comparative study of three methods of calculating atomic charge in a molecule
DESCRIPTION
Comparative Study of Three Methods of Calculating Atomic Charge in a Molecule. Wanda Lew Heather Harding Sharam Emami Shungo Miyabe San Francisco State University Tomekia Simeon Jackson State University Source of Wisdom: Sergio Aragon January 16, 2004. - PowerPoint PPT PresentationTRANSCRIPT
Comparative Study of Three Methods of Comparative Study of Three Methods of Calculating Atomic Charge in a MoleculeCalculating Atomic Charge in a Molecule
Wanda Lew Wanda Lew Heather Heather Harding Harding
Sharam Emami Sharam Emami Shungo MiyabeShungo MiyabeSan Francisco State UniversitySan Francisco State University
Tomekia SimeonTomekia SimeonJackson State UniversityJackson State University
Source of Wisdom: Sergio AragonSource of Wisdom: Sergio Aragon
January 16, 2004January 16, 2004
Why is assigning charges to various atoms Why is assigning charges to various atoms of a molecule of interest?of a molecule of interest?
Assigning charge to various atoms allowsAssigning charge to various atoms allows::
• Prediction of reactive sites in a moleculePrediction of reactive sites in a molecule
• Charge distribution determines all Charge distribution determines all molecular propertiesmolecular properties
Andrew S. IchimuraSFSU presentation 9/26/03
Why isn’t there just one best method that everyone Why isn’t there just one best method that everyone uses to calculate atomic charge?uses to calculate atomic charge?• No concensus on what criteria to use to judge No concensus on what criteria to use to judge
which method is better i.e. which method is better i.e.
a.a. Do we arbitrarily say that if a method is Do we arbitrarily say that if a method is basis set independentbasis set independent it is “better”?* it is “better”?*
b.b. Or is the better method one that’s Or is the better method one that’s able to able to account for anticipated changes in account for anticipated changes in charge distribution after various charge distribution after various perturbations to the moleculeperturbations to the molecule such as: such as:
● ● varying dihedral angles* in a varying dihedral angles* in a moleculemolecule
We Decided to Examine Three Methods We Decided to Examine Three Methods for Assigning Charges to Atoms in a for Assigning Charges to Atoms in a
MoleculeMolecule
• Population Analysis (R.S. Mulliken, 1955)Population Analysis (R.S. Mulliken, 1955)
• Atoms in Molecule (R.W.F. Bader, 1965)Atoms in Molecule (R.W.F. Bader, 1965)
• Electrostatic Potential (Merz-Sing-Kollman)Electrostatic Potential (Merz-Sing-Kollman)
What is Population Analysis?What is Population Analysis?• This method was proposed by R.S. Mulliken This method was proposed by R.S. Mulliken
Sample Molecule:Sample Molecule: A-B A-B
• To assign charge on atom A, uses a molecular To assign charge on atom A, uses a molecular orbital function represented by a linear orbital function represented by a linear combination of the atomic orbitalscombination of the atomic orbitals
=C=CAAAA + C + CBBB B =N(C=N(CA A 22 + + 2C2CAACCBBSSABAB+ C+ CB B
22 ))
Mulliken Charge on Atom A would be:Mulliken Charge on Atom A would be: Q QAA=N(C=N(CAA
22 + + CCAACCBBSSABAB))• Weaknesses:Weaknesses:
a.a. Divides overlap term symmetricallyDivides overlap term symmetrically
b.b. Atomic orbital term Atomic orbital term CCAA2 2 assigned to atom even if assigned to atom even if
the charge on that atom is polarized/diffuse the charge on that atom is polarized/diffuse enough to bleed some e- density into neighboring enough to bleed some e- density into neighboring atomatom
Electrostatic PotentialElectrostatic Potential• Ability to compute the degree to which a Ability to compute the degree to which a
positive or negative test charge is attracted positive or negative test charge is attracted to or repelled by the molecule that is being to or repelled by the molecule that is being represented by the multipole expansion.represented by the multipole expansion.
• ESP is directly calculated from the electron ESP is directly calculated from the electron density using a many electron wavefunction density using a many electron wavefunction and point charges of the nuclei.and point charges of the nuclei.
• Electrostatic potential is both Electrostatic potential is both a molecular property and a a molecular property and a spatial property.spatial property.
• It depends on what charges It depends on what charges exist in the molecule and how exist in the molecule and how they there are distributed.they there are distributed.
