Multiply Charged Ions

Quantum Chemical Computations Trento, May 2002 Lecture 3

Multi-Reference Methods

Unrestricted Hartree-Fock 

true

 H 2 , r     

A

    1 

B

2  

B

    1

A

2 

UHF

 H 2 , r     

A

    1

B

2

Multi-Configuration Self Consistent Field (MCSCF)  MCSCF 

i

 

n co n fig i



c i



i

 1  2  

n



i



n b a sis



c ij



j j

• Bond Dissociation • Multi-configuration nature • E.g. O 3 • TiF 3+ ( 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)

He 2 2+ – avoided crossing

Density Functional Theory Hohenberg & Kohm: E = E(  ) E = V NN + T(  ) + V Ne (  ) + V ee (  ) Kohn-Sham:  =  i 2

DFT – 2 E(  ) = V NN + T S (  ) + V Ne (  ) + J(  )+E XC (  ) E XC (  ) 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: N 4 • MP2: N 5 • DFT: N 3 • CCSD(T): N 7 • MCSCF, MR-CISD: e N • Efficient codes for HF, MP2, DFT, CCSD(T)

Programs Gaussian (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)