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MCSCF orbitals

Let us note that the two conditions ej,=0 and < Pj >=0 (i 7 j) can be satisfied only with canonical SCF orbitals. Thus, in fact, the present theory can be applied only in such cases. However it has been demonstrated (12) that in most systems, the strongly occupied MCSCF orbitals and the SCF orbitals are extremely close one to the others. Therefore, in practice, the present theory also applies to the strongly occupied MCSCF orbitals. [Pg.28]

We have demonstrated formally that the optimum orbitals of any given molecular system (canonical SCF orbitals or strongly occupied MCSCF orbitals that are closed to the SCF ones) can be described very simply in the regions surrounding each nucleus... [Pg.35]

It is furthermore logical to use some sets of orbitals that are coherent with the zeroth-order space used the natural MCSCF orbitals issued from an MCSCF treatment using the space defined previously are then attraetive eandidates for the perturbation. [Pg.45]

Table 1. Energies of full and truncated SDTQ-Cl FORS-1 and FORS-2 calculations with and without MCSCF orbital optimization for the molecules HNO and NCCN (values in Hartrees unless noted otherwise). Table 1. Energies of full and truncated SDTQ-Cl FORS-1 and FORS-2 calculations with and without MCSCF orbital optimization for the molecules HNO and NCCN (values in Hartrees unless noted otherwise).
Because a particular active orbital may be occupied by zero, one, or two electrons in any given determinant, these MCSCF orbitals do not have unique eigenvalues associated with them, i.e., one cannot discuss the energy of the orbital. Instead, one can describe the occupation number of each such orbital i as... [Pg.206]

We consider a multireference Cl (MRCI) wave function calculated from a set of MCSCF orbitals. The Cl reference state is denoted by CI> at X0 and by CI(g)> at the displaced geometry X0 + g. In addition to the reorthonormalization part, the MRCI orbital connection contains the MCSCF orbital... [Pg.203]

The electronic gradient /(1) (which has no orbital part) has the same structure as the configuration part of the MCSCF electronic gradient [Eq. (84)] and may be constructed in the configuration basis, requiring /, SU), /<0>), and k(1 I(0) in the MO basis. (The k(1),/(0> integrals are needed since the orbital connection includes the MCSCF orbital reoptimization effects.)... [Pg.207]

Let us summarize. The calculation of Cl first anharmonicities requires no storage or transformation of second and third derivative two-electron integrals, but the full set of first derivative MO integrals is needed. One must construct and transform one set of effective density elements for third derivative integrals and 3M — 6 sets of effective densities for second derivative integrals. In addition to the 3N — 6 MCSCF orbital responses k(1) and the Handy-Schaefer vector Cm needed for the Hessian, the first anharmonicity requires the solution of 3JV — 6 response equations to obtain (1). [Pg.210]

Ignoring the field dependence of the dipole operator (MCSCF orbital connections are field independent) we write... [Pg.229]

MCSCF. Alternatively, a UHF (when different from the RHF) type wave function may also be used. The total UHF density, which is the sum of the a and /3 density matrices, will also provide fractional occupation numbers since UHF includes some electron correlation. The procedure may still fail. If the underlying RHF wave function is poor, the MP2 correction may also give poor results, and selecting the active MCSCF orbitals based on such MP2 occupation numbers may again lead to erroneous results. In practice, however, selecting active orbitals based on for example MP2 occupation numbers appears to be quite efficient, and better than... [Pg.121]

When more than one state of a system is to be investigated, it is possible to perform separate MCSCF calculations, followed by MRCI calculations, on each state. This, however, can be a very expensive process, and if transition properties between states are desired, such as transition dipole moments for spectroscopic intensities, the nonorthogonality between the MCSCF orbitals for the different states creates complications. A simple alternative is to perform an MCSCF optimization of a single average energy for all states of interest. All states are thereby described using a common set of MOs. Although these MOs are obviously not optimum for any of the states, experience shows this has little effect on the final MRCI results. [Pg.108]