• The electrostatic potential The electrostatic potential created by a system of created by a system of charges at a particular point charges at a particular point in space, (in space, (x, y, zx, y, z), is equal to ), is equal to the change in potential the change in potential energy that occurs when a +1 energy that occurs when a +1 ion is introduced at this ion is introduced at this point.point.
It also depends on what point It also depends on what point
• (x, y, z)(x, y, z) we choose to investigate. If we select a point where we choose to investigate. If we select a point where the +1 charge is attracted by the molecule, the potential will be the +1 charge is attracted by the molecule, the potential will be negative at this point. negative at this point.
• On the other hand, if we select a point where the +1 charge is On the other hand, if we select a point where the +1 charge is repelled, the potential will be positive.repelled, the potential will be positive.
AIM AIM
• Let Let (r) be the electron density (r) be the electron density
• Gradient of Gradient of (r) is a vector that points in the direction of (r) is a vector that points in the direction of maximum increase in the density. One makes an maximum increase in the density. One makes an infinitesimal step in this direction and then recalculates infinitesimal step in this direction and then recalculates the gradient to obtain the new direction. By continued the gradient to obtain the new direction. By continued repetition of this process, one traces out a trajectory of repetition of this process, one traces out a trajectory of (r).(r).
AIM (cont.)AIM (cont.)
• A gradient vector map generated for ethene:A gradient vector map generated for ethene:
• Since the density exhibits a maximum at the position of Since the density exhibits a maximum at the position of each nucleus, sets of trajectories terminate at each each nucleus, sets of trajectories terminate at each nucleus. The nuclei are the nucleus. The nuclei are the attractorsattractors of the gradient of the gradient vector field of the electron density. vector field of the electron density.
AIM (cont.)AIM (cont.)
• The molecule is disjointly and exhaustively partitioned into The molecule is disjointly and exhaustively partitioned into basins, a basin being the region of space traversed by the basins, a basin being the region of space traversed by the trajectories terminating at a given nucleus or attractor. trajectories terminating at a given nucleus or attractor.
• An An atomatom is defined as the union of an attractor and its basin is defined as the union of an attractor and its basin
Comparison of 3 Ways to Calculate Charge Comparison of 3 Ways to Calculate Charge on Atom in a Molecule (MUL, AIM, ESP) on Atom in a Molecule (MUL, AIM, ESP) Using 7 Different MoleculesUsing 7 Different Moleculesa.a. Molecules StudiedMolecules Studied: :
Urea, Proprionitrile, 1,2-difluoroethane, Glycine, Urea, Proprionitrile, 1,2-difluoroethane, Glycine, Serine, Propylaldehyde, propane, propanol Serine, Propylaldehyde, propane, propanol
b.b. Calculation Methods Used: Calculation Methods Used: Hartree-Fock (HF) Hartree-Fock (HF) Density Functional (DFT, specifically B3LYP)Density Functional (DFT, specifically B3LYP)
c.c. Criteria used to evaluate quality of methodCriteria used to evaluate quality of method::i. independence of basis set (STO-3g, 321g, 631g, i. independence of basis set (STO-3g, 321g, 631g, 6311g, 6311g*, 6311g**)6311g, 6311g*, 6311g**)ii. How charge on atom changes with change in ii. How charge on atom changes with change in dihedral anglesdihedral angles
Andrew S. IchimuraSFSU presentation 9/26/03
Basis Set Dependence of MUL, AIM and ESP –HF Basis Set Dependence of MUL, AIM and ESP –HF MethodMethod
Urea Mulliken Charge with Hartree-Fock Method at Optimal Geometry
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8 9
