quantum chemical molecular modellingmichalak/mmod2008/l2.pdf · input datainput data atoms zmatrix...
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Quantum chemical molecular modelling
Dr. hab. Artur MichalakDepartment of Theoretical Chemistry
Faculty of ChemistryJagiellonian University
Kraków, Poland
http://www.chemia.uj.edu.pl/~michalak/mmod/http://www.chemia.uj.edu.pl/~michalak/mmod2008/
In Polish: http://www.chemia.uj.edu.pl/~michalak/mmod2007/
Ck08
Lecture 2
• Basic ideas and methods of quantum chemistry:Wave-function; Electron density; Schrodinger equation; Density Functional theory; Born-Oppenheimer approximation; Variational principles in wave-function mechanics and DFT; One-electron approximation; HF method; Electron correlation; KS method; Wave-function-based electron correlation methods;
• Input data for QM calculations, GAMESS program:Molecular geometry, Z-Matrix, Basis sets in ab initio
calculations; input, output;
• Geometry of molecular systems: Geometry optimization; Constrained optimization; Conformational analysis; Global minimum problem
• Electronic structure of molecular systems: Molecular orbitals (KS orbitals); Chemical bond; Deformation density; Localized orbitals; Population analysis; Bond-orders
•Molecular vibrations, Thermodynamics; Chemical Reactivity:Vibrational analysis; Thermodynamic properties; Modeling chemical reactions; Trantition state optimization and validation; Intrinsic Reaction Coordinate; Chemical reactivity indices; Molecular Electrostatic Potential; Fukui Functions; Single- and Two-Reactant Reactivity Indices
• Other Topics:Modelling of complex chemical processes – examples from catalysis; Molecular spectroscopy from ab initio
calculations; Advanced methods for electron correlation;Molecular dynamics; Modelling of large systems –hybrid approaches (QM/MM); Solvation models
SoftwareSoftware
• GAUSSIAN• GAMESS• NWCHEM• TURBOMOLE• DMol• DeMon• DGauss• DeFT• ADF
• and many others
• GAUSSIAN• GAMESS• NWCHEM• TURBOMOLE• DMol• DeMon• DGauss• DeFT• ADF
• and many others
SoftwareSoftware
• GAUSSIAN• GAMESS• NWCHEM• TURBOMOLE• DMol• DeMon• DGauss• DeFT• ADF
• and many others
• GAUSSIAN• GAMESS• NWCHEM• TURBOMOLE• DMol• DeMon• DGauss• DeFT• ADF
• and many others
Static calculations(BO approximation)Static calculations
(BO approximation)
• Wave-function / electron density optimization (for assumed molecular geometry) ���� the electronic energy
• Geometry optimization
• Vibrational frequencies
• Molecular properties based on the wave-function / electron density
• Wave-function / electron density optimization (for assumed molecular geometry) ���� the electronic energy
• Geometry optimization
• Vibrational frequencies
• Molecular properties based on the wave-function / electron density
Input dataInput dataatoms zmatrix
1 H 0 0 0 0.0 0.0 0.0
2 O 1 2 0 0.99 0.0 0.0
3 H 2 1 3 0.99 105.0 0.0
end
basis
type sz
core none
end
xc
lda scf vwn
end
symmetry tol=0.001
geometry
optim all internal
iterations 30
step rad=0.15 angle=10.0
hessupd bfgs
converge e=1.0e-3 grad=1.0e-2 rad=1.0e-2 angle=0.5
end
scf
iterations 50
converge 1.0e-6 1.0e-3
mixing 0.2
lshift 0.0
diis n=10 ok=0.5 cyc=5 cx=5.0 cxx=10.0
end
integration 3.0 4.0 4.0
units
length angstrom
$CONTRL SCFTYP=RHF RUNTYP=OPTIMIZE
COORD=ZMT ICHARG=0 MULT=1 $END
$SYSTEM TIMLIM=90 MEMORY=1000000 $END
$STATPT OPTTOL=1.0E-3 NSTEP=100 $END
$BASIS GBASIS=STO NGAUSS=3 $END
$SCF DIRSCF=.TRUE. $END
$GUESS GUESS=HUCKEL $END
$DATA
h2o
C1
H
O 1 1.0
H 2 1.0 1 105.0
$END
$CONTRL SCFTYP=RHF RUNTYP=OPTIMIZE
COORD=ZMT ICHARG=0 MULT=1 $END
$SYSTEM TIMLIM=90 MEMORY=1000000 $END
$STATPT OPTTOL=1.0E-3 NSTEP=100 $END
$BASIS GBASIS=STO NGAUSS=3 $END
$SCF DIRSCF=.TRUE. $END
$GUESS GUESS=HUCKEL $END
$DATA
h2o
C1
H
O 1 1.0
H 2 1.0 1 105.0
$END
GAMESS
ADF1. Text file:
keywords, values of parametrers, etc.
