Quantum chemical molecular modelling Dr. hab. Artur Michalak Department of Theoretical Chemistry Faculty of Chemistry Jagiellonian 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
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Quantum chemical molecular modellingmichalak/mmod2008/L2.pdf · Input dataInput data atoms 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
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Quantum chemical molecular modelling
Dr. hab. Artur MichalakDepartment of Theoretical Chemistry
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
• 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)
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)
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)
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