A configuration

Wlien first proposed, density llinctional theory was not widely accepted in the chemistry conununity. The theory is not rigorous in the sense that it is not clear how to improve the estimates for the ground-state energies. For wavefiinction-based methods, one can include more Slater detenuinants as in a configuration interaction approach. As the wavellmctions improve via the variational theorem, the energy is lowered. In density fiinctional theory, there is no... 

In the internal region r> a, the electron-atom complex behaves almost as a bound state so that a configuration... 

Atomic natural orbital (ANO) basis sets [44] are fonned by contracting Gaussian fiinctions so as to reproduce the natural orbitals obtained from correlated (usually using a configuration interaction with... 

Figure C2.16.6. The energy states of a metastable and bistable muonium in Si are illustrated in a configuration diagram. It plots the defect energy as a function of a coordinate which combines position and all the relaxations and distortions of the crystal. The specific example, discussed in the text, illustrates acceptor and donor levels, metastability, bistability and negative- U [50] behaviour.

A configurational Monte Carlo algorithm based on uniform random trial moves and the acceptance probability... 

Continuous chirality measure is then defined as follows given a configuration of points P = I, its chirality content is determined by finding the nearest configuration of points Pi - 2 which has an improper element of symmetry, and by calculating the distance between the two sets using Eq. (26). 

HyperChem always com putes the electron ic properties for the molecule as the last step of a geometry optimization or molecular dyn am ics calcu lation. However, if you would like to perform a configuration interaction calculation at the optimized geometry, an additional sin gle poin t calcu lation is requ ired with theCI option being turned on. 

Some of the ways in which excitai-state wavefunctions can be included in a configuration interaction Illation (Figure adapted from Hehre W ], L Roikiin, P zi R Schleyer and ] A Hehre 1986. Ab initio Molecular aital Theory. New York, Wiley.)... 

Obtain a configuration of the system by randomly generating 3N Cartesian coordinate which are assigned to the particles. 

In summary, an atom or molecule has many orbitals (core, bonding, non-bonding, Rydberg, and antibonding) available to it occupancy of these orbitals in a particular manner gives rise to a configuration. If some orbitals are partially occupied in this configuration. 

If, instead of a configuration like that treated above, one had a 52 configuration, the above analysis would yield F, and symmetries (because the two 5 orbitals m values could be combined as 2 + 2, 2 - 2, -2 + 2, and -2 -2) the wavefunctions would be identical to those given above with the 7ii orbitals replaced by 82 orbitals and 71.1 replaced by 5.2. Likewise, dp- gives rise to H, and symmetries. 

The lowest-lying n=>7i states correspond to a configuration (only those orbitals... 

The probability of a configuration occurring is a function of the energy of that configuration. This energy is the sum of the potential energy from inter-... 

A configuration interaction wave function is a multiple-determinant wave function. This is constructed by starting with the HF wave function and making new determinants by promoting electrons from the occupied to unoccupied or-... 

A configuration interaction calculation uses molecular orbitals that have been optimized typically with a Hartree-Fock (FIF) calculation. Generalized valence bond (GVB) and multi-configuration self-consistent field (MCSCF) calculations can also be used as a starting point for a configuration interaction calculation. 

Which of these two opposite stereochemical possibilities operates was determined in experiments with optically active alkyl halides In one such experiment Hughes and Ingold determined that the reaction of 2 bromooctane with hydroxide ion gave 2 octanol having a configuration opposite that of the starting alkyl halide... 

A configuration interaction calculation is available only for single points when the reference ground state is obtained from an RHF calculation. 

Generally, a vibration analysis calculation should be performed after a geometry optimization with the same method. This ensures that the calculation of second derivatives is performed at a configuration for which all first derivatives are zero. 

The UHF option allows only the lowest state of a given multiplicity to be requested. Thus, for example, you could explore the lowest Triplet excited state of benzene with the UHF option, but could not ask for calculations on an excited singlet state. This is because the UHF option in HyperChem does not allow arbitrary orbital occupations (possibly leading to an excited single determinant of different spatial symmetry than the lowest determinant of the same multiplicity), nor does it perform a Configuration Interaction (Cl) calculation that allows a multitude of states to be described. 

HyperChem uses single determinant rather than spin-adapted wave functions to form a basis set for the wave functions in a configuration interaction expansion. That is, HyperChem expands a Cl wave function, in a linear combination of single Slater determ in ants... 

If a molecule has a plane of symmetry, for which the symbol is a, reflection of all the nuclei through the plane to an equal distance on the opposite side produces a configuration indistinguishable from the initial one. Figure 4.3(a) shows the two planes of symmetry, (7 (xz) and (yfyz), of H2O using conventional axis notation. Just as theyz plane, the plane of the molecule, is a plane of symmetry so any planar molecule has at least one plane of symmetry. The subscript u stands for vertical and implies that the plane is vertical with respect to the highest-fold axis, C2 in this case, which defines the vertical direction. 

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