计算化学概述及qchem程序简介 于建国
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• Assumes that the exact, N-body wave function of the system can be approximated by a single Slater determinant. • MO’s were assumed to be a linear combination of a finite number of basis functions. (LCAO)
Ab Initio
Calculating Methods to Account for Electron Correlation
• Møller-Plesset perturbation theory (MP2, MP3, MP4, etc.) • Configuration Interaction (CI. CIS, CID, etc.) • Multi-configurational self-consistent field (MCSCF, CASSCF) • Coupled Cluster (CC. CCSD, CCSDT, etc)
• MP0 = E(MP0) =
∑ε
i =1
N
i
• MP1 = MP0 + E(MP1) = E(HF)
• E ( MP 2)
= ∑∑
i < j a <b
occ vir
[< φiφ j | φaφb > − < φiφ j | φbφa >]2
εi + ε j − εa − εb
Ab Initio
Ψ ( r1 , r2 ,..., rn ) = ψ 1 (r1 )ψ 2 (r2 )... ψ n (rn )
From Quantum Mechanism to Computational Chemistry ‘Orbital’ Approximation (single-electronic Approximation): • The Pauli principle needs that the total electronic wave function must be antisymmetric. • The wave function in Slater determination is antisymmetric. ψ (r )ψ (r )...ψ (r )
i i j
n
n
n
=
（ ε ∑
i
i
+ H ii )
2.0∑ P µν ( H µν + Fµν )
µ ,ν
Solve HFR equation iteratively
Ab Initio
Closed Shell and Open Shell
• Closed
Shell: RHF • Open Shell: UHF, ROHF
From Quantum Mechanism to Computational Chemistry Time-independent Schrödinger Equation HΨ = EΨ Relativistic Approximation
Born-Oppenheimer Approximation
– The Møller-Plesset Perturbation Theory (MP) – Configuration Interaction (CI) – Coupled Claser (CC)
Take into consideration electron correlation
Ab Initio
Computational Chemistry
Theory, Methods and Software
于建国
College of Chemistry, Beijing Normal University
8/15-16/2011, Guangzhou, CHINA
Outline
• Theories computational chemistry based on • Methods and algorithms of CC • The problems CC can solve • Software in CC world today
Pµν =
OCC i =1
∑ 2Cµ Cν
i
i
S µν = < φµ | φν >
Ab Initio
Hartree-Fock-Rootheen Equation
ε = 2∑ H ii + ∑ ∑ (2 J ij − K ij )
i i j n n n
= 2∑ ε i − ∑ ∑ (2 J ij − K ij )
• Coulomb correlation: Because single determinant wavefunction • Fermi correlation: Preventing two parallel-spin electrons from being found at the same point in space • Dynamic correlation: is the correlation of the movement of electrons (CI) • Static correlation: is important for molecules where the ground state is well described only with more than one (nearly-)degenerate determinant (MCSCF)
Computational Chemistry and Software
Computational chemistry: A branch of chemistry that uses principles of computer science to assist in solving chemical problems. • Use the results of theoretical chemistry • Incorporate into efficient computer programs • Calculate the structures and properties of molecules and solids. --- Wikipedia （维基百科）
µ
Ab Initio
Hartree-Fock-Rootheen Equation
FC = SCE
1 Fµν = H µν + ∑ Pλσ ( µν | λσ ) − ( µλ | νσ ) 2 λσ
ˆ |φ 〉 〈φµ | h H µν = ν ZC 1 2 = 〈φµ | − ∇ | φν 〉 + 〈φµ | −∑ | φν 〉 2 C rC
Ab Initio
Configuration Interaction
• The reference state of CI, Φ0, can be got by HF calculations 2 2 0 0 0 Φ0 = | ψ 1ψ 2 ...ψ n | ψ 12ψ 2 ... ψn ψ n +1ψ n ... ψ +2 n+m • Excited electrons from the occupied orbitals to the empty orbitals to form the excited configurations (CIS, CID, CISD, … full CI) • Solve (iteratively) the CI equation to get interaction coefficients CI • MRCI, Multi-reference CI
ψ i (r ) = ∑ Cµiφµ (r )
• The effect of other electrons are accounted for in a mean-field theory context • Based on theΒιβλιοθήκη Baiduvariational theorem, get HartreeFock-Rootheen equation.
