Configuration interaction computational procedure

The doublet ( A") potential energy surface for H + O2 has been studied in detail by configuration interaction computational procedures [55,56], which show the formation of a bent intermediate, HO2, with almost no activation barrier however subsequent dissociation to O + OH has De > 60 kcal/mole. (The hydroperoxyl radical, HO2, is of considerable interest in several different areas [57].) We examined an alternative pathway, going through a linear quartet transition state that leads directly to O + OH. 

The oscillator strengths obtained for the different transitions studied in the present work with the RQDO methodology, and the use of the two forms of the transition operator, the standard one, and that corrected for core-valence polarization, are collected in Tables 1 to 8, where other data, from several theoretical and experimental sources, have been included for comparative purposes. The former comprise the large-scale configuration interaction performed with the use of the CIVS computer package [19] by Hibbert and Hansen [20] The configuration interaction (Cl) procedure of... 

The second step of the calculation involves the treatment of dynamic correlation effects, which can be approached by many-body perturbation theory (62) or configuration interaction (63). Multireference coupled-cluster techniques have been developed (64—66) but they are computationally far more demanding and still not established as standard methods. At this point, we will only focus on configuration interaction approaches. What is done in these approaches is to regard the entire zeroth-order wavefunc-tion Tj) or its constituent parts double excitations relative to these reference functions. This produces a set of excited CSFs ( Q) that are used as expansion space for the configuration interaction (Cl) procedure. The resulting wavefunction may be written as... 

To taike advantage of procedures used for configuration interaction calculations, eigenvalues of the symmetrized matrices, H -I- H, are computed. 

The electron correlation problem remains a central research area for quantum chemists, as its solution would provide the exact energies for arbitrary systems. Today there exist many procedures for calculating the electron correlation energy (/), none of which, unfortunately, is both robust and computationally inexpensive. Configuration interaction (Cl) methods provide a conceptually simple route to correlation energies and a full Cl calculation will provide exact energies but only at prohibitive computational cost as it scales factorially with the number of basis functions, N. Truncated Cl methods such as CISD (A cost) are more computationally feasible but can still only be used for small systems and are neither size consistent nor size extensive. Coupled cluster... 

A. Koslowski, M. E. Beck, and W. Thiel. Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach, J. Comput. Chem., 24 714-726 (2003). 

There are several problems in the physics of quantum systems whose importance is attested to by the time and effort that have been expended in search of their solutions. A class of such problems involves the treatment of interparticle correlations with the electron gas in an atom, a molecule (cluster) or a solid having attracted significant attention by quantum chemists and solid-state physicists. This has led to the development of a large number of theoretical frameworks with associated computational procedures for the study of this problem. Among others, one can mention the local-density approximation (LDA) to density functional theory (DFT) [1, 2, 3, 4, 5], the various forms of the Hartree-Fock (HF) approximation, 2, 6, 7], the so-called GW approximation, 9, 10], and methods based on the direct study of two-particle quantities[ll, 12, 13], such as two-particle reduced density matrices[14, 15, 16, 17, 18], and the closely related theory of geminals[17, 18, 19, 20], and configuration interactions (Cl s)[21]. These methods, and many of their generalizations and improvements[22, 23, 24] have been discussed in a number of review articles and textbooks[2, 3, 25, 26]. 

An accurate procedure for performing calculations that incorporate spin-orbit and other relativistic effects, and that represents intermediate coupling states for molecules containing heavy atoms, is based on A-S coupling in conjunction with the use of the ab initio REP-based spin-orbit operator and extended configuration interaction. The coupling scheme is more familiar than co-co coupling to chemists and physicists. In addition, the complexity of calculations necessary to achieve reliable results is computationally tractable. 

It is apparent from our description of the HFR procedure (and has been well established numerically) that the time required for a HFR calculation increases as somewhere between the third and fourth power of the size of the basis set. Similarly, the time required for going beyond HFR by configuration interaction increases as about the sixth power of the basis-set size for conventional Cl calculations. These important results explain why dramatic increases in computer speed lead only to modest increases in the size of systems treatable by such methods. For example, an increase of 1000 in computer speed increases the size of molecules tractable by Cl by slightly more than a factor of three, and those accessible to HFR procedures by a factor of about six. Thus, it appears that Cl techniques are directly applicable to only the simplest models of the species occurring in solid minerals. Even an approach to the Hartree-Fock limit wave... 

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