Quantum chemical molecular modellingmichalak/mmod2008/L2.pdf · Input dataInput data atoms zmatrix...

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

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.




MoleculeMolecule



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)


N atoms - 3N cartesian coords

3N-6 internal coorrds



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



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



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



ni

j

k

i, j

k

nββββnijk = 120o






ni

j

k

i, j

k

n

ββββnijk = 180o






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)



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



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



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



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



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



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



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



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



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



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)



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




j.k 1i2

Angles: 1-k-j-i 0o

2-k-j-i 180o




j.k 1i2

j.k1

i

2

3

αααα



Angles: 1-k-j-i αααα2-k-j-i α + α + α + α + 1203-k-j-i α α α α – 120


Angles: 1-k-j-i 0o

2-k-j-i 180o


Methyl acrylate, CH2=CH-COOCH3



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



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!!!!



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




ni

j

k

i, j

k






i, j

k


ni

j

k





ni

j

k

i, j

k

nββββnijk = ???????





i, j

k

nββββnijk = -60o !!!!n

ij

k





ni

j

k

i, j

k






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




– 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




– torsion ill-defined‘ghost atoms’ can be introduced, i.e. auxiliary reference points

Acrylonitril CH2=CH-CN




123

4

5

6

7



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




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



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




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




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)




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



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



1

2

3

4

5

6

Increase in bond-angles may result in ring opening (increase in the distance1-6)



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



Exercise 0.• Ethane, C2H6 , eclipsed and staggered

conformation• Butane, 1-butene, butadiene• Aniline, C6H5NH2



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)









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


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


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


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


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


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


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


Polarization functionsadded to DZ,DZV,TZ, TZV, QZ, QZV,… sets

Gives

DZP, DZVP, TZP, TZVP, QZP, QZVP, etc.


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


Diffuse functions – additional functions with small exponent

used eg. for anions


Hydrogen atom orbitals –Slater-type functions

Problems with 3- and 4-center integrals

)exp( rα−


)exp( 2rα−

Gaussian functions

Analytical expressions for all sorts of integrals


Hydrogen atom orbitals –Slater-type functions

Problems with 3- and 4-center integrals

)exp( rα−

R

STOGTO


R

STO1 GTO

Slater-type function may be approximated

by a combination of gaussian-type functions

2 GTO


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)


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++


• 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

Quantum chemical molecular modellingmichalak/mmod2008/L2.pdf · Input dataInput data atoms zmatrix...

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