Multiconfiguration VB

Other multiconfiguration VB methods have also been devised, like the biorthogonal valence bond method of McDouall (35,36) or the spin-free approach of McWeeny (37). For an overview of these methods, the reader is advised to consult a recent review (1). 

C (62). This program can perform multiconfiguration VB calculations with fixed orbitals, plus a number of MO-based calculations like RHF, ROHF, UHF (followed by MP2), Orthogonal Cl, and MCSCF. 

The author and his students have used the term multiconfiguration valence bond (MCVB) to describe a linear variation calculation involving more than one VB structure (function). This practice will be continued in the present book. Other terms have been used that mean essentially the same thing[34]. We defer a fuller... 

This is, of course, the approach used by all of the early VB workers. In more recent times, after computing machinery allowed ab initio treatments, this is the sort of wave function proposed by Balint-Kurti and Karplus[34], which they called a multi structure approach. The present author and his students have proposed the multiconfiguration valence bond (MCVB) approach, which differs from the Balint-Kurti-Karplus wave function principally in the way the , are chosen. 

An analysis in terms of VB structures (see exercise 3) shows that this configurational mixing corresponds to approximately 40% diradical character in the wave function for ozone. The RHF wave function, on the other hand, contains only 12% of the diradical VB structure (the result was obtained using Hiickel values for the coefficients of the orbitals (2 11)). It is clear from these considerations that a correct treatment of the electronic structure for the ozone molecule must be based on a multiconfigurational wave function. 

Since a CASSCF calculation is faster than a direct SC calculation, owing to the advantages associated with orbital orthogonality in CASSCF, it is practical to extract an approximate SC wave function (or another type of VB function, e.g., a multiconfigurational one) from a CASSCF wave function. The conversion from one wave function to the other relies on the fact that a CASSCF wave function is invariant under linear transformations of the active orbitals. Based on this invariance principle, two different procedures were developed and both share the same name CASVB . Thus, CASVB is not a straightforward VB method, but rather a projection method that bridges between CASSCF and VB wave functions. 

In the CASVB method of Thorsteinsson et al. (22,23), one transforms the canonical CASSCF orbitals so that the wave function (which we recall, is kept unchanged in this process) involves a dominant component of a VB-type wave function, TVb, which is chosen in advance and may be single- or multiconfiguration, as in Equation 9.5 ... 

The Valence Bond Self-Consistent Field (VBSCF) method has been devised by Balint-Kurti and van Lenthe (32), and was further modified by Verbeek (6,33) who also developed an efficient implementation in a package called TURTLE (11). Basically, the VBSCF method is a multiconfiguration SCF procedure that allows the use of nonorthogonal orbitals of any type. The wave function is given as a linear combination of VB structures, (Eq. 9.7). 

The original Heitler-London treatment with its various extensions was a VB treatment that included several configurations, e.g., the total wave function is a sum of terms with spatial functions made up of different subsets of the orbitals. This is the essence of multiconfiguration methods. The most direct extension of this sort of approach is, of course, the inclusion of larger numbers of configurations and the application to larger molecules. The computational power allowed calculations of this sort. 

In its simplest form, the CASVB approach may be used simply to generate representations of a CASSCF wavefunction 4 CAS in which a single- or multiconfiguration modem-VB component 4,VB is dominant. Writing... 

The method is referred to simply as GMCSC when a fixed basis set is used. In this case, it can be viewed as a non-orthogonal variant of the Multiconfiguration Self-Consistent Field (MCSCF) approach. However, GMCSC s methodological roots are firmly planted in the Modem VB camp, and more specifically in the late Joe Gerratt s Spin-Coupled theory [3]-[4]. 

It is important to dispense with the received wisdom that MO theory is in some sense more fundamental than VB approaches. On the other hand, it is certainly not our intention to argue that the MO description is somehow wrong . In the particular case of benzene, we quantify to what extent the conventional MO and VB models can be considered reliable approximate representations of a particular type of multiconfigurational wavefunction that is more sophisticated than those obtained from either approach. We conclude that we should not have any serious qualms about switching between the MO and VB representations, according to the nature of the particular problem being addressed. 

The accurate calculation of such surfaces allows the definition of the geometries of intermolecular complexes, of intermediates and transition states and is useful for further studies of molecular dynamics, reaction kinetics, vibronic couplings etc. The PCM is here used to describe the solvent effect, the CASSCF to perform the calculation in a multiconfigurational framework and the VB to analyze the process from a chemical point of view. 

The CASVB strategy provides a very practical means for transforming the total CASSCF wave frinction into representations in which a very compact and easy-to-interpret modem VB component is dominant. Much the same technology can be, and has been, used to generate flilly-variational single and multiconfigurational modem VB wave functions [7], but this is not an aspect that we have pursued in much detail in the present account. 

The wave function of fragment A, ll a, can either be a single determinant from HF theory or Kohn-Sham DFT, or a multiconfiguration wave function derived from complete active space self-consistent field (CASSCF) or valence bond (VB) calculations. 

The molecular orbital (MO) is the basic concept in contemporary quantum chemistry. " It is used to describe the electronic structure of molecular systems in almost all models, ranging from simple Hiickel theory to the most advanced multiconfigurational treatments. Only in valence bond (VB) theory is it not used. Here, polarized atomic orbitals are instead the basic feature. One might ask why MOs have become the key concept in molecular electronic structure theory. There are several reasons, but the most important is most likely the computational advantages of MO theory compared to the alternative VB approach. The first quantum mechanical calculation on a molecule was the Heitler-London study of H2 and this was the start of VB theory. It was found, however, that this approach led to complex structures of the wave funetion when applied to many-electron systems and the mainstream of quantum ehemistry was to take another route, based on the success of the central-field model for atoms introduced by by Hartree in 1928 and developed into what we today know as the Hartree-Foek (HF) method, by Fock, Slater, and co-workers (see Ref. 5 for a review of the HF method for atoms). It was found in these calculations of atomic orbitals that a surprisingly accurate description of the electronic structure could be achieved by assuming that the electrons move independently of each other in the mean field created by the electron cloud. Some correlation was introduced between electrons with... 

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