. Can. J. Chem. 70, 6 12 (1992). Relativistic compact effective potentials (RCEP), which replace the atomic core electrons in molecular calculations, have been derived from numerical Dirac-Fock atomic wavefunctions using shape-consistent valence pseudo-orbitals and an optimizing procedure based on an energy-overlap functional. Potentials are presented for the third-, fourth-, and fifthrow atoms of the Periodic Table (excluding the lanthanide series). The efficiency of molecular calculations is enhanced by using compact Gaussian expansions (no more than three terms) to represent the radial components of the potentials, and energy-optimized, shared-exponent, contracted-Gaussian atomic orbital basis sets. Transferability of the potentials has been tested by comparing calculated atomic excitation energies and ionization potentials with values obtained from numerical relativistic Hartree-Fock calculations. For the alkali and alkaline earth atoms, core polarization potentials (CPP) have been derived which may be added to the RCEP to make possible accurate molecular calculations without explicitly including core-valence correlating configurations in the wavefunction. Introduction two rows (Li-Ar) of the Periodic Table ( 5 ) . We designatedThe use of atomic effective core potentials (ECP) and model potentials (MP) to eliminate chemically inactive atomic core electrons from quantum mechanical calculations has become routine in the past decade. The development of such potentials in the early 1970's and applications through the mid-1980's have been reviewed previously (1). The use of such potentials in molecular calculations has gained widespread acceptance, and sets of effective potentials are included in widely distributed quantum chemistry programs such as HONDO ( 2 ) , GAMESS (3), and GAUSSIAN (4). We previously published accurate compact effective potentials (CEP) and matching basis sets for the atoms of the first '~u t h o r to whom correspondence may be addressed. 'NRC-NAS Postdoctoral Fellow, NIST, 1984NIST, -1986. Current address: California State University, San Marcos, CA 92096, U.S.A.Primed in Canada -the potentials "compact" because they are represented analytically by small Gaussian expansions and, therefore, offer significant economy in molecular calculations where the computer time required to construct the electronic integrals is proportional to the complexity of the potentials. In this report, we present effective potentials and basis sets of similar quality for the third, fourth, and fifth rows of the Periodic Table derived from numerical, relativistic, Dirac-Fock atomic wavefunctions. The analytic expansions of these POtentials are also limited to a few Gaussian terms (three or less), so we have designated them as "relativistic compact effective potentials" (RCEP).Recently, several compilations of model potentials and effective core potentials for use in molecular calculations have appeared in the literature. For the heavier atoms, relativistic effects have been incorporated by deriving the potentials ...

Compact effective potentials, which replace the atomic core electrons in molecular calculations, are presented for atoms in the first and second rows of the periodic table. The angular-dependent components of these potentials are represented by compact one- and two-term Gaussian expansions obtained directly from the appropriate eigenvalue equation. Energy-optimized Gaussian basis set expansions of the atomic pseudo-orbitals, which have a common set of exponents (shared exponents) for the s and p orbitals, are also presented. The potentials and basis sets have been used to calculate the equilibrium structures and spectroscopic properties of several molecules. The results compare extremely favorably with corresponding all-electron calculations.

In this paper a complete set of effective core potentials (ECPs) and valence basis sets for the lanthanides (Ce to Lu) are derived. These ECPs are consistent not only within the lanthanide series, but also with the third-row transition metals which bracket them. A 46-electron core was chosen to provide the best compromise between computational savings and chemical accuracy. Thus, the 5s and 5p are included as ‘‘outer’’ core while all lower energy atomic orbitals (AOs) are replaced with the ECP. Generator states were chosen from the most chemically relevant +3 and +2 oxidation states. The results of atomic calculations indicate that the greatest error vs highly accurate numerical potential/large, even-tempered basis set calculations results from replacement of the large, even-tempered basis sets with more compact representations. However, the agreement among atomic calculations remains excellent with both basis set sizes, for a variety of spin and oxidation states, with a significant savings in time for the optimized valence basis set. It is expected that the compact representation of the ECPs and valence basis sets will eventually encourage their use by computational chemists to further explore the bonding and reactivity of lanthanide complexes.

