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# Special Topics

Population analysis

Mulliken population analysis

R.S. Mulliken, Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I, J. Chem. Phys. 23, 1833 (1955)

HF stability analysis

J. Paldus and J. Cizek, Stability Conditions for the Solutions of the Hartree–Fock Equations for Atomic and Molecular Systems. II. Simple Open‐Shell Case, J. Chem. Phys. 52, 2919 (1970)
R. Seeger and J.A. Pople, Self‐consistent molecular orbital methods. XVIII. Constraints and stability in Hartree–Fock theory, J. Chem. Phys. 66, 3045 (1977)
T.D. Crawford, J.F. Stanton, W.D. Allen, and H.F. Schaefer III, Hartree–Fock orbital instability envelopes in highly correlated single-reference wave functions, J. Chem. Phys. 107, 10626 (1997)

Effective-Core Potentials

L.R. Kahn, P. Baybutt, and D.G. Truhlar, Ab initio effective core potentials: Reduction of all‐electron molecular structure calculations to calculations involving only valence electrons, J. Chem. Phys. 65, 3826 (1976)
A.V. Mitin and C. van Wüllen, Two-component relativistic density-functional calculations of the dimers of the halogens from bromine through element 117 using effective core potential and all-electron methods, J. Chem. Phys. 124, 064305 (2006); implementation used within CFour

Local correlation methods

definition of localized orbitals
P. Pipek and P.G. Mezey, A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions, J. Chem. Phys. 90, 4916 (1989); available within CFour
C. Edminston and K. Ruedenberg, Localized Atomic and Molecular Orbitals, Rev. Mod. Phys. 35, 457 (1963)
F. Boys, Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another, Rev. Mod. Phys. 32, 296 (1960); J.M. Foster and F. Boys Canonical Configurational Interaction Procedure, Rev. Mod. Phys. 32, 300 (1960); available within CFour

general concepts
S. Saebo and P. Pulay, Local treatment of electron correlation, Ann. Rev. Phys. Chem. 44, 213 (1993); review

local MP2

A. El Azhary, G. Rauhut, P. Pulay, and H.-J. Werner, Analytical energy gradients for local second-order Møller–Plesset perturbation theory J. Chem. Phys. 108, 5185 (1998); implementation within MOLPRO

local MP2 polarizabilities and NMR chemical shifts
J. Gauss and H.-J. Werner, NMR chemical shift calculations within local correlation methods: the GIAO-LMP2 approach, Phys. Chem. Chem. Phys. 2, 2083 (2000); pilot implementation

Basis-Set Superposition Error

definition
B. Liu and A.D. McLean, Accurate calculation of the attractive interaction of two ground state helium atoms, J. Chem. Phys. 59, 4557 (1973)

couterpoise correction
S.F. Boys and F. Bernardi, The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors, Mol. Phys. 19, 553 (1970)