Multiply Charged IonsQuantum Chemical ComputationsTrento, May 2002Lecture 3

Multi-Reference Methods

Unrestricted Hartree-Fock 21212 r,H rrrr ABBAtrue

212 r,H rr BAUHF

Multi-Configuration Self-Consistent Field (MCSCF)

basis

config

n

jjiji

ni

n

iii

c

c

21

MCSCF • Bond Dissociation• Multi-

configuration nature

• E.g. O3• TiF3+ (1+)

MR-CI(SD)

• Only MR-CISD practical• Size inconsistent

(“Davidson correction”)• MR-ACPF, MR-AQCC• CASPT2, MR-MBPT,

CASMP2

Excited States

• CIS, TD-DFT, CCSD-EOM• MC-SCF• (Spin, symmetry)

He22+ – avoided crossing

Density Functional Theory

Hohenberg & Kohm: E = E()

E = VNN + T() + VNe() + Vee()

Kohn-Sham: = i2

DFT – 2

E() = VNN + TS() + VNe() + J()+EXC()

EXC() not known

LDA, BP86, BLYP, GGA (PW91), B3LYP

Relativity

• Scalar Effects• Spin-orbit Coupling

Accuracy• HF: good geometries• MP2: good geometry, energy when

appropriate• DFT: good geom + energy• CCSD(T) / MR-CISD: excellent

energetics where applicable

Expense• HF: N4

• MP2: N5

• DFT: N3

• CCSD(T): N7

• MCSCF, MR-CISD: eN

• Efficient codes for HF, MP2, DFT, CCSD(T)

ProgramsGaussian (98) - John Pople

ACES II (R. J. Bartlett, Floride - CC methods)ADF (Amsterdam, DFT)

CADPAC (Cambridge, U.K.)Columbus (I. Shavitt, Columbus, Ohio)

Dalton (Norway)Gamess-USA (M. Gordon, M. Schmidt, Iowa)

Gamess-UK (Daresbury, UK)Jaguar (Schrödinger, inc - R. Friesner, Portland, Oregon)

MOLCAS (Lund, Suède, B. Roos)MOLPRO (P. Knowles / H.-J. Werner, UK/Allemagne)

NWChem (PNL, USA)Q-Chem (Gill, Head-Gordon, Schaeffer, …)

Spartan (W. Hehre, Wavefunction inc.)Turbomole (R. Ahlrichs)