Wave function zero-order

The zero-order wave function is the HF determinant, and the zero-order energy is just a sum of MO energies. The first-order energy correction is the average of the perturbation operator over the zero-order wave function (eq. (4.36)). 

The main limitation of perturbation methods is the assumption that the zero-order wave function is a reasonable approximation to the real wave function, i.e. the perturbation operator is sufficiently small . The poorer the HF wave function describes... 

Moller-Plesset perturbation theory (MPPT) aims to recover the correlation error incurred in Ilartree- Fock theory for the ground state whose zero-order description is ,. The Moller-Plesset zero-order Hamiltonian is the sum of Fock operators, and the zero-order wave functions are determinantal wave functions constructed from HF MOs. Thus the zero-order energies are simply the appropriate sums of MO energies. The perturbation is defined as the difference between the sum of Fock operators and the exact Hamiltonian ... 

In a non-relativistic approximation the usual fine structure (splitting) of the energy terms is considered as a perturbation whereas the hyperfine splitting - as an even smaller perturbation, and they both are calculated as matrix elements of the corresponding operators with respect to the zero-order wave functions. 

Configuration Interaction by Perturbation with Multiconfigurational Zero-Order Wave Function Selected by Iterative Process Configuration Interaction with Singles and Doubles Density Functional Theory Effective Core Potential Generalized Gradient Approximation Hartree-Fock... 

Therefore, two main different kinds of variational localized-site cluster expanded ansatze have so far been considered first the Neel-state-based ansatze (NSBA), where the Neel state is the zero order wave-function from which the trial wave-functions are generated, and second the Resonating... 

The cluster expanded wave-function ansatze in this section are based upon the Neel state as a zero-order wave-function,... 

Since the zero-order wave function of a diamagnetic state is a linear combination of the degenerate basis wave functions and the diamagnetic interaction allows for extension of dipole selection rules to Al = 1, 3, the equation for the coefficient q is modified to read (we consider the lower state to be non-degenerate, with l = m ) ... 

Here b) and X, 0) designate the zero order wave function of the states 61E+ and X3E-respectively with Ms — 0 for the triplet ground state. The 61 E+ — X3E-(Ms = 1) transition moment in 02 is now magnetic dipole allowed and equal to... 

Zero-Order Wave Function Selected by Iterative Process CISD Configuration Interaction with Singles and Doubles... 

Schrodinger equation have been performed using molecular orbital methods. The zero-order wave function is constructed as a single Slater determinant and the MOs are expanded in a set of atomic orbitals, the basis set. In a subsequent step the wave function may be improved by adding electron correlation with either Cl, MP or CC methods. There are two characteristics of such approaches (1) the one-electron functions, the -MQs, are delocalized over the whole molecule, and (2) an accurate treatment of the... 

If the charge-transfer excited states of the pyridine moieties are represented by the zero-order wave functions P°cti and P°ct2, then the resulting symmetric and anti-symmetric combinations are given in Eqs. 26a and b ... 

Finally, the last PEC represents = ao T + and is obtained from a MRCISD calculation based on the CASSCF (4, 8)/2s + 2p zero-order wave-function. In such a calculation, the corrections that are taken into account by are considered part of the D correlation. The difference befween the last two curves is very small. Obviously, when additional correlations of the D type (in terms of configurations and basis sets) are included in a full Cl compulation, the inner minimum goes down close to its true value while the outer one disappears [95,103,115]. The same occurs in the present work using the larger CASSCF (4, 26) reference wavefunction with the Be Fermi-sea of (2s, 2p, 3s, 3p, 3d] orbitals. 

It is well known that for CS and HS OS systems the widely employed second order MBPT [often referred to as the M0ller-Plesset PT (MP2) when a RHF or UHF operator is used as the unperturbed Hamiltonian (14)] provides computationally the cheapest, yet reasonably reliable, results. Surprisingly enough, no such method exists for the low spin OSS state mentioned above, as far as we know. This is likely due to the fact that the zero order wave function describing these states involves two Slater determinants and thus cannot be handled by the conventional MBPT relying on the spin orbital formalism. At the same time, in the MR theory... 

If the molecules are sufficiently far apart, the zero-order wave function may be written in terms of the wave functions Bi(l) and Bi(2) of the free molecules,... 

The Fock space approach assumes that the reference wave functions for the states of interest can be written in terms of determinants that share a common closed shell core. This closed shell core is then considered as the zero order wave function from which the energy of states of interest can be calculated as an electron affinity or ionization energy. In the calculation of these quantities one may incorporate the necessary multireference character by allowing mixing between different reference wave functions. The first step of the procedure is to define the reference or model space that spans a number of sectors of the Fock... 

---