Full configuration interaction application

Finally, in order to illustrate the role of the 1-MZ purification procedure in improving the approximated 2-RDMs obtained by application of the independent pair model within the framework of the SRH theory, all the different spin-blocks of these matrices were purified. The energy of both the initial (non-purified) and updated (purified) RDMs was calculated. These energies and those corresponding to a full configuration interaction (full Cl) calculation are reported in Table 111. As can be appreciated from this table, the nonpurified energies of all the test systems lie below the full Cl ones while the purified ones lie above and very close to the full Cl ones. 

Table 2.7 contains five columns of numbers for excitation energies in Be. The first two are from Ref. [106]. The acronyms SC-SF-CIS and FCI stand for "spin-complete, spin-flip, configuration-interaction singles" and "full configuration interaction," respectively. In this case, the application of SPSA employs the differences of only the Fermi-sea energies given in the previous subsection (15a, 16c, and 19). Also, the Fermi-sea wavefunction for the... 

This second approach leads to what Pople and his co-workers term a theoretical model chemistry. In practical applications, the complete basis set limit for full configuration interaction cannot be achieved with finite computing resources, except for the very smallest systems. Compromises have to be made in order to achieve a wide range of applicability. Geometry optimization may, for example, be carried out with some lower level theory and/or basis set of moderate size followed by more accurate calculations using higher level theory and/or an extended ... 

It is well known that the major deficiency of the Hartree-Fock model is its incapacity to account for the correlation effect associated with the motions of electrons of opposite spin. In principle, this contribution can be computed using a full configuration interaction (Cl) method, where the wavefunction corresponds to a variationally optimized combination of all possible electronic configurations. However, the application of this method to molecules of chemical interest can involve a number of configurations which rapidly... 

Full configuration interaction (FCI) by definition gives the exact n-particle energy within the given basis set. (Since it is the exact solution, this happens irrespective of the quality of the zero-order wave function.) Because its computational requirements ascend factorially with the size of the system, application to practical systems using one-particle basis sets of useful size will be essentially impossible for the foreseeable future. Even using the fastest available computational hardware and parallelized codes, an FCI calculation on H2O in a double-zeta plus polarization basis set is about the state of the art at present. ... 

Use of a complete set of CSFs in the expansion (7) is referred to as the complete or full configuration interaction (FCI). Since FCI calculations are computationally very demanding, they are only feasible for small orbital sets and a small number of electrons. In chemical applications of the Cl method we are therefore confined to considerably smaller expansions. Standard levels of the Cl method are termed according to the extent of the Cl expansion CI-S, CI-SD, CI-SDT, and CI-SDTQ correspond to expansions through singly, doubly, triply, and quadruply excited CSFs, respectively. 

MNDOC is a correlated version of MNDO. Unlike all previously discussed methods, MNDOC includes electron correlation explicitly and thus differs from MNDO at the level of the underlying quantum chemical approach (a) while being completely analogous to MNDO in all other aspects (b)-(d) except for the actual values of the parameters. In MNDOC electron correlation is treated conceptually by full configuration interaction, and practically by second-order perturbation theory in simple cases (e.g., closed-shell ground states) and by a variation-perturbation treatment in more complicated cases (e.g., electronically excited states).The MNDOC parameters have been determined at the correlated level and should thus be appropriate in all MNDO-type applications which require an explicit correlation treatment for a qualitatively suitable zero-order description. In closed-shell ground states... 

Thus the one-particle basis determines the MOs, which in turn determine the JV-particle basis. If the one-paxticle basis were complete, it would at least in principle be possible to form a complete jV-particle basis, and hence to obtain an exact wave function variationally. This wave function is sometimes referred to as the complete Cl wave function. However, a complete one-paxticle basis would be of infinite dimension, so the one-paxticle basis must be truncated in practical applications. In that case, the iV-particle basis will necessarily be incomplete, but if all possible iV-paxticle basis functions axe included we have a full Cl wave function. Unfortunately, the factorial dependence of the iV-paxticle basis size on the one-particle basis size makes most full Cl calculations impracticably large. We must therefore commonly use truncated jV-paxticle spaces that axe constructed from truncated one-paxticle spaces. These two truncations, JV-particle and one-particle, are the most important sources of uncertainty in quantum chemical calculations, and it is with these approximations that we shall be mostly concerned in this course. We conclude this section by pointing out that while the analysis so fax has involved a configuration-interaction approach to solving Eq. 1.2, the same iV-particle and one-particle space truncation problems arise in non-vaxiational methods, as will be discussed in detail in subsequent chapters. 

Christiansen has reviewed the reeently developed theoretieal methods for the calculation of vibrational energies and wavefunetions. The main focus is on wavefunction methods using the vibrational self-eonsistent field (VSCF) method as starting point, and ineludes vibrational eonliguration interaction (VCI), vibrational Moller-Plesset (VMP), and vibrational coupled cluster (VCC) approaches. The eonvergenee of these different sets of methods towards the full vibrational configuration interaction (FVCI) result has been discussed as well as the application of this formalism to determine vibrational contributions to response properties. 

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