1 1 2 1 N 1
Ψ SD
1 ψ 1 (r2 )ψ 2 (r2 )...ψ N (r2 ) = N ! ................................ ψ 1 (rN )ψ 2 (rN )...ψ N (rN )
Ab Initio
Hartree-FockTheory Or self-consistent field method (SCF)
Electronic Correlation
• The interaction between electrons in the electronic structure of a quantum system. • Correlation Energy
Ab Initio
Electronic Correlation
– Hartree-Fock (HF)
• The simplest ab initio calculation • The major disadvantage of HF calculations is that electron correlation is not taken into consideration.
Ab Initio
Møller-Plesset Perturbation Theory
• Adding electron correlation effects by means of Rayleigh– Schrödinger perturbation theory (RS-PT). • Usually to second (MP2), third (MP3) or fourth (MP4) order. • The unperturbed Hamilton operator is taken as a sum over Fock operators. Then
Configuration Interaction
• Configuration, for example, (1s)2(2s)2(2p)1... • Generally, using the linear combination of Slater determinants descripts configuration wave function. (For the closed shell grounded state, one SD is enough.) • Interaction means the mixing (interaction) of different electronic configurations (states). • CI wave function:
α β
RHF singlet
UHF doublet
Based on Hartree-Fock-Roothaan Equation
SE
Post SCF
FC=SCE
VB MM
DFT
Ab Initio
Ab Initio
• Ab initio translated from Latin means “from first principles.” This refers to the fact that no experimental data is used and computations are based on quantum mechanics. • Different Levels of Ab Initio Calculations
HeΨi = EeΨi
Zα Z β Zα 1 1 2 H e =− ∑ ∇i + ∑ ∑ + ∑∑ − ∑∑ 2 i α β >α Rαβ α i i> j r i r ij iα
From Quantum Mechanism to Computational Chemistry ‘Orbital’ Approximation (single-electronic Approximation): • Consider each electron to move in some sort of "average potential" which incorporates the interactions with all the nuclei and an "averaged interaction" with the other electrons. • The wavefunction is taken to be a product of one electron wavefunctions (Molecular Orbital, MO):
Ab Initio
Calculating Methods to Account for Electron Correlation
• Møller-Plesset perturbation theory (MP2, MP3, MP4, etc.) • Configuration Interaction (CI. CIS, CID, etc.) • Multi-configurational self-consistent field (MCSCF, CASSCF) • Coupled Cluster (CC. CCSD, CCSDT, etc)
• MP0 = E(MP0) =
∑ε
i =1
N
i
• MP1 = MP0 + E(MP1) = E(HF)
• E ( MP 2)
= ∑∑
i < j a <b
occ vir
[< φiφ j | φaφb > − < φiφ j | φbφa >]2
εi + ε j − εa − εb
Ab Initio
Ψ ( r1 , r2 ,..., rn ) = ψ 1 (r1 )ψ 2 (r2 )... ψ n (rn )
From Quantum Mechanism to Computational Chemistry ‘Orbital’ Approximation (single-electronic Approximation): • The Pauli principle needs that the total electronic wave function must be antisymmetric. • The wave function in Slater determination is antisymmetric. ψ (r )ψ (r )...ψ (r )
i i j
n
n
n
=
（ ε ∑
i
i
+ H ii )
2.0∑ P µν ( H µν + Fµν )
µ ,ν
Solve HFR equation iteratively
Ab Initio
Closed Shell and Open Shell
• Closed
Shell: RHF • Open Shell: UHF, ROHF
From Quantum Mechanism to Computational Chemistry Time-independent Schrödinger Equation HΨ = EΨ Relativistic Approximation
Born-Oppenheimer Approximation
– The Møller-Plesset Perturbation Theory (MP) – Configuration Interaction (CI) – Coupled Claser (CC)
Take into consideration electron correlation
Ab Initio
Computational Chemistry
Theory, Methods and Software
于建国
College of Chemistry, Beijing Normal University
8/15-16/2011, Guangzhou, CHINA
Outline
• Theories computational chemistry based on • Methods and algorithms of CC • The problems CC can solve • Software in CC world today
Pµν =
OCC i =1
∑ 2Cµ Cν
i
i
S µν = < φµ | φν >
Ab Initio