Input dataInput data
Interfejs graficznyprogramuADF 2005
2. GUI (graphical user interface)
Data set for quantum chemical calculations
Data set for quantum chemical calculations
• Unique definition of the molecule and its electronic state
• Choice of methodology
• Basis set specification
• Choice of computational details: alghoritms, parameters characteristic for a given method, etc. (that influence accuracy of calculations); choice of properties to be calculated
• Unique definition of the molecule and its electronic state
• Choice of methodology
• Basis set specification
• Choice of computational details: alghoritms, parameters characteristic for a given method, etc. (that influence accuracy of calculations); choice of properties to be calculated
Default charge - 0Default charge - 0Nuclei: H, C, N
Charge 0
(14 electrons)
MoleculeMolecule
• Number and types of nuclei forming the molecule;• Number and types of nuclei forming the molecule;
• Number of electrons (charge of molecule)• Number of electrons (charge of molecule)
HCN CNH TS
• Positions of nuclei• Positions of nuclei
• Electronic state (multiplicity, numbers of αααα and ββββ electrons)• Electronic state (multiplicity, numbers of αααα and ββββ electrons)
Singlet: nαααα-nββββ = 0 = 0 = 0 = 0 (default)
Doublet: nαααα-nββββ = 1= 1= 1= 1
Triplet: nαααα-nββββ = 2, = 2, = 2, = 2, etc.
Singlet: nαααα-nββββ = 0 = 0 = 0 = 0 (default)
Doublet: nαααα-nββββ = 1= 1= 1= 1
Triplet: nαααα-nββββ = 2, = 2, = 2, = 2, etc.
MoleculeMolecule
• Number and types of nuclei forming the molecule;• Number and types of nuclei forming the molecule;
• Number of electrons (charge of molecule)• Number of electrons (charge of molecule)
Units??? a.u. (bohr)Å
Molecular geometry -cartesian coordinatesMolecular geometry -cartesian coordinates
z
cartesian angstrom
H 0.00 0.00 0.00
C 0.00 0.00 1.00
N 0.00 0.00 2.20
end
Molecular geometry -cartesian coordinatesMolecular geometry -cartesian coordinates
Bond lengths, bond angles, torsional angles
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
N atoms - 3N cartesian coords
3N-6 internal coorrds
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Choice of atom order
Choice of coordinates (reference atoms)
Choice of atom order
Choice of coordinates (reference atoms)
zmatrix angstrom
H
C 1 1.00
N 2 1.20 1 180.0
end
1 2 3
zmatrix angstrom
H
C 1 1.00
N 1 2.20 2 0.0
end
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl
H
H
H
H
H
end
12
4
3 5
67
8
9
chloropropylene
(3-chloro-propene)
For the 4th atom and following we have to specify:Distance and 2 angles,
i.e. bond angleandtorsion
For the 4th atom and following we have to specify:Distance and 2 angles,
i.e. bond angleandtorsion
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
In general: for atom n , defined with respect to atoms i j k,
we specify distance rni, , angle ααααnij and ββββnijk
Torsion ββββnijk is defined as rotation of the n-i bond around thei-j bond, with respect to the j-k bond.
