Full configuration interaction wavefunction

Dynamics calculations of reaction rates by semiempirical molecular orbital theory. POLYRATE for chemical reaction rates of polyatomics. POLYMOL for wavefunctions of polymers. HONDO for ab initio calculations. RIAS for configuration interaction wavefunctions of atoms. FCI for full configuration interaction wavefunctions. MOLSIMIL-88 for molecular similarity based on CNDO-like approximation. JETNET for artificial neural network calculations. More than 1350 other programs most written in FORTRAN for physics and physical chemistry. 

It is possible to use full or limited configuration interaction wavefunctions to construct poles and residues of the electron propagator. However, in practical propagator calculations, generation of this intermediate information is avoided in favor of direct evaluation of electron binding energies and DOs. 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

Ground-State Energies from the ACSE with V, NY, and M 3-RDM Reconstructions Compared with the Energies from Several Wavefunction Methods, Including Hartree-Fock (HF), Second-Order Many-Body Perturbation Theory (MP2), Coupled-Cluster Singles-Doubles (CCSD), and Full Configuration Interaction (FCI), for Molecules in Valence Double-Zeta Basis Sets."... 

A new algorithm is presented for the calculation of energy levels and their associated second-order density matrices, which aims to produce the exact energy as in full configuration interaction but without the V-particle wavefunction. 

Conceptually, the most straightforward approach is the so-called full configuration interaction model. Here, the wavefunction is written as a sum, the leading term of which, Fo, is the Hartree-Fock wavefunction, and remaining terms, Fs, are wavefunctions derived from the Hartree-Fock wavefunction by electron promotions. 

The HF (Hartree-Fock) Slater determinant is an inexact representation of the wavefunction because even with an infinitely big basis set it would not account fully for electron correlation (it does account exactly for Pauli repulsion since if two electrons had the same spatial and spin coordinates the determinant would vanish). This is shown by the fact that electron correlation can in principle be handled fully by expressing the wavefunction as a linear combination of the HF determinant plus determinants representing all possible promotions of electrons into virtual orbitals full configuration interaction. Physically, this mathematical construction permits the electrons maximum freedom in avoiding one another. 

Truncated Cl Wavefunctions.—Between the limits of a minimal and a full configuration interaction one is faced with the problem of choosing how many configurations and more importantly, which configurations are to be included. A computational problem arises because of the very slow convergence, generally... 

The effectiveness of NSO s in reducing the expansion size in systems with more than two electrons is not as great and, in fact, for larger systems, their use is not practical. The loss in practicality is immediately obvious when one realizes that in order to obtain them, one must diagonalize the first-order density matrix of the exact wavefunction, i.e. a full configuration interaction must first be performed. Two methods have been introduced in order to regain the initial usefulness of natural orbitals the pseudonatural orbital method and the approximate or iterative natural orbital method. 

The full configuration interaction method [34-36] is exact in the sense that after choosing appropriate atomic basis functions (defining the model in this way), the resulting many-electron wavefunction is an exact eigenfunction of the model Hamiltonian, the computational effort, nevertheless, increases in an exponential manner. Truncation of the full Cl expansion (especially after single and double excitations, CI-SD) considerably reduces the necessary computational resources, but leads unfortunately to the serious problem of nonsize-consistency [37, 38] which makes the results even for medium systems unrealistic. The coupled-cluster method [39, 40] theoretically properly describes extended systems as well, but numerous experiences show the enormous increase of computational work with the size of the system. 

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... 

Table I summarizes the results for Hg. In order to calculate the activation energy the results shown in Table II for the H atom and Hg molecule at the same level of approximation were used. The total energy, of course, improves as the wavefunction is allowed more variation. However, because the cusp in the wavefunction is poorly represented by one or two Gaussians the total energy is still far from the experimental value. In comparison with the Gaussian work of Schwartz and Schaad,i our best total energy, which involves full configuration interaction, is naturally better than their double Gaussian SCF calculation but not as good as their results with larger basis sets.

The conceptually simplest approach to solve for the -matrix elements is to require the wavefunction to have the form of equation (B3 4.4). supplemented by a bound function which vanishes in the as5miptote [32, 33, 34 and 35] This approach is analogous to the full configuration-interaction (Cl) expansion in electronic structure calculations, except that now one is expanding the nuclear wavefunction. While successful for intermediate size problems, the resulting matrices are not very sparse because of the use of multiple coordinate systems, so that this t5q)e of method is prohibitively expensive for diatom-diatom reactions at high energies. 

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... 

The exact correlated wavefunction with a given basis set can be obtained by carrying out a full configuration interaction (Cl) calculation. However, full Cl calculations are computationally prohibitive, even for very small systems. A major research thrust in quantum chemistry is aimed at developing methods which approximate full Cl results, but which are computationally tractable for systems of interest. The following are three of the more popular methods. 

We take the initial wavefunctions to be very limited configuration-interaction expansions, containing only s orbitals. Thus, we take as the first wavefunc-tion in the one formed by all single and double excitations generated from the basic configuration [Is ] by substitutions comprising the 2s orbital for the second wavefunction, we span over the 2s and 3s orbitals and for the third one, we use orbitals Is, 2s and 3s. Hence, are all these wavefunctions are full Cl wavefunctions for such bases. Explicitly, these wavefunctions are... 

The above expansion of the full N-electron wavefunction is termed a "configuration-interaction" (Cl) expansion. It is, in principle, a mathematically rigorous approach to expressing P because the set of all determinants that can be formed from a complete set of spin-orbitals can be shown to be complete. In practice, one is limited to the number of orbitals that can be used and in the number of CSFs that can be included in the Cl expansion. Nevertheless, the Cl expansion method forms the basis of the most commonly used techniques in quantum chemistry. 

The other approach most frequently used to describe a correlated wavefunction beyond the independent-particle model is based on configuration interaction (Cl). (If the expansion is made on grounds of other basis sets, the approach is often called superposition of configurations, SOC, in order to distinguish it from the Cl method.) According to the general principles of quantum mechanics, the exact wavefunction which is a solution of the full Hamiltonian H can be obtained as an expansion in any complete set of basis functions which have the same symmetry properties ... 

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