TY - JOUR

T1 - Spin-coupled theory for 'N electrons in M orbitals' active spaces

AU - Karadakov, Peter B

AU - Cooper, David L

AU - Salter-Duke, Brian J

AU - Li, Jiabo

PY - 2012

Y1 - 2012

N2 - Spin-coupled (SC) theory, an ab initio valence bond (VB) approach which uses a compact and an easy-to-interpret single-orbital product wave function comparable in quality to a N in N complete-active-space self-consistent field [CASSCF(N,N)] construction, is extended to N in M (N M) active spaces. The SC(N,M) wave function retains the essential features of the original SC model: It involves just the products of nonorthogonal orbitals covering all distributions of N electrons between M orbitals in which as few orbitals as possible, N - M , are doubly occupied (for N > M) or missing (for N <M) and all other orbitals are singly occupied; each of these products is combined with a flexible spin function which allows any mode of coupling of the spins of the orbitals within the product. The SC(N,M) wave function remains much more compact than a CASSCF(N,M) construction; for example, the SC(6,7) wave function includes 35 configuration state functions (CSFs) as opposed to the 490 CSFs in the CASSCF case. The essential features of the SC(N,M) method are illustrated through a SC(6,5) calculation on the cyclopentadienyl anion, C 5H5 -, and a SC(6,7) calculation on the tropylium cation, C 7H7 +. The SC(6,5) and SC(6,7) wave functions for C 5H5 - and C 7H7 + are shown to provide remarkably clear modern VB models for the electronic structures of these aromatic cyclic ions which closely resemble the well-known SC model of benzene and yet recover almost all of the correlation energy included in the corresponding CASSCF(6,5) and CASSCF(6,7) wave functions: over 97 in the case of C 5H5 - and over 95 in the case of C 7H7 +.

AB - Spin-coupled (SC) theory, an ab initio valence bond (VB) approach which uses a compact and an easy-to-interpret single-orbital product wave function comparable in quality to a N in N complete-active-space self-consistent field [CASSCF(N,N)] construction, is extended to N in M (N M) active spaces. The SC(N,M) wave function retains the essential features of the original SC model: It involves just the products of nonorthogonal orbitals covering all distributions of N electrons between M orbitals in which as few orbitals as possible, N - M , are doubly occupied (for N > M) or missing (for N <M) and all other orbitals are singly occupied; each of these products is combined with a flexible spin function which allows any mode of coupling of the spins of the orbitals within the product. The SC(N,M) wave function remains much more compact than a CASSCF(N,M) construction; for example, the SC(6,7) wave function includes 35 configuration state functions (CSFs) as opposed to the 490 CSFs in the CASSCF case. The essential features of the SC(N,M) method are illustrated through a SC(6,5) calculation on the cyclopentadienyl anion, C 5H5 -, and a SC(6,7) calculation on the tropylium cation, C 7H7 +. The SC(6,5) and SC(6,7) wave functions for C 5H5 - and C 7H7 + are shown to provide remarkably clear modern VB models for the electronic structures of these aromatic cyclic ions which closely resemble the well-known SC model of benzene and yet recover almost all of the correlation energy included in the corresponding CASSCF(6,5) and CASSCF(6,7) wave functions: over 97 in the case of C 5H5 - and over 95 in the case of C 7H7 +.

UR - http://pubs.acs.org/doi/pdfplus/10.1021/jp303998h

U2 - 10.1021/jp303998h

DO - 10.1021/jp303998h

M3 - Article

VL - 116

SP - 7238

EP - 7244

JO - The Journal of Physical Chemistry A

JF - The Journal of Physical Chemistry A

SN - 1089-5639

IS - 26

ER -