Atom Number
Cha
rge
hfsto3g
hf321g
hf631g
hf6311g
Urea AIM Charge with Hartree-Fock Method at Optimal Geometry
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5 6 7 8 9
Atom Number
Cha
rge
hfsto3g
hf321g
hf631g
hf6311g
Urea ESP Charge w ith Hartree-Fock Method at Optimal Geometry
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8 9
Atom Number
Ch
arg
e
hfsto3g
hf321g
hf631g
hf6311g
Urea
1
2
4 38
67
5
Basis Set Dependence MUL, AIM and ESP -- DFT Basis Set Dependence MUL, AIM and ESP -- DFT MethodsMethods
Urea Mulliken Charge with DFT Method at Optimal Geometry
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 1 2 3 4 5 6 7 8 9
Atom Number
Cha
rge
blypsto3g
blyp631g
blyp6311g
blyp6311g+
blyp6311g++
blyp6311g++dp
Urea AIM Charge with DFT Method at Optimal Geometry
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5 6 7 8 9
Atom Number
Cha
rge
blypsto3g
blyp631g
blyp6311g
blyp6311g+
blyp6311g++
blyp6311g++dp
Urea ESP Charge w ith DFT Method at Optimal Geometry
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8 9
Atom Number
Ch
arg
e
blypsto3g
blyp631g
blyp6311g
blyp6311g+
blyp6311g++
blyp6311g++dp
Urea
1
2
345
6
7
8
Dihedral Angle Dependence of MUL, AIM and ESP Dihedral Angle Dependence of MUL, AIM and ESP with HF Methodswith HF Methods
Urea Mulliken Charge (HF6311g) w ith Varying Dihedral
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8 9
Atom Number
Ch
arg
e
0
45
90
135
Urea AIM Charge (HF 6311g) with Varied Dihedral Angle
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 1 2 3 4 5 6 7 8 9
Atom Number
0
45
90
135
Urea ESP Charge (HF6311g) with Varied Dihedral Angle
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8 9
Atom Number
Cha
rge
0
45
90
135
Urea
1
2
348
5
6
7
Dihedral Angle Dependence of MUL, AIM Dihedral Angle Dependence of MUL, AIM and ESP with DFT Methodsand ESP with DFT Methods
Urea ESP Charge (BLYP6311g) with Varied Dihedral Angles
-1.5
-1
-0.5
0
0.5
1
1.5
0 1 2 3 4 5 6 7 8 9
Atom Number
Ch
arg
e
0
45
90
135
Urea AIM Charges (BLYP6311g) with Varied Dihedral Angles
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 1 2 3 4 5 6 7 8 9
Atom Number
Ch
arg
e
0
45
90
135
Urea Mulliken (BLYP6311g) with Varied Dihedral Angles
-1
-0.5
0
0.5
1
0 1 2 3 4 5 6 7 8 9
Atom Number
Cha
rge
0
45
90
135
Basis Set Dependence of MUL, AIM and ESP with Basis Set Dependence of MUL, AIM and ESP with HF MethodsHF Methods
Propionitrile Mulliken Charge via Hartree-Fock Method at Optimal Geometry
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0 2 4 6 8 10
Atom Number
Ch
arg
e
hfsto3g
hf321g
hf631g
hf6311g
Propioniltrile AIM Charge via Hartree-Fock Method at Optimal Geometry
-1.5
-1
-0.5
0
0.5
1
0 1 2 3 4 5 6 7 8 9
Atom Number
Ch
arg
ehfsto3g
hf321g
hf631g
hf6311g
Proprionitrile ESP Charge via Hartree-Fock Method at Optimal Geometry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 2 4 6 8 10
Atom Number
Cha
rge
hfsto3g
hf321g
hf631g
hf6311g
ProprionitrileProprionitrile
1
2
3
4
5678
9
Basis Set Dependence of MUL, AIM and ESP Basis Set Dependence of MUL, AIM and ESP with DFT Methodswith DFT Methods
Proprionitrile Mulliken Charge via DFT Method at Optimal Geometry
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0 1 2 3 4 5 6 7 8 9 10
Atom Number
Ch
arg
e
blypsto3g
blyp631g
blyp6311g
blyp6311g+
blyp6311g++
blyp6311g++dp
Proprionitrile AIM Charges via DFT Method at Optimal Geometry
-1.5
-1
-0.5
0
0.5
1
-0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
Atom Number
Cha
rge
blypsto3g
blyp631g
blyp6311g
blyp6311g+
blyp6311g++
blyp6311g++dp
Propionitrile ESP Charge via DFT Method at Optimal Geometry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 2 4 6 8 10
Atom Number
Ch
arg
e
blypsto3g
blyp631g
blyp6311g
blyp6311g+
blyp6311g++
blyp6311g++dp
Dihedral Angle Dependence of Charges on Atoms in Dihedral Angle Dependence of Charges on Atoms in Proprionitrile Using MUL, AIM and ESP with HF Proprionitrile Using MUL, AIM and ESP with HF MethodsMethods
