Electronic structure methods configuration interaction method

In the last few years, the improvements in computer hardware and software have allowed the simulation of molecules and materials with an increasing number of atoms. However, the most accurate electronic structure methods based on N-particle wavefunctions, for example, the configuration interaction (Cl) method or the coupled-cluster (CC) method, are computationally too expensive to be applied to large systems. There is a great need for treatments of electron correlation that scale favorably with the number of electrons. 

B.O. Roos and P.E.M. Siegbahn, The Direct Configuration Interaction Method from Molecular Integrals, in Methods of Electronic Structure Theory (H.F. Schaefer III, ed.), Plenum Press, New York (1977). 

Electronic configurations are the MO equivalents of resonance structures. Sometimes a molecular state cannot adequately be represented by a single configuration, just as benzene or an enolate ion cannot be represented by only one Kekule structure. The molecular state is then better described by a linear combination of several electronic configurations (configuration interaction method). 

Other theoretical studies of ozone and its excited states have been previously reported and also indicate a relatively low lying state corresponding to a six jr-electron cyclic structure. In particular, recent ab initio calculations using the generalized valence bond and configuration interaction methods with a double zeta basis set, predict that trioxirane lies about 35 kcal/mol higher in energy than ozone but that it is a potential minimum. 

For a recent review of configuration interaction methods, see I. Shavitt, H. F. Schaeffer 111, Ed., in Modern Theoretical Chemistry, Vol. Ill, Methods of Electronic Structure Theory, Plenum Press, New York, 1976. 

As follows from the form of the QM/MM Hamiltonian (Eq. 5.8), any electronic structure method can be used for describing the QM and MM parts of the system. Applications discussed in the following session mainly deal with understanding photochemistry in the condensed phase, with a common choice of the excited state methods from the equation of motion coupled cluster (EOM-CC) family [61-64], time-dependent density functional theory (TD-DFT) [65-66], or configuration interaction (Cl) methods. The MM Hamiltonian is represented by either EFPl or EFP Hamiltonian from Eq. 5.1 or Eq. 5.7. //qm-mm coupling term in the QM/EFPl... 

However, from a computational point of view, the LDA is much easier to implement and, relative to configuration interaction methods, is much less computationally intensive. Yin and Cohen, along with others, had used the LDA to construct pseudopotentials from first principles [5]. These ab initio pseudopotentials were very helpful in describing the electronic structure of surfaces, molecules, defects, etc., but they were not viewed as tools for computing the total energy of a solid. 

Roos, B. O. and Siegbahn, P. E. M., The direct configuration interaction method firom molecular integrals, in Methods of Electronic Structure Theory H. F. Schaefer HI (Ed.), Plenum, New York, 1977, p. 277. A discussion by the originators of an important metht in which the Cl matrix is never explicitly constructed. 

As in the Hartree-Fock molecular orbital theory, which is based on the independent particle model, the above Hartree product method also lacks enough correlation among the orbitals, and thereby the resultant accuracy is limited. To overcome the drawback, one can take account of the interaction among possible configurations (or the Hartree products) as in the configuration interaction method and multiconfiguration SCF methods in electronic structure theory. The multiconfigulational time-dependent Hartree... 

The spectral representations above are not computationally efficient, as they would require knowledge of all intermediate excited states. Computationally tractable formulas for the response functions within the various approximate methods are obtained instead through the following steps (1) choose a time-independent reference wavefunction (2) choose a parametrization of its time-development, for instance an exponential parametrization (3) set up the appropriate equations for the time development of the chosen wavefunction parameters (4) solve these equations in orders of the perturbation to obtain the wavefunction (parameters) (5) insert the solutions of these equations into the expectation value expression and obtain the RTFs and (6) identify the excited-state properties from the poles and residues. The computationally tractable formulas for the response functions therefore differ depending on the electronic structure method at hand, and the true spectral representations given above are only valid in the limit of a frill-configuration interaction (FCI) wavefunction. For approximate methods (i.e., where electron correlation is only partially included), matrix equations appear instead of the SOS expressions, for example. 

The basis set convergence error is separate from the accuracy of the particular electronic structure method used to solve the Schrodinger equation (Hartree-Fock, singles and doubles configuration interaction, second-order perturbation theory, etc.). The methods error is defined by... 

Carbenes A Testing Ground for Electronic Structure Methods Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Mpller-Plesset Perturbation Theory Natural Orbitals Transition State Theory Unimolecu-lar Reaction Dynamics. 

For small monomers, the intermoleciflar potentials can be computed by standard electronic structure methods that account for electron correlation. This is done by using the supermolecular approach, i.e. for each configuration of fixed nuclei (the Born-Oppenheimer approximation), the interaction energy int is obtained by subtracting the total energies of monomers from the total energy of the cluster [11,12]... 

Of the 33 invited speakers and the seven who contributed talks, 17 accepted our invitation to contribute a chapter to this book. These chapters are complemented by three additional chapters from individuals to help develop a more cohesive book as well as an overview chapter. Approximately half of the chapters are focused on the development of ab initio electronic structure methods and consideration of specific challenging molecular systems using electronic structure theory. Some of these chapters document the dramatic developments in the range of applicability of the coupled-cluster method, including enhancements to coupled-cluster wavefunctions based on additional small multireference configuration interaction (MR-CISD) calculations, the method of moments, the similarity transformed equation of motion (STEOM) method, a state-specific multireference coupled-cluster method, and a computationally efficient approximation to variational coupled-cluster theory. The concentration on the coupled-cluster approach is balanced by an approximately equal number of chapters discussing other aspects of modem electronic stracture theory. In particular, other methods appropriate for the description of excited electronic states, such as multireference... 

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