Quantum chemical calculations self-consistent field theory

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. 

Density-Functional Theory. Transition metals pose a problem for classical quantum chemical methods like self-consistent field (SCF), perturbation theory, configuration interaction (Cl), and variations on these methods, because of the very large electron correlation. SCF underestimates binding substantially, and post-SCF methods are so expensive for transition metals that one can do a calculation only on models with few atoms. DFT on the other hand is relatively cheap it is about as expensive as SCF. Moreover, with the development of the generalized-gradient approximations it is also reasonably accurate. A large majority of quantum chemical... 

All quantum chemical calculations are based on the self-consistent field (SCF) method of Hatree and Fock (1928-1930) and the MO theory of Hund, Lennard-Jones, and Mulliken (1927-1929). A method of obtaining SCF orbitals for closed shell systems was developed independently by Roothaan and Hall in 1951. In solving the so-called Roothan equations, ab initio calculations, in contrast to semiempirical treatments, do not use experimental data other than the values of the fundamental physical constants. 

An additional source of chemical shielding anisotropies is that of ab initio theoretical calculations.20 25 There has been considerable progress in this area of molecular quantum mechanics, particularly with the use of gauge-invariant atomic orbitals within the framework of self-consistent-field (SCF) perturbation theory.26 In many cases the theoretical quantities have been extremely accurate and have served not only as a corroboration of experimental quantities but also as a reliable source of new data for molecules of second-row atoms (i.e., Li through F). 

The present quantum-chemical calculations of fullerenes deal with the optimized geometries [177-181] obtained at semiempirical, ab initio Hartree-Fock Self-Consistent Field (HF SCF) or density functional theory (DFT) level while ab initio... 

Table 1 contains some further information useful to characterize the different contributions to the molecule/surface interaction orientation dependence and the typical strength of the different contributions, and whether or not they can be understood on a purely classical basis. If one wants to calculate molecule/surface interactions by means of quantum-mechanical or quantum-chemical methods, the most important question is whether standard density functional (DPT) or Hartree-Fock theory (self consistent field, SCF) is sufficient for a correct and reliable description. Table 1 shows that all contributions except the Van der Waals interaction can be obtained both by DPT and SCF methods. However, the results might be connected with rather large errors. One famous example is that the dipole moment of the CO molecule has the wrong sign in the SCF approximation, with the consequence that SCF might yield a wrong orientation of CO on an oxide surface (see also below). In such cases, the use of post Hartree-Fock methods or improved functionals is compulsory. 

The theory of solvent-effects and some of its applications have been overviewed. The generalized self-consistent reaction field theory has been used to give a unified approach to quantum chemical calculations of subsystems embedded in a given milieu. The statistical mechanical theory of projected equation of motion has been briefly described. This theory underlies applications of molecular dynamics simulations to the study of solvent and thermal bath effects on carefully defined subsystems of interest. The relationship between different approaches used so far to calculate solvent effects and the general approach advocated by this reviewer has been established. Applications to molecular properties in a time independent framework have been presented. 

Table 5.6 gives the results of a self-consistent field (SCF) quantum chemical calculation for H2O using an orbital basis set of the atomic orbitals of O and the LGOs of an H—H fragment. The axis set is as defined in Fig. 5.15. (a) Use the data to construct pictorial representations of the MOs of H2O and confirm that Fig. 5.15 is consistent with the results of the calculation, (b) How does MO theory account for the presence of lone pairs in H2O ... 

Further, it is understood that each matrix element consists of the components originating in the pure QM, the est and the vdW contribution. The est components are conveniently computed by the quantum chemical calculation package. For instance, in GAUSSIAN program [25], several approximate methods of electronic state calculations are available, e.g., the Hartree-Fock (HF), second-order Moller-Plesset perturbation theory (MP2), conhguration interaction field (CIS), complete active space self-consistent field (CASSCF) method, and the density functional theory (DFT) methods. On the other hand, since the vdW components are expressed as such analytical functions of the mw Cartesian coordinate variables involved in the same atom (A = B) as follows. 

Combined Quantum Mechanical and Molecular Mechanical Potentials Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Configuration Interaction Configuration Interaction Semiempirical Calculations Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Force Fields A General Discussion Hybrid Methods MNDO Quantum Mechanical/Molecular Mechanical (QM/MM) Coupled Potentials Quantum Mecha-nics/Molecular Mechanics (QM/MM). 

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