Proprionitrile Mulliken Charges via Hartree-Fock Method at Varying Dihedral Angles
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 2 4 6 8 10
Atom Number
Ch
arg
e
15 Degrees
60 Degrees
105 Degrees
150 Degrees
195 DegreesPropionitrile AIM Charges via Hartree-Fock
Method at Varying Dihedral Angles
-1.5
-1
-0.5
0
0.5
1
0 2 4 6 8 10
Atom Number
Cha
rge
15Degrees60Degrees105Degrees150Degrees195Degrees
Proprionitrile ESP Charges via Hartree-Fock Method at Varying Dihedral Angles
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 2 4 6 8 10
Atom Number
Ch
arg
e
15Degrees60Degrees105Degrees150Degrees195Degrees
Dihedral Angle Dependence of Charges on Dihedral Angle Dependence of Charges on Atoms in Proprionitrile Using MUL, AIM and Atoms in Proprionitrile Using MUL, AIM and ESP with DFT MethodsESP with DFT Methods
Proprionitrile Mulliken Charges via DFT Method at Varying Dihedral Angle
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 2 4 6 8 10
Atom Number
Ch
arg
e
15 Degrees
60 Degree
105 degree
150 degree
195 degree Proprionitrile AIM Charges via DFT Methods at Varying Dihedral Angle
-1
-0.8-0.6
-0.4-0.2
00.2
0.40.6
0.8
0 2 4 6 8 10
Atom Number
Ch
arg
e
15Degrees60Degree105degree150degree195degree
Proprionitrile ESP Charges via DFT Method at Varying Dihedral Angle
-0.6
-0.4
-0.2
0
0.2
0.4
0 2 4 6 8 10
Atom Number
Ch
arg
e
15Degrees60 Degree
105degree150degree195degree
GlycineGlycine
12
3
4
5
6
7
8
9
10
Basis Set Dependence of Charges on Basis Set Dependence of Charges on Atoms in Glycine Using a Mulliken Atoms in Glycine Using a Mulliken Population AnalysisPopulation Analysis
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10
atom
ch
arg
e
HF321
HF631
HF6311
DFT631
DFT6311++d
DFT6311++dp
Basis Set Dependence of Charges Basis Set Dependence of Charges on Atoms in Glycine Using AIMon Atoms in Glycine Using AIM
-1.3
-0.8
-0.3
0.2
0.7
1.2
1 2 3 4 5 6 7 8 9 10
atom
ch
arg
e
HF321
HF631
HF6311
DFT631
DFT6311++d
DFT6311++dp
Basis Set Dependence of Charges Basis Set Dependence of Charges on Atoms in Glycine Using ESPon Atoms in Glycine Using ESP
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10
atom
ch
arg
e
HF321
HF631
HF6311
DFT631
DFT6311++d
DFT6311++dp
Glycine – Different Dihedral Angles
Optimized 45º
90º
Dihedral Angle Dependence of Dihedral Angle Dependence of Charges on Atoms in Glycine Using Charges on Atoms in Glycine Using MUL with DFTMUL with DFT
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8 9 10
atom
ch
arg
e
optimized
45 dihedral
90 dihedral
Dihedral Angle dependence of Dihedral Angle dependence of Charges on Atoms in Glycine Using Charges on Atoms in Glycine Using AIM with DFTAIM with DFT
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10
atom
ch
arg
e optimized
45 dihedral
90 dihedral
Dihedral Angle dependence of Dihedral Angle dependence of Charges on Atoms in Glycine Using Charges on Atoms in Glycine Using ESP with DFTESP with DFT
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10
atom
ch
arg
e optimized
45 dihedral
90 dihedral
Basis Set Dependence of Charges on Basis Set Dependence of Charges on Atoms in Serine Using MUL, AIM and Atoms in Serine Using MUL, AIM and ESP with Hartree-Fock MethodsESP with Hartree-Fock Methods
Atomic charge using Hartree-Fock and Mulliken method for serine as a function of basis set
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14ato
mic
ch
arg
e
HF STO-3G MUL
HF 321-G MUL
HF 6311-G d MUL
Atomic charge using Hartree-Fock and AIM for serine as a function of basis set
-1.5
-1
-0.5
0
0.5
1
1.5
2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ato
mic
ch
arg
e
HF STO-3G AIM
HF 321-G AIM
HF 6311-G d AIM
Atomic charge using Hartree-Fock and ESP method for serine as a function of basis set
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ato