Indicate the simplifications that occur in the formulas for the A and B matrix elements in Eqs. (2.29) and (2.30), when converged MCSCF orbitals are used for evaluating the A and B matrices. [Pg.118]

The optimum MCSCF orbitals can be found by an iterative process somewhat similar to the iterative process used to find SCF wave functions see A. C Wahl and G. Das, Chapter 3 in Schaefer, Methods of Electronic Structure Theory. By optimizing the orbitals, one can get good results with inclusion of relatively few CSFs. Because the orbitals are varied, the amount of calculation required in the MCSCF procedure is great, but advances in methods of computing MCSCF wave functions [R. Shepard, Adv. Chem. Phys., 69,63 (1987)] have led to wide use of the MCSCF and related methods... [Pg.448]

A straightforward extension of the Hg model of Jankowski et al. [60] (see Sect. 3.3) is displacement of all four H2 molecules [64]. In particular to study size extensivity, all H2 molecules are symmetrically displaced to infinity or as a practical matter in this work to the D4 , dissociation geometry of a = 994ao. A C localized orbital (LO) set computed from the symmetrically orthonormalized atomic orbitals [18] is employed. This set corresponds to the orthonormal MOs that are closest in the least squares sense to the atomic orbitals. Thus, these molecular calculations are performed without a preliminary SCF or MCSCF orbital optimization step. The order of levels in the Shavitt... [Pg.25]

The configuration interaction (Cl) procedure is one of the commonly used methods for determination of electronically excited states [30]. Starting from a finite set l/j of orthonormal one-electron basis functions (which can be either Hartree-Fock (HF) or canonical multiconfigurational self-consistent field (MCSCF) orbitals) [30], a subset of all possible antisymmetrized products have to be constructed ... [Pg.33]

The operator U carries the so-called orbital rotation parameters Kpq, which are the means to change, i.e., to optimize the MCSCF orbitals. For the sake of... [Pg.429]

My personal special emphasis has always been on the wavefunction itself. Since the wavefunction is not an observable, it is not possible to carry out an empirical calibration of a model wavefunction. Rather one must place it in the context of a sequence of wavefunctions that ultimately converges to the exact answer and produces correct properties without empirical corrections. At the same time, I prefer wavefunctions that apply to as wide a range of molecular systems as possible but that have some chance of being interpreted. The Cl wavefunctions generated for small molecules using natural or MCSCF orbitals are of this type. More modern wavefunctions such as MPn, full Cl, or coupled clusters calculated with Hartree-Fock virtual orbitals are not interpretable, and are usually never even looked at. [Pg.374]

Hence, after a decade of false starts, chemists finally learned that the correct basis set should consist of functions that could represent the atomic Hartree-Fock orbitals plus allow for contraction and polarization corrections in the region where they are largest. Similarly it was realized that the Hartree-Fock virtual molecular orbitals were too diffuse for representing the correction to the SCF wavefunction due to electron correlation. Rather, correlation effects are best represented using excitations to nonphysical molecular orbitals that are of the same size as the occupied MOs. Initially this was learned by transforming existing wavefunctions to natural orbital form. Later, MCSCF orbital optimizations were used to obtain these localized correlating orbitals. [Pg.376]


See other pages where MCSCF orbitals is mentioned: [Pg.121]    [Pg.153]    [Pg.193]    [Pg.205]    [Pg.206]    [Pg.227]    [Pg.242]    [Pg.68]    [Pg.246]    [Pg.129]    [Pg.404]    [Pg.142]    [Pg.65]    [Pg.1170]    [Pg.32]    [Pg.34]    [Pg.42]    [Pg.92]    [Pg.115]    [Pg.115]    [Pg.144]    [Pg.157]    [Pg.237]    [Pg.71]    [Pg.259]    [Pg.423]   
See also in sourсe #XX -- [ Pg.423 ]




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