ni
j
k
i, j
k
n
ββββnijk = 90o
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
ni
j
k
i, j
k
nββββnijk = 120o
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
In general: for atom n , defined with respect to atoms i j k,
we specify distance rni, , angle ααααnij and ββββnijk
Torsion ββββnijk is defined as rotation of the n-i bond around thei-j bond, with respect to the j-k bond.
ni
j
k
i, j
k
n
ββββnijk = 180o
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
In general: for atom n , defined with respect to atoms i j k,
we specify distance rni, , angle ααααnij and ββββnijk
Torsion ββββnijk is defined as rotation of the n-i bond around thei-j bond, with respect to the j-k bond.
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H
H
H
H
H
end
12
4
3 5
67
8
9
chloropropylene
(3-chloropropene)
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H 1 1.09 2 120.0 3
H
H
H
H
end
12
4
3 5
67
8
9
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
chloropropylene
(3-chloropropene)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H 1 1.09 2 120.0 3 0.0
H
H
H
H
end
12
4
3 5
67
8
9
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
chloropropylene
(3-chloropropene)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H 1 1.09 2 120.0 3 0.0
H 1 1.09 2 120.0 3
H
H
H
end
12
4
3 5
67
8
9
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
chloropropylene
(3-chloropropene)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H 1 1.09 2 120.0 3 0.0
H 1 1.09 2 120.0 3 180.0
H
H
H
end
12
4
3 5
67
8
9
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
chloropropylene
(3-chloropropene)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H 1 1.09 2 120.0 3 0.0
H 1 1.09 2 120.0 3 180.0
H 2 1.09 1 120.0 6
H
H
end
12
4
3 5
67
8
9
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
chloropropylene
(3-chloropropene)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H 1 1.09 2 120.0 3 0.0
H 1 1.09 2 120.0 3 180.0
H 2 1.09 1 120.0 6 0.0
H
H
end
12
4
3 5
67
8
9
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
chloropropylene
(3-chloropropene)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H 1 1.09 2 120.0 3 0.0
H 1 1.09 2 120.0 3 180.0
H 2 1.09 1 120.0 6 0.0
H 3 1.09 2 109.5 1
H 3 1.09 2 109.5 1
end
12
4
3 5
67
8
9
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
chloropropylene
(3-chloropropene)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H 1 1.09 2 120.0 3 0.0
H 1 1.09 2 120.0 3 180.0
H 2 1.09 1 120.0 6 0.0
H 3 1.09 2 109.5 1
H 3 1.09 2 109.5 1
end
12
4
3 5
67
8
9
3,21
4
8
9
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
chloropropylene
(3-chloropropene)
zmatrix angstrom
C
C 1 1.38
C 2 1.50 1 120.0
Cl 3 1.83 2 109.5 1 0.0
H 1 1.09 2 120.0 3 0.0
H 1 1.09 2 120.0 3 180.0
H 2 1.09 1 120.0 6 0.0
H 3 1.09 2 109.5 1 120.0
H 3 1.09 2 109.5 1 -120.0
end
12
4
3 5
67
8
9
3,21
4
8
9
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
chloropropylene
(3-chloropropene)
j.k1
i
2
3
Atoms 1, 2, 3 linked toatom k - with sp3 hybridization
Angles: 1-k-j-i 0o
2-k-j-i 120o
3-k-j-i 240o (–120o)
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
j.k1
i
2
3
Atomy 1, 2, 3 połączone zatomem k - o hybrydyzacji sp3
Angles: 1-k-j-i αααα2-k-j-i α + α + α + α + 1203-k-j-i α α α α – 120