mic
ch
arg
eHF STO-3G ESP
HF 321-G ESP
HF 6311-G d ESP
Basis Set Dependence of Charges on Basis Set Dependence of Charges on Atoms in Serine Using MUL, AIM and Atoms in Serine Using MUL, AIM and ESP with Density Functional Theory ESP with Density Functional Theory MethodsMethods
Atomic charge using DFT and Mulliken method for serine as a function of basis set
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ato
mic
ch
arg
e
DFT STO-3G MUL
DFT 321-G MUL
DFT 6311-G d MUL
Atomic charge using DFT and AIM method for serine as a function of basis set
-1.5
-1
-0.5
0
0.5
1
1.5
2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ato
mic
ch
arg
e
DFT STO-3G AIM
DFT 321-G AIM
DFT 6311-G d AIM
Atomic charge using DFT and ESP method for serine as a function of basis set
-1.5
-1
-0.5
0
0.5
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14a
tom
ic c
ha
rge
DFT STO-3G ESP
DFT 321-G ESP
DFT 6311-G d ESP
Comparison of methods using 6311-G Comparison of methods using 6311-G d basis set using DFT and HFd basis set using DFT and HF
Atomic charge of sering using Mulliken with DFT and HF
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14
HF 6311-G d MUL
DFT 6311-G d MUL
Atomic charge of serine using AIM with DFT and HF
-1.5
-1
-0.5
0
0.5
1
1.5
2
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ato
mic
ch
arg
e
HF 6311-G d AIM
DFT 6311-G d AIM
Atomic charge of serine using ESP with DFT and HF
-1.5
-1
-0.5
0
0.5
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14
atom
ic c
harg
eHF 6311-G d ESP
DFT 6311-G d ESP
Basis Set Dependence of Charges on Basis Set Dependence of Charges on Atoms in Propyl Aldehyde Using MUL, Atoms in Propyl Aldehyde Using MUL, AIM and ESP with Hartree-Fock AIM and ESP with Hartree-Fock Methods at theta~2.318Methods at theta~2.318
Atomic charge using Hartree-Fock and Mulliken method for propyl aldehyde as a function of basis set
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
1 2 3 4 5 6 7 8 9 10
ato
mic
ch
arg
e
HF STO-3G MUL
HF 321-G MUL
HF 6311-G d MUL
Atomic charge using Hartree-Fock and AIM method for propyl aldehyde as a function of basis set
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
1 2 3 4 5 6 7 8 9
ato
mic
ch
arg
e
HF STO-3G AIM
HF 321-G AIM
HF 6311-G d AIM
Atomic charge using Hartree-Fock and ESP method for propyl aldehyde as a function of basis set
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
1 2 3 4 5 6 7 8 9
ato
mic
ch
arg
e
HF STO-3G ESP
HF 321-G ESP
HF 6311-G d ESP
Comparison of Mulliken and Comparison of Mulliken and AIM using HF and DFT methodsAIM using HF and DFT methods
Mulliken vs. AIM for propyl aldehyde
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10
E HF 321-G MUL
E HF 6311-G d MUL
E B3LYP 6311-G d MUL
E HF 321-G AIM
E HF 6311-G d AIM
E B3LYP 6311-G d AIM
Basis Set Dependence of Charges on Basis Set Dependence of Charges on Atoms in Propyl Aldehyde Using MUL, Atoms in Propyl Aldehyde Using MUL, AIM and ESP with Density Functional AIM and ESP with Density Functional Theory MethodsTheory Methods
Atomic charge using DFT and AIM method for propyl aldehyde as a function of basis set
-1.5
-1
-0.5
0
0.5
1
1 2 3 4 5 6 7 8 9 10
ato
mic
ch
arg
e
B3LYP STO-3G AIM
B3LYP 321-G AIM
B3LYP 6311-G d AIM
Atomic charge using DFT and ESP method for propyl aldehyde as a function of basis set
-1.5
-1
-0.5
0
0.5
1
1 2 3 4 5 6 7 8 9 10
ato
mic
ch
arg
e
B3LYP STO-3G ESP
B3LYP 321-G ESP
B3LYP 6311-G d ESP
Atomic charge using DFT and Mulliken method for propyl aldehyde as a function of basis set
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
1 2 3 4 5 6 7 8 9 10
ato
mic
ch
arg
e
B3LYP STO-3GMULB3LYP 321-G MUL
B3LYP 6311-G dMUL
Basis Set Dependence of Charges on Basis Set Dependence of Charges on Atoms in Propyl Aldehyde Using MUL, Atoms in Propyl Aldehyde Using MUL, AIM and ESP with Hartree-Fock AIM and ESP with Hartree-Fock Methods at theta~127.46Methods at theta~127.46
