Self-consistent field calculations molecules

F, St-Amant A, I Papai and D R Salahub 1992. Gaussian Density Functional Calculations on Hydrogen-Bonded Systems, journal of the American Chemical Society 114 4391-4400. ter J C1974. Quantum Theory of Molecules and Solids Volume 4 The Self-Consistent Field for Molecules and Solids. New York, McGraw-Hill. 

Calculations of vibrational frequencies in a three-center bond as a function of Si—Si separation were performed by Zacher et al. (1986), using linear-combination-of-atomic-orbital/self-consistent field calculations on defect molecules (H3Si—H—SiH3). The value of Van de Walle et al. for H+ at a bond center in crystalline Si agrees well with the value predicted by Zacher et al. for a Si—H distance of 1.59 A. 

In principle, this kind of scheme may be carried out for any molecule, with any number of electrons and any number of atomic orbitals y in the LCAO basis set. The practical calculation, however, involves the tedious evaluation of a large number of integrals, a number which increases so rapidly with the number of electrons that, for large molecules, complete self-consistent field calculations are not really feasible on a large scale. 

Straight self-consistent field calculations have been carried out on the interaction of water with neon and argon.30 Here it is possible to obtain some of the attractive contribution to the intermolecular force since there will be an inductive second-order interaction caused by the large dipole of the water molecule. Such interactions appear at the SCF level and the authors find a minimum in the potential at an O -Ne distance of 3.63 A, with a binding energy of 0.71 kJ mol-1. There is a shallower minimum in the case of argon. Calculations at a similar level of sophistication have been carried out on the H2----He system,31 primarily, however, from the... 

With the success of these calculations for isolated molecules, we began a systematic series of supermolecule calculations. As discussed previously, these are ab initio molecular orbital calculations over a cluster of nuclear centers representing two or more molecules. Self-consistent field calculations include all the electrostatic, penetration, exchange, and induction portions of the intermolecular interaction energy, but do not treat the dispersion effects which can be treated by the post Hartree-Fock techniques for electron correlation [91]. The major problems of basis set superposition errors (BSSE) [82] are primarily associated with the calculation of the energy. 

Interest in this question was revived by Ruedenberg,48 who demonstrated from available self-consistent field calculations that relation (84) was obeyed well for molecules at equilibrium. He suggested a coefficient 1.55 from his semi-empirical studies, which involved relation (97) of Politzer. The author49 drew attention to the fact that the simplest density description, combined with the equilibrium form of the virial theorem, would lead back to equation (84) for molecules. 

Table 11 has been constructed from available self-consistent field calculations for a variety of molecules. As the argument of Mucci and March implied, both signs of A are found in Table 11. 

There is generally little ambiguity associated with calculations of molecular orbitals for closed-shell molecules. The Hartree-Fock method (as appoximated by self-consistent field calculations in necessarily finite atomic orbital basis sets11) provides a solution that obeys some of the symmetry properties that must... 

In 1995 the electron affinities of organic molecules calculated using the standard MINDO/3 or AMI semi-empirical self-consistent field calculations agreed with experiment for molecules containing only CH and O to about 0.1 eV. However, the calculated values differed from experiment for molecules containing N and the halogens by as much as 1 eV. 

In the area of electron affinities of organic molecules, other electrochemical measurements were made and compared with half-wave reduction potentials. Quantum mechanical calculations for aromatic hydrocarbons were carried out using self-consistent field calculations. Many advances were made in the determination of the acidity of organic molecules. The effect of substitution and replacement on electron affinities and bond dissociation energies was recognized. This work is summarized in Chapters 10 and 12. A. S. Streitweiser provides an excellent review of the role of anions in organic chemistry up to 1960 [12]. 

Adiabatic electron affinity, energy difference between the ground state of the anion and the most stable state of the neutral molecule. A particular semi-empirical self-consistent field calculation. It stands for Austin Model-1. 

Mohanty, A. and Clementi, E. (1990) Dirac-Fock self-consistent field calculations for closed-shell molecules with kinetic balance and finite nuclear size. In Modem Techniques in Computational Chemistry MOTECC-90 (ed. E. Clementi), pp. 693—730. ESCOM, Leiden. Mohanty, A. K. and Clementi, E. (1991) Int. J. Quant. Chem 39,487-517. 

Pisani, L. and Clementi, E. (1993) Dirac-Fock self-consistent field calculations for closed-shell molecules with kinetic balance. In Gementi (1993), pp. 345-360. 

The same group used analytical arguments and numerical self-consistent field calculations to compare the interfacial tensions for a system of A and B homopolymers, immiscible with each other, having AB diblocks and comb copolymers localized at the interface [330,331]. In this case the overall molecular weight of the compatibilizer molecule was kept constant and the architecture was varied. At fixed N and > as the number of teeth increased the comb becomes less efficient at reducing the interfacial tension as compared to the diblock. At high values of N and x> the difference between the architectures becomes more pronounced. The diblock produces the lowest interfacial tension at the lowest concentrations. On the other hand, long combs with multiple teeth were found to be more efficient compatibilizers than short diblocks. 

A. Mohanty, E. dementi, Dirac-Fock Self-Consistent Field Calculations for Closed-Shell Molecules with Kinetic Balance and Finite Nuclear Size, in E. dementi (Ed.), Modern Techniques in Computational Chemistry MOTECC-90, ESCOM, Leiden, 1990, pp. 693-730. 

The isodensity surface is varied in each iteration of the self-consistent field calculation. In each iteration the solute density is updated, and consequently, the isodensity surface used for the cavity is relaxed to the isodensity surface of the solvated molecule. However, it is important to realize that this process is not fully self-consistent with respect to the isodensity surface, since there are no direct terms in the Hamiltonian that couple the isodensity surface to the solute. 

Butadiene is calculated by the simple MO method to have the same average number of it electrons at each atom. Therefore, it is often designated as a molecule with a self-consistent field. The self—consistent field calculated for butadiene is important in lending credence to the validity of of the assumption that Piz = Pzs particularly that i = aj. 

Note that the sharpness of the transition in the change on going from the depletion zone to the parabolic zone is due to limitations in the analytical function and does not reflect real transition behaviour. The more gentle transitions indicated in the theoretical SCF profile are more realistic. In the self-consistent field calculation a lattice model is not presumed the volume fraction of the tethered chains is calculated from a diffusion equation that involves polymer propagators and a (z-dependent) potential function that includes enthalpic interactions between the two copolymer blocks and between each block and the solvent. Initially the potential function is set to zero, the pol)nner propagators are calculated and then the volume fraction variation of the tethered block. A new potential is calculated from this volume fraction profile and the process reiterated imtil the difference in volume fraction profiles calculated by sequential iterations is smaller than some defined tolerance. The approach bears similarities to the SCF approach of Shull (1991) but makes no allowance for the dry brush case, i.e. that in which the relative molecular mass of the solvent approaches that of the tethered polymer molecule. 

Fig. 1, Eight natural orbitals for the water molecule. They were obtained from a complete active spare self-consistent-field calculation using a basis set of the size (OAs2>p2d/ms2p)...

By the end of 1936, Coulson was already delineating an extensive program of postdoctoral work on organic molecules, which included the development of new calculational techniques the conceptual clarification of criteria used for comparing the molecular orbital method with the valence bond method the comparison of resonance energies of molecules by the molecular orbital and valence bond methods and the extension of these considerations to polyatomic molecules, that is, the extension of the molecular orbital method and the self-consistent field calculations to polyatomic molecules. 

---