α
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Atoms 1, 2, 3 linked toatom k - with sp3 hybridization
j.k 1i2
Angles: 1-k-j-i 0o
2-k-j-i 180o
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Atoms 1, 2, 3 linked toatom k - with sp2 hybridization
j.k 1i2
j.k1
i
2
3
αααα
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Angles: 1-k-j-i αααα2-k-j-i α + α + α + α + 1203-k-j-i α α α α – 120
Atoms 1, 2, 3 linked toatom k - with sp3 hybridization
Angles: 1-k-j-i 0o
2-k-j-i 180o
Atoms 1, 2, 3 linked toatom k - with sp2 hybridization
Methyl acrylate, CH2=CH-COOCH3
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
123
4
5
67
89
10
1112
zmatrix angstromCC 1 1.33C 2 1.45 1 120.0OOCHHHHHH
123456789
101112
123
4
5
67
89
10
1112
zmatrix angstromCC 1 1.33C 2 1.45 1 120.0O 3 1.25 2 120.0 1 0.0OCHHHHHH
123456789
101112
123
4
5
67
89
10
1112
zmatrix angstromCC 1 1.33C 2 1.45 1 120.0O 3 1.25 2 120.0 1 0.0O 3 1.35 2 120.0 1 180.0CHHHHHH
123456789
101112
123
4
5
67
89
10
1112
zmatrix angstromCC 1 1.33C 2 1.45 1 120.0O 3 1.25 2 120.0 1 0.0O 3 1.35 2 120.0 1 180.0C 5 1.35 3 109.5 2 180.0HHHHHH
123456789
101112
123
4
5
67
89
10
1112
zmatrix angstromCC 1 1.33C 2 1.45 1 120.0O 3 1.25 2 120.0 1 0.0O 3 1.35 2 120.0 1 180.0C 5 1.35 3 109.5 2 180.0H 1 1.10 2 120.0 3 0.0HHHHH
123456789
101112
123
4
5
67
89
10
1112
zmatrix angstromCC 1 1.33C 2 1.45 1 120.0O 3 1.25 2 120.0 1 0.0O 3 1.35 2 120.0 1 180.0C 5 1.35 3 109.5 2 180.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0HHHH
123456789
101112
123
4
5
67
89
10
1112
zmatrix angstromCC 1 1.33C 2 1.45 1 120.0O 3 1.25 2 120.0 1 0.0O 3 1.35 2 120.0 1 180.0C 5 1.35 3 109.5 2 180.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0H 2 1.10 1 120.0 7 180.0HHH
123456789
101112
123
4
5
67
89
10
1112
zmatrix angstromCC 1 1.33C 2 1.45 1 120.0O 3 1.25 2 120.0 1 0.0O 3 1.35 2 120.0 1 180.0C 5 1.35 3 109.5 2 180.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0H 2 1.10 1 120.0 7 180.0H 6 1.10 5 109.5 3 0.0HH
123456789
101112
123
4
5
67
89
10
1112
zmatrix angstromCC 1 1.33C 2 1.45 1 120.0O 3 1.25 2 120.0 1 0.0O 3 1.35 2 120.0 1 180.0C 5 1.35 3 109.5 2 180.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0H 2 1.10 1 120.0 7 180.0H 6 1.10 5 109.5 3 0.0H 6 1.10 5 109.5 3 120.0 H 6 1.10 5 109.5 3 -120.0
123456789
101112
Linear molecules(or with linear arrangement of a few atoms)
acetylene
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
acetylene
HC 1 1.10C 2 1.25 1 180.0
H 3 1.10 2 180.0 1 ?????1
2
3
4
Torsion ill-defined!!!!
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Linear molecules(or with linear arrangement of a few atoms)
„dangerous” value of the bond angle: 180o
– torsion ill-defined
ni
j
k
i, j
k
nββββnijk = 120o
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
ni
j
k
i, j
k
nββββnijk = 120o
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
„dangerous” value of the bond angle: 180o
– torsion ill-defined
ni
j
k
i, j
k
nββββnijk = 120o
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
„dangerous” value of the bond angle: 180o
– torsion ill-defined
i, j
k
nββββnijk = 120o
ni
j
k
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
„dangerous” value of the bond angle: 180o
– torsion ill-defined
ni
j
k
i, j
k
nββββnijk = ???????
