
4
E B3LYP/6-311gd
3
-0.5
2
A B3LYP/6-311gd
1
0
C
Charge
O
4
H
1
2
H7
H
9
H
1
0
H
1
1
H6
H
8
H5
H
7
H4
H
6
C3
H
5
-1
C2
C
3
C1
C
2
0
C
1
A MP2/6-311gd
Charge
Charge
1
AIM
0
-1
C1
C2
C3
H4
H5
H6
H7
H8
-2
-3
Atom Number
H10 O11 H12
ESP
Mulliken
-2
-2.5
H9
Atom Number
C2H4F2
MK_100_321G_B3LYP
Mulliken (100)
Charge
MK100_HF631G
0.6
MK_100_B3LYP_G311G
0.4
MK_100_HF_6311G
0.2
0
-0.2
1
2
3
4
5
6
7
8
-0.4
-0.6
Atom
ESP_100_321G_B3LYP
ESP (100)
Charge
ESP_100_HF631G
0.6
ESP_100_B3LYP_G311G
0.4
ESP_100_HF_6311G
0.2
0
-0.2
1
2
3
4
5
-0.4
-0.6
Atom
6
7
8
STDEV (100,various basis sets)
AIM_100_STDEV
0.1
MK_100_STDEV
0.09
ESP_100_STDEV
0.08
0.07
SD
0.06
0.05
0.04
0.03
0.02
0.01
0
1
2
3
4
Atom
5
6
7
8
MK_75_321G_RB3LYP
Mulliken (75)
Charge
MK75_631G_RHF
0.6
MK_75_HF_321G
0.4
MK_75_631G_B3LYP
0.2
0
1
2
3
4
5
6
7
8
-0.2
-0.4
-0.6
Atom
AIM_75_321G_RB3LYP
AIM (75)
Charge
AIM_75_631G_RHF
0.8
0.6
0.4
0.2
0
-0.2 1
-0.4
-0.6
-0.8
AIM_75_HF_321G
AIM_75_631G_B3LYP
2
3
4
5
6
7
8
Atom
ESP_75_321G_RB3LYP
ESP (75)
Charge
ESP_75_631G_RHF
0.6
ESP_75_HF_321G
0.4
ESP_75_631G_B3LYP
0.2
0
-0.2 1
2
3
4
5
-0.4
-0.6
Atom
6
7
8
STDEV (75,various basis sets)
0.09
0.08
0.07
SD
0.06
AIM_75_STDEV
0.05
MK_75_STDEV
0.04
ESP_75_STDEV
0.03
0.02
0.01
0
1
2
3
4
5
Atom
6
7
8
MK_120_321G_HF
Mulliken (120)
Charge
MK_120_631G_HF
0.6
MK_120_B3LYP_631G
0.4
MK_120_321G_B3LYP
0.2
0
-0.2 1
2
3
4
5
6
7
8
-0.4
-0.6
Atom
AIM_120_321G_HF
AIM (120)
AIM_120_631G_HF
0.8
AIM_120_B3LYP_631G
0.6
AIM_120_321G_B3LYP
Charge
0.4
0.2
0
-0.2
1
2
3
4
5
6
7
8
-0.4
-0.6
-0.8
Atom
ESP_120_321G_HF
ESP (120)
Charge
ESP_120_631G_HF
0.6
ESP_120_B3LYP_631G
0.4
ESP_120_321G_B3LYP
0.2
0
-0.2 1
2
3
4
5
-0.4
-0.6
Atom
6
7
8
STDEV (120,various basis sets)
0.12
0.1
0.08
AIM_120_STDEV
SD
MK_120_STDEV
ESP_120_STDEV
0.06
0.04
0.02
0
1
2
3
4
5
Atom
6
7
8
AIM for different angles
0.6
0.4
AIM_75_321G_B3LYP
AIM_100_321G_B3LYP
Charge
0.2
AIM_120_321G_B3LYP
0
1
2
3
4
5
-0.2
-0.4
-0.6
Atom
6
7
8
ESP (for different angles)
0.3
ESP_75_321G_B3LYP
0.2
ESP_100_321G_B3LYP
ESP_120_321G_B3LYP
Charge
0.1
0
1
2
3
4
5
-0.1
-0.2
-0.3
Atom
6
7
8
MK (for different angles)
0.3
0.2
Charge
0.1
0
MK_75_321G_B3LYP
1
2
3
4
5
6
7
8
MK_100_321G_B3LYP
MK_120_321G_B3LYP
-0.1
-0.2
-0.3
-0.4
Atom
Error 2070
• WARNING: RMS ERROR HAS INCREASED.
NEWTON STEP FAILED FOR SURFACE
SHEET n.
• Many molecules resulted in error 2070 in
Gaussian98 when running AIM. (i.e. ethyl
formate, alanine, cysteine)
References:
1. Politzer, P.; Harris, R.R. J. Chem.Phys. 1970, 92, 6451.
2. McQuarrie, D.A.; Simon, J.D. Physical Chemistry: A Molecular
Approach. University Science Books: Sausalito, California, 1997.
3.
http://www.chemistry.mcmaster.ca/faculty/bader/aim/aim_1.html
Acknowledgments
• Inspiration for Project:
Dr. Sergio Aragon and Dr. Mario Blanco
(Their debate about Mulliken vs AIM method
assignment of charges on atoms in
molecules made this project happen)
• PASI/Caltech