# Truncated configuration interaction cis cisd cisdt

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Truncated configuration interaction: CIS, CISD, CISDT, etc. We start with a reference wavefunction, for example the Hartree-Fock determinant. We then select determinants for the wavefunction expansion by substituting orbitals of the reference determinant by orbitals that are not occupied in the reference state (virtual orbitals). Singles (S) indicate that 1 orbital is replaced, doubles (D) indicate 2 replacements, triples (T) indicate 3 replacements, etc., leading to CIS, CISD, CISDT, etc. N N k j i 3 2 1 HF etc. etc. , 3 2 1 , 3 2 1 N N N k b a ab ij N k j a a i
its.unc.edu 39 Truncated Configuration Interaction Truncated Configuration Interaction Level of excitation Number of parameters Example CIS n (2N – n) 300 CISD + [n (2N – n)] 2 78,600 CISDT …+ [n (2N – n)] 3 18 10 6 Full CI n N 2 10 9 Number of linear variational parameters in truncated CI for n = 10 and 2N = 40.
its.unc.edu 40 Multi-Configuration Self-Consistent Field (MCSCF) Multi-Configuration Self-Consistent Field (MCSCF) The MCSCF wavefunctions consists of a few selected determinants or CSFs. In the MCSCF method, not only the linear weights of the determinants are variationally optimized, but also the orbital coefficients. One important selection is governed by the full CI space spanned by a number of prescribed active orbitals (complete active space, CAS). This is the CASSCF method. The CASSCF wavefunction contains all determinants that can be constructed from a given set of orbitals with the constraint that some specified pairs of - and -spin-orbitals must occur in all determinants (these are the inactive doubly occupied spatial orbitals). Multireference CI wavefunctions are obtained by applying the excitation operators to the individual CSFs or determinants of the MCSCF (or CASSCF) reference wave function. k C C c k k k k ) ˆ ˆ ( CISD - MR 2 1 k k k k k k d C k C c 2 1 ˆ ) ˆ ( MRCI - IC Internally-contracted MRCI:
its.unc.edu 41 Coupled-Cluster Theory Coupled-Cluster Theory System of equations is solved iteratively (the convergence is accelerated by utilizing Pulay’s method, direct inversion in the iterative subspace ”, DIIS). CCSDT model is very expensive in terms of computer resources. Approximations are introduced for the triples: CCSD(T), CCSD[T], CCSD-T. Brueckner coupled-cluster ( e.g ., BCCD) methods use Brueckner orbitals that are optimized such that singles don’t contribute. By omitting some of the CCSD terms, the quadratic CI method ( e.g ., QCISD) is obtained.
its.unc.edu 42 Møller-Plesset Perturbation Theory Møller-Plesset Perturbation Theory The Hartree-Fock function is an eigenfunction of the n -electron operator . We apply perturbation theory as usual after decomposing the Hamiltonian into two parts: More complicated with more than one reference determinant ( e.g ., MR-PT, CASPT2, CASPT3, …) F ˆ F H H F H H F H H H H ˆ ˆ ˆ ˆ ˆ ˆ ˆ 1 0 1 0 MP2, MP3, MP4, …etc. number denotes order to which energy is computed (2n+1 rule)
its.unc.edu 43

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