Molecular wavefunctions, calculation

This routine takes the data describing the basis functions and the molecular geometry and sets up the logic to calculate all the molecular integrals needed for a molecular wavefunction calculation. ARGUMENTS... 

Alkanethiols (cont.) molecular total energy 12 molecular wavefunction calculations 81-86... 

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, ... 

Tie first consideration is that the total wavefunction and the molecular properties calculated rom it should be the same when a transformed basis set is used. We have already encoun-ered this requirement in our discussion of the transformation of the Roothaan-Hall quations to an orthogonal set. To reiterate suppose a molecular orbital is written as a inear combination of atomic orbitals ... 

In order to conserve the total energy in molecular dynamics calculations using semi-empirical methods, the gradient needs to be very accurate. Although the gradient is calculated analytically, it is a function of wavefunction, so its accuracy depends on that of the wavefunction. Tests for CH4 show that the convergence limit needs to be at most le-6 for CNDO and INDO and le-7 for MINDO/3, MNDO, AMI, and PM3 for accurate energy conservation. ZINDO/S is not suitable for molecular dynamics calculations. 

A Guide to Molecular Mechanics and Molecular Orbital Calculations in Spartan, W.J. Hehre, J. Yu and RE. Klunzinger, Wavefunction, Inc., Irvine, CA. 

In standard quantum-mechanical molecular structure calculations, we normally work with a set of nuclear-centred atomic orbitals Xi< Xi CTOs are a good choice for the if only because of the ease of integral evaluation. Procedures such as HF-LCAO then express the molecular electronic wavefunction in terms of these basis functions and at first sight the resulting HF-LCAO orbitals are delocalized over regions of molecules. It is often thought desirable to have a simple ab initio method that can correlate with chemical concepts such as bonds, lone pairs and inner shells. A theorem due to Fock (1930) enables one to transform the HF-LCAOs into localized orbitals that often have the desired spatial properties. 

The raw output of a molecular structure calculation is a list of the coefficients of the atomic orbitals in each LCAO (linear combination of atomic orbitals) molecular orbital and the energies of the orbitals. The software commonly calculates dipole moments too. Various graphical representations are used to simplify the interpretation of the coefficients. Thus, a typical graphical representation of a molecular orbital uses stylized shapes (spheres for s-orbitals, for instance) to represent the basis set and then scales their size to indicate the value of the coefficient in the LCAO. Different signs of the wavefunctions are typically represented by different colors. The total electron density at any point (the sum of the squares of the occupied wavefunctions evaluated at that point) is commonly represented by an isodensity surface, a surface of constant total electron density. 

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 calculations, or from some kind of empirical fitting ... 

The applicability of the discussed two-step algorithms for calculation of wavefunctions of molecules with heavy atoms is a consequence of the fact that the valence and core electrons may be considered as two subsystems, interaction between which is described mainly by some integrated properties of these subsystems. The methods for consequent calculation of the valence and core parts of electronic structure of molecules give us a way to combine the relative simplicity and accessibility both of molecular RFCP calculations in gaussian basis set, and of relativistic finite-difference one-center calculations inside a sphere with the atomic core radius. 

Bartlett, R. J. 2000. Perspective on On the Correlation Problem in Atomic and Molecular Systems. Calculations of Wavefunction Components in Ursell-type Expansion Using Quantum-field Theoretical Methods Theor. Chem. Acc., 103, 273. 

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. (13-14), 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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