Atomic charge using Hartree-Fock and Mulliken method for propyl aldehyde (127.46) as a function of basis set
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8 9 10
ato
mic
ch
arg
e
HF STO-G MUL
HF 321-G MUL
HF 6311-G d MUL
Atomic charge using Hartree-Fock amd AIM method for propyl aldehyde (127.46) as a function of basis set
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10
ato
mic
ch
arg
e
HF STO-3G AIM
HF 321-G AIM
HF 6311-G d AIM
Atomic charge using DFT and ESP method for propyl aldehyde (127.46) as a function of basis set
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
1 2 3 4 5 6 7 8 9 10at
om
ic c
har
ge
B3LYP STO-3G ESP
B3LYP 321-G ESP
B3LYP 6311-G d ESP
Basis Set Dependence of Charges on Basis Set Dependence of Charges on Atoms in Propyl Aldehyde Using MUL, Atoms in Propyl Aldehyde Using MUL, AIM and ESP with DFT Methods at AIM and ESP with DFT Methods at theta~127.46theta~127.46
Atomic charge using DFT and Mulliken method for propyl aldehyde (127.46) as a function of basis set
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
1 2 3 4 5 6 7 8 9 10
B3LYP STO-3G MUL
B3LYP 321-G MUL
B3LYP 6311-G d MUL
Atomic charge using DFT and AIM method for propyl aldehyde (127.46) as a function of basis set
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10
ato
mic
ch
arg
e
B3LYP STO-3G AIM
B3LYP 321-G AIM
B3LYP 6311-G d AIM
Atomic charge using DFT and ESP method for propyl aldehyde (127.46) as a function of basis set
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
1 2 3 4 5 6 7 8 9 10at
om
ic c
har
ge
B3LYP STO-3G ESP
B3LYP 321-G ESP
B3LYP 6311-G d ESP
Comparison of Charges on Atoms in Comparison of Charges on Atoms in Propyl Aldehyde Using MUL and AIM as Propyl Aldehyde Using MUL and AIM as a function rotating carbonyl groupa function rotating carbonyl group
Charges on Atoms in Propyl Aldehyde Charges on Atoms in Propyl Aldehyde Using MUL and AIM with HF and DFT Using MUL and AIM with HF and DFT Methods as a function of rotating Methods as a function of rotating carbonyl groupcarbonyl group
Mulliken charges as a function of dihedral angle of carbonyl group
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8 9 10
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
AIM atomic charges as a function of dihedral angle of the carbonyl group
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10
Comparison of single and Comparison of single and double bonded propyl double bonded propyl aldehyde!aldehyde!
Mulliken vs. AIM vs. ESP for prop// di=0.000
-1.5
-1
-0.5
0
0.5
1
1 2 3 4 5 6 7 8
MUL1
AIM1
ESP1
Comparison of HF and DFT using Mulliken Method for propyl aldehyde with single and double bonds
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 2 3 4 5 6 7 8 9 10
ato
mic
ch
arg
e
321-G MUL HF/
321-G MUL DFT/
321-G MUL HF//
Comparison of charges using Mulliken Comparison of charges using Mulliken and AIM with HF and DFT @ dihedral and AIM with HF and DFT @ dihedral angle = 127.46angle = 127.46
Mulliken vs. AIM for butylaldehyde @ 127.46
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10 11 12 13
M1
M2
M3
AIM1
AIM2
AIM3
Comparison of Mulliken and AIM for Comparison of Mulliken and AIM for Butyl Aldehyde using HF and DFT @ Butyl Aldehyde using HF and DFT @ dihedral angle ~0.000dihedral angle ~0.000
MUL VS AIM FOR BUTYL @0.065
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10 11 12 13
M1
M2
M3
AIM1
AIM2
AIM3
Comparison of charge as a function of Comparison of charge as a function of dihedral angle for butyl aldehyde using dihedral angle for butyl aldehyde using HF and DFT with AIM and MULHF and DFT with AIM and MUL
Charge as a function of dihedral angle for 6311-G d using HF and DFT with AIM
-1.5
-1
-0.5
0
0.5
1
1.5
1 2 3 4 5 6 7 8 9 10 11 12 13
ato
mic
ch
arg
e
6311-G d HF AIM 127.46
6311-G d DFT AIM 127.46
6311-G d HF AIM ~0.00
6311-G d DFT AIM ~0.00
