Molecular wavefunction

Woon D E 1994 Benchmark calculations with correlated molecular wavefunctions. 5. The determination of accurate ab initio intermolecular potentials for He2, Ne2, and A 2 J. Chem. Phys. 100 2838... 

For Iran sition metals th c splittin g of th c d orbitals in a ligand field is most readily done using HHT. In all other sem i-ctn pirical meth -ods, the orbital energies depend on the electron occupation. HyperCh em s m oiccii lar orbital calcii latiori s give orbital cri ergy spacings that differ from simple crystal field theory prediction s. The total molecular wavcfunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals arc the residue of SCT calculations, in that they are deemed least suitable to describe the molecular wavefunction, ... 

Simple Basis Set for Molecular Wavefunctions Containing First- and Second-Row Atoms E. Clementi... 

As outlined in Section III.A, knowledge of the molecular wavefunction implies knowledge of the electron distribution. By setting a threshold value for this function, the molecular boundaries can be established, and the path is open to a definition of molecular shape. A quicker, but quite effective, approach to this entity is taken by assuming that each atom in a molecule contributes an electron sphere, and that the overall shape of a molecular object results from interpenetration of these spheres. The necessary radii can be obtained by working backwards from the results of MO calculations21, or from some kind of empirical fitting22. 

Initial conditions for the total molecular wavefunction with n = I (including electronic, vibrational and rotational quantum numbers) can be imposed by adding elementary solutions obtained for each set of initial nuclear variables, keeping in mind that the xi and 5 depend parametrically on the initial variables... 

CONSTRUCTION OF MOLECULAR WAVEFUNCTIONS AND POTENTIAL SURFACES THE CS INDO MODEL... 

Wachters, A. J. H., 1970, Gaussian Basis Set for Molecular Wavefunctions Containing Third-Row Atoms , J. Chem. Phys., 52, 1033. 

It is evident that the operator Hd couples only the small components of the relativistic molecular wavefunctions. Since the small components as well as the nuclear electric fields are prominent in and around the nuclear regions, the dominant contribution to the matrix elements of Hj comes from that region. It should be noted that the absence of the screening term Eq in Eq.(42) will overestimate the //d matrix element. However, the amount of overestimation is expected to be small. 

The approximate molecular wavefunction T is a Slater determinant of the single particle orbitals (j). 

Like (5.15b), the multipole approximation (5.19) is dependent on the long-range assumption (5.14) both approximations fail (for different reasons) if the molecular wavefunctions f and fi" overlap appreciably. 

Pack, R.T., Beyers Brown, W. Cusp conditions for molecular wavefunctions. J. Chem. Phys. 1966, 45, 556-9. 

Hence the approach privileged here, based on Eq. (4.47), that uses the variations of effective nuclear-electronic potential energies Ay g dictated by local atomic electron populations. Regarding the latter, they are deduced along classical lines, rooted in molecular wavefunctions that determine the electron density at any given point in space. 

Knowledge of the molecular wavefunction enables us to determine the electron density at any given point in space. Here we inquire about the amount of electronic charge that can be associated in a meaningful way with each individual atom of a A -electron system. Our analysis covers Mulliken s celebrated population analysis [31], as well as a similar, closely related method. 

Within the approximation that the electronic, vibrational, and rotational states of a molecule can be treated as independent, the total molecular wavefunction of the "initial" state is a product... 

The Born-Oppenheimer approximation may then be thought of as keeping the electronic eigenfunctions independent and not allowing them to mix under the nuclear coordinates. This may be seen by expanding the total molecular wavefunction using the adiabatic eigenfunctions as a basis... 

Further, we will find in this chapter that wavefunctions (nuclear or electronic) must be functions which form bases for the irreducible representations of the point group to which the molecule belongs. With this knowledge we are able to determine which integrals over molecular wavefunctions are necessarily zero and this in turn (next chapter) leads to well known spectroscopic selection rules. 

The Born-Oppenheimer adiabatic approximation is introduced by neglecting the coupling terms in eq. (4-6). The molecular wavefunctions then reduce to the simple product form... 

The conventional procedure is to retain only the linear term in the expansion (8-3). It should be noted that while the indicated truncation may be justified in the Jahn-Teller problem, it is likely not to be as accurate in our case, where molecular wavefunctions at large nuclear displacements must be considered. In this context, it is interesting to draw the reader s attention to a classical calculation of the force constants for nuclear displacement in the excited electronic states of aromatic molecules.133 It... 

In eq. (13-1) the first equality gives the definition of the oscillator strength in the dipole-length representation, while the second equality gives the definition in the momentum (or velocity) representation. As usual, and T, are the total molecular wavefunctions for the final and initial states, and Ef and Et are the energies of the final and initial states, respectively. 

In eq. (13-14), b is the distance from the molecular center to any atom. It is seen that the effective quantum defect for this molecular wavefunction is /xs — 0.5 = 0.54. By coincidence, this is precisely one of the defects for molecular benzene given by Wilkinson.218 The other calculated defects do not compare as well with those quoted by Wilkinson. They are 0.23 for the eiuiPx.y) and e2u(j>z) orbitals and 0.73 for the a2u pz) orbital, whereas Wilkinson gives 0.84, 0.89, and 0.96. 

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