Hartree-Fock-Rootheen Equation
ε = 2∑ H ii + ∑ ∑ (2 J ij − K ij )
i i j n n n
= 2∑ ε i − ∑ ∑ (2 J ij − K ij )
• Coulomb correlation: Because single determinant wavefunction • Fermi correlation: Preventing two parallel-spin electrons from being found at the same point in space • Dynamic correlation: is the correlation of the movement of electrons (CI) • Static correlation: is important for molecules where the ground state is well described only with more than one (nearly-)degenerate determinant (MCSCF)
Computational Chemistry and Software
Computational chemistry: A branch of chemistry that uses principles of computer science to assist in solving chemical problems. • Use the results of theoretical chemistry • Incorporate into efficient computer programs • Calculate the structures and properties of molecules and solids. --- Wikipedia （维基百科）
µ
Ab Initio
Hartree-Fock-Rootheen Equation
FC = SCE
1 Fµν = H µν + ∑ Pλσ ( µν | λσ ) − ( µλ | νσ ) 2 λσ
ˆ |φ 〉 〈φµ | h H µν = ν ZC 1 2 = 〈φµ | − ∇ | φν 〉 + 〈φµ | −∑ | φν 〉 2 C rC
Ab Initio
Configuration Interaction
• The reference state of CI, Φ0, can be got by HF calculations 2 2 0 0 0 Φ0 = | ψ 1ψ 2 ...ψ n | ψ 12ψ 2 ... ψn ψ n +1ψ n ... ψ +2 n+m • Excited electrons from the occupied orbitals to the empty orbitals to form the excited configurations (CIS, CID, CISD, … full CI) • Solve (iteratively) the CI equation to get interaction coefficients CI • MRCI, Multi-reference CI
ψ i (r ) = ∑ Cµiφµ (r )
• The effect of other electrons are accounted for in a mean-field theory context • Based on theΒιβλιοθήκη Baiduvariational theorem, get HartreeFock-Rootheen equation.
1 1 2 1 N 1
Ψ SD
1 ψ 1 (r2 )ψ 2 (r2 )...ψ N (r2 ) = N ! ................................ ψ 1 (rN )ψ 2 (rN )...ψ N (rN )
Ab Initio
Hartree-FockTheory Or self-consistent field method (SCF)
Electronic Correlation
• The interaction between electrons in the electronic structure of a quantum system. • Correlation Energy
Ab Initio
Electronic Correlation
– Hartree-Fock (HF)
• The simplest ab initio calculation • The major disadvantage of HF calculations is that electron correlation is not taken into consideration.
Ab Initio
Møller-Plesset Perturbation Theory
• Adding electron correlation effects by means of Rayleigh– Schrödinger perturbation theory (RS-PT). • Usually to second (MP2), third (MP3) or fourth (MP4) order. • The unperturbed Hamilton operator is taken as a sum over Fock operators. Then
Configuration Interaction
• Configuration, for example, (1s)2(2s)2(2p)1... • Generally, using the linear combination of Slater determinants descripts configuration wave function. (For the closed shell grounded state, one SD is enough.) • Interaction means the mixing (interaction) of different electronic configurations (states). • CI wave function:
α β
RHF singlet
UHF doublet
Based on Hartree-Fock-Roothaan Equation
SE
Post SCF
FC=SCE
VB MM
DFT
Ab Initio
Ab Initio
• Ab initio translated from Latin means “from first principles.” This refers to the fact that no experimental data is used and computations are based on quantum mechanics. • Different Levels of Ab Initio Calculations
HeΨi = EeΨi
Zα Z β Zα 1 1 2 H e =− ∑ ∇i + ∑ ∑ + ∑∑ − ∑∑ 2 i α β >α Rαβ α i i> j r i r ij iα
From Quantum Mechanism to Computational Chemistry ‘Orbital’ Approximation (single-electronic Approximation): • Consider each electron to move in some sort of "average potential" which incorporates the interactions with all the nuclei and an "averaged interaction" with the other electrons. • The wavefunction is taken to be a product of one electron wavefunctions (Molecular Orbital, MO):