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
„dangerous” value of the bond angle: 180o
– torsion ill-defined
i, j
k
nββββnijk = -60o !!!!n
ij
k
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
„dangerous” value of the bond angle: 180o
– torsion ill-defined
ni
j
k
i, j
k
nββββnijk = 120o
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
„dangerous” value of the bond angle: 180o
– torsion ill-defined
acetylene
5
1
2
6
3
4
CC 1 1.10XX 2 1.00 1 90.0XX 1 1.00 2 90.0 3 0.0
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
„dangerous” value of the bond angle: 180o
– torsion ill-defined‘ghost atoms’ can be introduced, i.e. auxiliary reference points
acetylen
5
1
2
6
3
4
CC 1 1.10XX 2 1.00 1 90.0XX 1 1.00 2 90.0 3 0.0H 1 1.10 4 90.0 3 180.0H 2 1.10 3 90.0 4 180.0
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
„dangerous” value of the bond angle: 180o
– torsion ill-defined‘ghost atoms’ can be introduced, i.e. auxiliary reference points
Acrylonitril CH2=CH-CN
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Acrylonitril CH2=CH-CN
123
4
5
6
7
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Ethylene
12
3
45
6zmatrix angstromCC 1 1.33H 2 1.10 1 120.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0H 2 1.10 1 109.5 4 0.0
123456
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Acrylonitril CH2=CH-CN
123
4
5
6
7zmatrix angstromCC 1 1.33C 2 1.40 1 120.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0H 2 1.10 1 109.5 4 0.0
123456
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
123
4
5
6
7zmatrix angstromCC 1 1.33C 2 1.40 1 120.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0H 2 1.10 1 109.5 4 0.0N 3 1.15 2 180.0 1 ?????
1234567
ill-defined
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Acrylonitril CH2=CH-CN
123
4
5
6
8zmatrix angstromCC 1 1.33C 2 1.40 1 120.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0H 2 1.10 1 109.5 4 0.0XX 3 1.00 2 90.0 1 180.0N 3 1.15 7 90.0 2 180.0
12345678
7
XX
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Acrylonitril CH2=CH-CN
123
4
5
6
7zmatrix angstromCC 1 1.33C 2 1.40 1 120.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0H 2 1.10 1 109.5 4 0.0N ??????????????????????????
1234567
Another trick(No GHOSTS)
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Acrylonitril CH2=CH-CN
123
4
5
6
7zmatrix angstromCC 1 1.33C 2 1.40 1 120.0H 1 1.10 2 120.0 3 0.0H 1 1.10 2 120.0 3 180.0H 2 1.10 1 109.5 4 0.0N 2 2.55 1 109.5 4 180.0
1234567
Change of reference atoms
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Acrylonitril CH2=CH-CNAnother trick(No GHOSTS)
Ring systems
1
2
3
4
5
6
Z-matrix comprises distances2-1, 3-2, 4-3, 5-4, 6-5,while the distance 1-6 is not included
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
1
2
3
4
5
6
Increase in bond-angles may result in ring opening (increase in the distance1-6)
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Ring systems
Z-matrix comprises distances2-1, 3-2, 4-3, 5-4, 6-5,while the distance 1-6 is not included
Ring systems
12
3
4
5
6
Ghost atom in the centre of the ring and defining all the real atoms with respect to its position2-13-1-24-1-3-25-1-4-36-1-5-47-1-6-5
7
identicaldistances and angles
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Exercise 0.• Ethane, C2H6 , eclipsed and staggered
conformation• Butane, 1-butene, butadiene• Aniline, C6H5NH2
Molecular geometry -internal coordinates (Z-matrix)
Molecular geometry -internal coordinates (Z-matrix)
Input data – the moleculeInput data – the molecule
• Positions of nuclei• Positions of nuclei
• Electronic state (multiplicity, numbers of αααα and ββββ electrons)• Electronic state (multiplicity, numbers of αααα and ββββ electrons)
Singlet: nαααα-nββββ = 0 = 0 = 0 = 0 (default)
Doublet: nαααα-nββββ = 1= 1= 1= 1
Triplet: nαααα-nββββ = 2, = 2, = 2, = 2, etc.
