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• W1567600838 abstract "Every electron is in either an occupied or a virtual level. Slater averaged the exchange potential of the homogeneous electron gas over all occupied orbitals to obtain a quantity that, by dimensional analysis alone, must be proportional to the cube root of the uniform density of the homogeneous electron-gas problem. Slater's average proportionality constant is reduced by a factor of 2/3 in a variational treatment that samples only electrons at the Fermi energy, which separates the energy eigen values of occupied and virtual orbitals in density functional theory (DFT). Schwarz found the values of that proportionality constant, α, which give the Hartree–Fock (HF) energy of the atom for each element. Any general method capable of using various α is called an “Xα” method. Any such method that uses Schwarz’ values of α can be said to be variational, if variational is taken to mean bounding the exact energy from above, because HF bounds the exact energy from above. The meaning of variational advocated in this work is mathematically variational, consistent Roothaan's work. For the rest of this work, the term “Xα” has been restricted to mean using the HF values of α. This chapter details the robust and variational fitting, the Slater–Roothaan method, symmetry and balanced DFT dynamics, and 2-D chemical dynamics. Spatial symmetry significantly speeds up calculations using effective quantum–chemical codes. Singlet H 2 is not stable enough relative to two completely polarized hydrogen atoms. The Xα method has been made analytic and variational via single-center, linear-combination-of-Gaussian-type-orbital (LCGTO), robust, and variational fitting. It has an independent parameter for each element that can be optimized to give some chemical property for each element and GTO orbital basis set. Despite well-flexibility the method behaves well for molecular dynamics involving more than one element— that is, multiple α's." @default.
• W1567600838 created "2016-06-24" @default.
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• W1567600838 date "2003-01-01" @default.
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• W1567600838 title "Quantum-Chemical Dynamics with the Slater-Roothaan Method" @default.
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• W1567600838 doi "https://doi.org/10.1016/s1380-7323(03)80007-9" @default.
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