Configuration interaction second-order

One important conclusion from the full Cl benchmark studies of Bauschlicher, Taylor, Langhoif, and others in the 1980 s is that the MR-CISD method based on CASSCF orbitals provides potential energy surfaces which accurately parallel the full Cl surfaces.14,15 234,238-240 242 254 For example, the CASSCF MR-CISD method predicts singlet-triplet energy separations in CH2 and SiH2 within 0.01 kcal mol-1 and 0.03 kcal mol-1, respectively, of the full Cl results.236,238 The best results are obtained when no threshold is used for reference selection that is, when all CSFs in the CASSCF wavefunction are used as references. This CAS-ref MR-CISD procedure is intimately related107 to second-order configuration interaction (SOCI), which distributes electrons in... 

In addition to MP2, MP3, and MP4 calculations, CCSD(T), CASSCF, FOCI (First-Order Configuration Interaction), and sometimes SOCI (Second-Order Configuration Interaction) approaches have been used to ensure the convergence of the results. The complete definitions of the variational spaces used are given in [61,62,63]. Electronically-excited states have been obtained by means of the MC/P method, recently developed in our group [64,65] it couples a variational treatment to deal with the nondynamic correlation effects and a perturbation treatment to account for the dynamic correlation effects as well as the non-dynamic effects not treated at the variational level becanse of their limited contributions to the phenomena investigated. All electronic transitions reported here are vertical transition energies. 

Complete active space (CAS) SCF plus second-order configuration interaction (SOCI) calculations [12] and MP4 calculations [13, 14] were performed. The following table lists values for the internuclear distance r, dissociation energy D, ionization energy Ej, and spectroscopic constants for NeN ( i ) Ne( S) + N ( P)) ... 

Figure 1.6. Schematic representation of first-order configuration interaction for alternant hydrocarbons. Within the PPP approximation, conHgurations corresponding to electronic excitation from MO 4>i into and from MO., into are degenerate. The two highest occupied MOs (i =, k = 2) and the two lowest unoccupied MOs (f = r and k = 2 ) are shown. Depending on the magnitude of the interaction, the HOMO- LUMO transition

In principle, one can extract from G(ti)) the complete series of the primary (one-hole, Ih) and excited (shake-up) states of the cation. In practice, one usually restricts the portion of shake-up space to be spanned to the 2h-lp (two-hole, one-particle) states defined by a single-electron transition, neglecting therefore excitations of higher rank (3h-2p, 4h-3p. ..) in the ionized system. In the so-called ADC[3] scheme (22), elertronic correlation effects in the reference ground state are included through third-order. In this scheme, multistate 2h-lp/2h-lp configuration interactions are also accounted for to first-order, whereas the couplings of the Ih and 2h-lp excitation manifolds are of second-order in electronic correlation. 

Curtiss, L. A. Raghavachari, K. Pople, J. A. Gaussian-2 theory use of higher level correlation methods, quadratic configuration interaction geometries, and second-order Mpller Plesset zero-point energies. J. Chem. Phys. 1995, 103, 4192-4120. 

Head-Gordon M, Oumi M, Maurice D (1999) Quasidegenerate second-order perturbation corrections to single-excitation configuration interaction. Mol Phys 96 593... 

Consider the case where the interaction between the molecules A and B is not yet very strong. The magnitude of Hq>P is almost linear with So,p, so that the second-order term in Eq. (3.9) is proportional to the square of So,p. The order of magnitude of So,p is equal to the rth power of an overlap integral s of an MO a of the molecule A and an MO b of the molecule B, where y is the minimum number of electron transfers between A and B required to shift the electron configuration from 0 to p. Therefore, the terms from monotransferred configurations in Eq. (3.9) have magnitudes of the order of Sab, while the monoex. and the ditr. terms are of Sob, and the monoex.-monotr. term s , the diex. term s , and so on. If the interaction is weak and s0 is small, the mono-transferred terms are important in comparison with the others. 

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