Charge as a function of dihedral angle using HF and DFT with Mulliken
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
1 2 3 4 5 6 7 8 9 10 11 12 13
ato
mic
ch
arg
e
6311-Gd HF MUL127.466311-G d DFT MUL127.466311-G d HF MUL~0.006311-G d DFT MUL~0.00
Propane Mulliken Charges (Basis Set 6-311gd)
-2
-1.5
-1
-0.5
0
0.5
1
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
Ch
arg
e B3LYP/6-311gd
MP2/6-311gd
HF/6-311gd
PropaneMulliken Charges via HF, Post HF
and DFT MethodsPropane Mulliken Charges
-1.5
-1
-0.5
0
0.5
1
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
Cha
rge
B3LYP/6-31gd
MP2/6-31gd
HF/6-31gd
Propane Electrostatic Charges (Basis Set 6-31gd)
-1
-0.5
0
0.5
1
1.5
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
Ch
arg
e B3LYP/6-31g
MP2/6-31g
HF/6-31g
Propane Electrostatic Charges(Basis Set 6-311gd)
-1.5
-1
-0.5
0
0.5
1
1.5
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
Ch
arg
e B3LYP/6-311gd
MP2/6-311gd
HF/6-311gd
Propane Electrostatic Charges via HF, Post HF and
DFT Methods
Atoms in Molecules Charges (Basis Set 6-31gd)
-0.1
0
0.1
0.2
0.3
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
C h
a r
g e
B3LYP/6-31g
MP2/6-31g
HF/6-31g
Atoms in Molecules Charges (Basis Set 6-311gd)
-0.1
-0.05
0
0.05
0.1
0.15
0.2
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
C h
a r
g e
B3LYP/6-311gd
MP2/6-311gd
HF/6-311gd
Atoms in Molecules via HF, Post HF and DFT Methods
Charge Type Analysis Propane
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
Ch
arg
e A HF/6-31g
E HF/6-31g
M HF/6-31gd
Charge Type Analysis Propane
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
Ch
arg
e A HF/6-311gd
E HF/6-311gd
M HF/6-311gd
Conformational Dependence of Charge
(Basis Set 6-31gd)
H50.20
2 0.079 0.013
H60.20
7 0.077 0.016
H70.21
3 0.101 0.022
H80.18
2 -0.02 -0.004
H9 0.21 -0.007 0.021
H100.17
7 -0.012 0.004
H110.20
2 0.06 0.033
H120.37
2 0.406 0.504
CTA
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
Char
ge
A MP2/6-31gd
E MP2/6-31gd
M MP2/6-31gd
CTA
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
C1
C2
C3
H4
H5
H6
H7
H8
H9
H10
H11
Atom Number
Cha
rge A MP2/6-311gd
E MP2/6-311gd
M MP2/6-311gd
Conformational Dependence of Charge(Basis Set 6-311gd)
CTA
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
Cha
rge
A B3LYP/6-31g
E B3LYP/6-31g
M B3LYP/6-31gd
CTA
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 H11
Atom Number
Char
ge
A B3LYP/6-311gd
E B3LYP/6-311gd
M B3LYP/6-311gd
PropanolMulliken Charges via
HF, Post HF and DFT Methods
Mullikan Charges
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 O11 H12
Atom Number
Ch
arg
e B3LYP/6-31gd
MP2/6-31gd
HF/6-31gd
Mullikan Charges
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 O11 H12
Atom
Ch
arg
e B3LYP/6-311gd
MP2/6-311gd
HF/6-311gd
ESP Charges Propanol (Basis Set 6-311gd)
-3
-2
-1
0
1
2
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 O11 H12
Atom Number
Char
ge
B3LYP/6-311gd
MP2/6-311gd
HF/6-311gd
Electrostatic Charges Propanol (Basis Set 6-31gd)
-3
-2
-1
0
1
2
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 O11 H12
Atom Number
Cha
rge
B3LYP/631gdMP2/631gd
HF/631gd
Propanol’s Electrostatic Charges via HF, Post HF and
DFT Methods
Atoms in Molecules Charges Propanol (Basis Set 6-31gd)
-4
-2
0
2
4
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 O11 H12
Atom Number
Cha
rge
B3LYP/6-31gd
MP2/6-31gd
HF/6-31gd
Atoms in Molecules Charges Propanol (Basis Set 6-311gd)
-4
-2
0
2
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 O11 H12
Atom Number
Char
ge
B3LYP/6-311gd
MP2/6-311gd
HF/6-311gd
Propanol’s Atoms in Molecules Charges via HF, Post HF and DFT Methods
Charge Type Analysis Propanol
-3
-2
-1
0
1
2
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 O11 H12
Atom Number
Ch
arg
e A HF/6-311gd
E HF/6-311gd
M HF/6-311gd
Charge Type Analysis Propanol
-3
-2
-1
0
1
2
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 O11 H12