The effective fragment potential (EFP) method is described and its capabilities illustrated using several applications. The original method, EFP1, was primarily developed to describe aqueous solvation, by representing Coulombic, induction and repulsive interactions via one-electron terms in the ab initio Hamiltonian. It is demonstrated, using water clusters, the Menshutkin reaction and the glycine neutral/ zwitterion equilibrium, that agreement with both fully ab initio calculations and experiment are excellent. More recently, the model has been extended so that it can treat any solvent, as well as more difficult links across covalent bonds. Disciplines Chemistry CommentsThis article is from Journal of Physical Chemistry A 105 (2001) The effective fragment potential (EFP) method is described and its capabilities illustrated using several applications. The original method, EFP1, was primarily developed to describe aqueous solvation, by representing Coulombic, induction and repulsive interactions via one-electron terms in the ab initio Hamiltonian. It is demonstrated, using water clusters, the Menshutkin reaction and the glycine neutral/zwitterion equilibrium, that agreement with both fully ab initio calculations and experiment are excellent. More recently, the model has been extended so that it can treat any solvent, as well as more difficult links across covalent bonds.

An effective fragment model is developed to treat solvent effects on chemical properties andreactions. The solvent, which might consist of discrete water molecules, protein, or othermaterial, is treated explicitly using a model potential that incorporates electrostatics,polarization, and exchange repulsion effects. The solute, which one can most generally envision as including some number of solvent molecules as well, is treated in a fully ab initio manner, using an appropriate level of electronic structure theory. In addition to the fragment model itself, formulae are presented that permit the determination of analytic energy gradients and, therefore, numerically determined energy second derivatives (hessians) for the complete system. Initial tests of the model for the water dimer and water-formamide are in good agreement with fully abinitio calculations. An effective fragment model is developed to treat solvent effects on chemical properties and reactions. The solvent, which might consist of discrete water molecules, protein, or other material, is treated explicitly using a model potential that incorporates electrostatics, polarization, and exchange repulsion effects. The solute, which one can most generally envision as including some number of solvent molecules as well, is treated in a fully ab initio manner, using an appropriate level of electronic structure theory. In addition to the fragment model itself, formulae are presented that permit the determination of analytic energy gradients and, therefore, numerically determined energy second derivatives ͑hessians͒ for the complete system. Initial tests of the model for the water dimer and water-formamide are in good agreement with fully ab initio calculations.

A formula to calculate the charge penetration energy that results when two charge densities overlap has been derived for molecules described by an effective fragment potential (EFP). The method has been compared with the ab initio charge penetration, taken to be the difference between the electrostatic energy from a Morokuma analysis and Stone's Distributed Multipole Analysis. The average absolute difference between the EFP method and the ab initio charge penetration for dimers of methanol, acetonitrile, acetone, DMSO, and dichloromethane at their respective equilibrium geometries is 0.32 kcal mol −1 . Walter J. Stevens Physical and Chemical Properties Division (838), National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8380 ͑Received 30 December 1999; accepted 10 February 2000͒ Keywords Ab initio calculations, Carrier density, Electrostatics Disciplines Chemistry Comments This article is fromA formula to calculate the charge penetration energy that results when two charge densities overlap has been derived for molecules described by an effective fragment potential ͑EFP͒. The method has been compared with the ab initio charge penetration, taken to be the difference between the electrostatic energy from a Morokuma analysis and Stone's Distributed Multipole Analysis. The average absolute difference between the EFP method and the ab initio charge penetration for dimers of methanol, acetonitrile, acetone, DMSO, and dichloromethane at their respective equilibrium geometries is 0.32 kcal mol Ϫ1 .

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