Singlet: nαααα-nββββ = 0 = 0 = 0 = 0 (default)
Doublet: nαααα-nββββ = 1= 1= 1= 1
Triplet: nαααα-nββββ = 2, = 2, = 2, = 2, etc.
• Number and types of nuclei forming the molecule;• Number and types of nuclei forming the molecule;
• Number of electrons (charge of molecule)• Number of electrons (charge of molecule)
Basis set choiceBasis set choice
Computational ab initio methodsComputational ab initio methods
Hartree-Fock-Roothana method
Linear combination approach (LCAO)
One-electron orbitals expressed as a linear combination of
the basis functions
)(...)()(
)1(...)1()1(
!
1
21
21
NNN
N
N
N
ϕϕϕ
ϕϕϕ
MMMM
MMMM=Ψ
∑=
=m
j
jiji c1
)1()1( χϕ
Basis functions
Computational ab initio methodsComputational ab initio methods
DFT approach: KS method
Linear combination approach (LCAO)
One-electron orbitals expressed as a linear combination of
the basis functions;
Electron density as sum of squares of orbitals
∑=
=m
j
jiji rcr1
)()( χϕ
2
1
)()( ∑=
=m
i
i rr ϕρBasis functions
Basis setsBasis sets
LCAO approach:Linear Combination of Atomic Orbitals
The basis set used in the calculations includesfunctions representing atomic orbitals for each atom
Minimal basis (single-zeta)one radial function for each occupied shell
eg. for O atom:1 radial function for 1s orbital1 radial function for 2s orbital1 radial function for 2p orbital
means – three 2p functions: 2px,2py,2pz
Basis setsBasis sets
Minimal basis (single-zeta, SZ)one radial function for each occupied shell
eg. for O atom:1 radial function for 1s orbital1 radial function for 2s orbital1 radial function for 2p orbital
Total number: 5 basis functionsφφφφ1s , φφφφ2s, φφφφ2px, φφφφ2py, φφφφ2pz
Basis setsBasis sets
Double-zeta basis sets (DZ)two radial functions for each occupied shell
eg. for O atom:2 radial functions for 1s orbital2 radial functions for 2s orbital2 radial functions for 2p orbital
Total number: 10 basis functionsφφφφ1s , φφφφ2s, φφφφ2px, φφφφ2py, φφφφ2pz, φφφφ’1s , φφφφ’2s, φφφφ’2px, φφφφ’2py, φφφφ’2pz
Basis setsBasis sets
Double-zeta valence basis sets (DZV)two radial functions for each occupied valence shell
eg. for O atom:1 radial function for 1s orbital (core orbital)2 radial functions for 2s orbital (valence shell)2 radial functions for 2p orbital (valence shell)
Total number: 9 basis functionsφφφφ1s , φφφφ2s, φφφφ2px, φφφφ2py, φφφφ2pz, , φφφφ’2s, φφφφ’2px, φφφφ’2py, φφφφ’2pz
Basis setsBasis sets
Triple-zeta basis sets (TZ)three radial functions for each occupied shell
eg. for O atom:3 radial functions for 1s orbital3 radial functions for 2s orbital3 radial functions for 2p orbital
Total number: 15 basis functionsφφφφ1s , φφφφ2s, φφφφ2px, φφφφ2py, φφφφ2pz, φφφφ’1s , φφφφ’2s, φφφφ’2px, φφφφ’2py, φφφφ’2pzφφφφ”1s , φφφφ”2s, φφφφ”2px, φφφφ”2py, φφφφ”2pz
Basis setsBasis sets
Triple-zeta valence basis sets (TZV)three radial functions for each occupied valence shell
eg. for O atom:1 radial function for 1s orbital (core orbital)3 radial functions for 2s orbital (valence shell)3 radial functions for 2p orbital (valence shell)
Total number: 13 basis functionsφφφφ1s , φφφφ2s, φφφφ2px, φφφφ2py, φφφφ2pz, , φφφφ’2s, φφφφ’2px, φφφφ’2py, φφφφ’2pz, φφφφ”2s, φφφφ”2px, φφφφ”2py, φφφφ”2pz
Basis setsBasis sets
Polarization functionsAdditional basis functions corresponding to the higher
l-number (unoccupied for given atom)
eg. for O atom:Occupied orbitals: s-type, p-typePolarization functions : d-type
Basis setsBasis sets
Polarization functionsadded to DZ,DZV,TZ, TZV, QZ, QZV,… sets
Gives
DZP, DZVP, TZP, TZVP, QZP, QZVP, etc.