Atom Number
Ch
arg
e A MP2/6-311gd
E MP2/6-311gd
M MP2/6-311gd
Charge Type Analysis Propanol
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
Atom Number
Ch
arg
e A B3LYP/6-311gd
E B3LYP/6-311gd
M B3LYP/6-311gd
A Comparsion of Propanol at Varying Dihedral Angles Conformational Dependence of Charge
(Basis Set 6-311gd)Charge Type Analysis forPropanol Dihedral Angle HF/6-
311gd
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Atom Number
Ch
arg
e
AIM
ESP
Mulliken
Charge Type Analysis for Propanol Dihedral AngleMP2/6-311gd
-3
-2
-1
0
1
2
Atom NumberC
ha
rge
AIM
ESP
Mulliken
Charge Type Analysis for Propanol
Dihedral Angle B3LYP/6-311gd
-3
-2
-1
0
1
2
C1 C2 C3 H4 H5 H6 H7 H8 H9 H10 O11 H12
Atom Number
Cha
rge AIM
ESP
Mulliken
CC22HH44FF22
Mulliken (100)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Atom
Ch
arg
e
MK_100_321G_B3LYP
MK100_HF631G
MK_100_B3LYP_G311G
MK_100_HF_6311G
AIM (100)
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 2 3 4 5 6 7 8
Atom
AIM_100_321G_B3LYP
AIM_100_HF631G
AIM_100_B3LYP_G311G
AIM_100_HF_6311G
ESP (100)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Atom
Ch
arg
e
ESP_100_321G_B3LYP
ESP_100_HF631G
ESP_100_B3LYP_G311G
ESP_100_HF_6311G
STDEV (100,various basis sets)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
1 2 3 4 5 6 7 8
Atom
SD
AIM_100_STDEV
MK_100_STDEV
ESP_100_STDEV
Mulliken (75)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Atom
Ch
arg
e
MK_75_321G_RB3LYP
MK75_631G_RHF
MK_75_HF_321G
MK_75_631G_B3LYP
ESP (75)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Atom
Ch
arg
e
ESP_75_321G_RB3LYP
ESP_75_631G_RHF
ESP_75_HF_321G
ESP_75_631G_B3LYP
AIM (75)
-0.8-0.6-0.4-0.2
0
0.20.40.60.8
1 2 3 4 5 6 7 8
Atom
Ch
arg
e
AIM_75_321G_RB3LYP
AIM_75_631G_RHF
AIM_75_HF_321G
AIM_75_631G_B3LYP
STDEV (75,various basis sets)
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
1 2 3 4 5 6 7 8
Atom
SD
AIM_75_STDEV
MK_75_STDEV
ESP_75_STDEV
AIM (120)
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 2 3 4 5 6 7 8
Atom
Ch
arg
e
AIM_120_321G_HF
AIM_120_631G_HF
AIM_120_B3LYP_631G
AIM_120_321G_B3LYP
Mulliken (120)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Atom
Ch
arg
e
MK_120_321G_HF
MK_120_631G_HF
MK_120_B3LYP_631G
MK_120_321G_B3LYP
ESP (120)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Atom
Ch
arg
e
ESP_120_321G_HF
ESP_120_631G_HF
ESP_120_B3LYP_631G
ESP_120_321G_B3LYP
STDEV (120,various basis sets)
0
0.02
0.04
0.06
0.08
0.1
0.12
1 2 3 4 5 6 7 8
Atom
SD
AIM_120_STDEV
MK_120_STDEV
ESP_120_STDEV
AIM for different angles
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1 2 3 4 5 6 7 8
Atom
Ch
arg
e
AIM_75_321G_B3LYP
AIM_100_321G_B3LYP
AIM_120_321G_B3LYP
ESP (for different angles)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
1 2 3 4 5 6 7 8
Atom
Ch
arg
eESP_75_321G_B3LYP
ESP_100_321G_B3LYP
ESP_120_321G_B3LYP
MK (for different angles)
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
1 2 3 4 5 6 7 8
Atom
Ch
arg
e MK_75_321G_B3LYP
MK_100_321G_B3LYP
MK_120_321G_B3LYP
Error 2070Error 2070
• WARNING: RMS ERROR HAS WARNING: RMS ERROR HAS INCREASED. NEWTON STEP FAILED INCREASED. NEWTON STEP FAILED FOR SURFACE SHEET n.FOR SURFACE SHEET n.
• Many molecules resulted in error 2070 Many molecules resulted in error 2070 in Gaussian98 when running AIM. (i.e. in Gaussian98 when running AIM. (i.e. ethyl formate, alanine, cysteine)ethyl formate, alanine, cysteine)
References: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
AcknowledgmentsAcknowledgments• Inspiration for Project:Inspiration for Project:
Dr. Sergio Aragon and Dr. Mario BlancoDr. Sergio Aragon and Dr. Mario Blanco
(Their debate about Mulliken vs AIM (Their debate about Mulliken vs AIM method assignment of charges on method assignment of charges on atoms in molecules made this project atoms in molecules made this project happen)happen)
• PASI/CaltechPASI/Caltech