A minimum principle for molecular systems allowing the use of discontinuous wave functions

1970 ◽  
Vol 4 (1) ◽  
pp. 5-20 ◽  
Author(s):  
G. G. Hall ◽  
J. Hyslop ◽  
D. Rees
Keyword(s):  
Minimum Principle ◽  
Wave Functions ◽  
Molecular Systems ◽  
Discontinuous Wave

Operators, Matrix Elements, and Wave Functions under Time-Reversal Symmetry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Quantum Chemistry ◽  
Time Reversal ◽  
Relativistic Quantum ◽  
Spin Symmetry ◽  
Computational Effort ◽  
Wave Functions ◽  
Time Reversal Symmetry ◽  
Molecular Systems ◽  
Self Consistent Field ◽  
Relativistic Quantum Chemistry

We now take on the task of developing the theory and methods for a relativistic quantum chemistry. The aim is to arrive at a qualitative as well as a quantitative understanding of the relativistic effects in molecules. We must be able to predict the effects of relativity on the wave functions and electron densities of molecules, and on the molecular properties arising from these. And we must develop methods and algorithms that enable us to calculate the properties and interactions of molecules with an accuracy comparable to that achieved for lighter systems in a nonrelativistic framework. Parts of this development follow fairly straightforwardly from our considerations of the atomic case in part II, but molecular systems represent challenges of their own. This is particularly true for the computational techniques. From the nonrelativistic experience we know that present-day quantum chemistry owes much of its success to the enormous effort that has gone into developing efficient methods and algorithms. This effort has yielded powerful tools, such as the use of basis-set expansions of wave functions, the exploitation of molecular symmetry, the description of correlation effects by calculations beyond the mean-field approximation, and so on. In developing a relativistic quantum chemistry, we must be able to reformulate these techniques in the new framework, or replace them by more suitable and efficient methods. In nonrelativistic theory, spin symmetry provides one of the biggest reductions in computational effort, such as in the powerful and elegant Graphical Unitary Group Approach (GUGA) for configuration interaction (CI) calculations (Shavitt 1988). For relativistic applications, time-reversal symmetry takes the place of spin symmetry, and this chapter is devoted to developing a formalism for efficient incorporation of this symmetry in our theory and methods. Time-reversal symmetry includes the spin symmetry of nonrelativistic systems, but there are significant differences from spin symmetry for systems with a Hamiltonian that is spin-dependent. The development of techniques that incorporate time-reversal symmetry presented here are primarily aimed at four-component calculations, but they are equally applicable to two-component calculations in which the spin-dependent operators are included at the self-consistent field (SCF) stage of a calculation.

scholarly journals On Certain Discontinuous Wave Functions

1947 ◽  
Vol 8 (1) ◽  
pp. 39-42
Author(s):  
A. Erdélyi
Keyword(s):  
Wave Equation ◽  
Wave Functions ◽  
Late Professor ◽  
Discontinuous Wave ◽  
The Many

Among the many solutions of the wave equation investigated by the late Professor Bateman there is one type which has so far received little attention.

Momentum distribution in molecular systems

1941 ◽  
Vol 37 (4) ◽  
pp. 397-405 ◽  
Author(s):  
W. E. Duncanson
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Momentum Distribution ◽  
Wave Functions ◽  
Appreciable Change ◽  
Hydrogen Molecular Ion ◽  
Molecular Ion ◽  
Molecular Systems ◽  
Similar Work ◽  
The One

The momentum distribution for the electron in the hydrogen molecular ion has been calculated for various wave functions, including the one used by James with which he obtained such a good value for the binding energy. The method adopted for this particular wave function is outlined and the results show appreciable change with improvement in the wave function. In conclusion there are discussed the implications of the present calculations on similar work on the H2 molecule.

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