Basis setsBasis sets
Double-zeta polarized basis sets (DZP)two radial functions for each occupied shell
+ polarization functions
eg. for O atom:2 radial functions for 1s orbital2 radial functions for 2s orbital2 radial functions for 2p orbital1 radial d function
Total number: 15 basis functions (or 16)φφφφ1s , φφφφ2s, φφφφ2px, φφφφ2py, φφφφ2pz, φφφφ’1s , φφφφ’2s, φφφφ’2px, φφφφ’2py, φφφφ’2pzφφφφdxy , φφφφdxz, φφφφdyz, φφφφx2-y2, φφφφz2
or φφφφdxy , φφφφdxz, φφφφdyz, φφφφx2, φφφφdy2, φφφφz2
Basis setsBasis sets
Diffuse functions – additional functions with small exponent
used eg. for anions
Basis setsBasis sets
Hydrogen atom orbitals –Slater-type functions
Problems with 3- and 4-center integrals
)exp( rα−
Basis setsBasis sets
)exp( 2rα−
Gaussian functions
Analytical expressions for all sorts of integrals
Basis setsBasis sets
Hydrogen atom orbitals –Slater-type functions
Problems with 3- and 4-center integrals
)exp( rα−
R
STOGTO
Basis setsBasis sets
R
STO1 GTO
Slater-type function may be approximated
by a combination of gaussian-type functions
2 GTO
Basis setsBasis sets
R
STO1 GTO
2 GTO
3 GTO5 GTO
Funkcje
STO-2G
STO-3G
STO-4G
STO-5G
itd.
STO-nG functions are minimal basis sets (SZ)
Basis setsBasis sets
Slater-type function may be approximated
by a combination of gaussian-type functions
functions
3-21G
6-31G
6-311G
etc.
split-valence basis set
corresponding to. DZV, TZV, etc.
With polarization functions
6-311G*
6-311G**
With diffuse functions:
6-311G+
6-311G++
Basis setsBasis sets
• Basic ideas and methods of quantum chemistry:Wave-function; Electron density; Schrodinger equation; Density Functional theory; Born-Oppenheimer approximation; Variational principles in wave-function mechanics and DFT; One-electron approximation; HF method; Electron correlation; KS method; Wave-function-based electron correlation methods;
• Input data for QM calculations, GAMESS program:Molecular geometry, Z-Matrix, Basis sets in ab initio
calculations; input, output;
• Geometry of molecular systems: Geometry optimization; Constrained optimization; Conformational analysis; Global minimum problem
• Electronic structure of molecular systems: Molecular orbitals (KS orbitals); Chemical bond; Deformation density; Localized orbitals; Population analysis; Bond-orders
•Molecular vibrations, Thermodynamics; Chemical Reactivity:Vibrational analysis; Thermodynamic properties; Modeling chemical reactions; Trantition state optimization and validation; Intrinsic Reaction Coordinate; Chemical reactivity indices; Molecular Electrostatic Potential; Fukui Functions; Single- and Two-Reactant Reactivity Indices
• Other Topics:Modelling of complex chemical processes – examples from catalysis; Molecular spectroscopy from ab initio
calculations; Advanced methods for electron correlation;Molecular dynamics; Modelling of large systems –hybrid approaches (QM/MM); Solvation models