Shaping the density to fit one‐electron properties: Constrained RHF calculations on N₂, FH, CO, and LiH

Abstract

The molecular density required to give the correct values for one-electron properties is rarely given by wave functions obtained from variation methods based on the total energy or the eigenvalues. Perhaps if we knew how the density should be shaped in any particular volume to fit a particular property, the whole molecular density might then be properly described to fit the whole volume. The secant-parametrization procedure is used to constrain minimum basis set RHF wave functions for N2, FH, CO, and LiH to determine the effects of different constraints on RHF wave functions, and to see how constraints improve the quality of small basis set RHF wave functions. Ode-electron property expectation values, energies, and unweighted and property weighted populations and electron density difference profiles are used to analyze the constrained wavefunctions. With the information from the constrained wave functions it should be possible to select a LCAO-CI basis and states to give the correct density for all properties. This should map onto the constrained wave function in the region of the constraint and at the same time minimize the energy of the total molecular wave function. Such a density would be suitable for the density analyses favored by Bader and Nguyen-Dang [Adv. show the real atom needed to generate the molecule. to the diamagnetic susceptibility, r i ; the electronic component of the Hellrnann-Feynman electric field strength at nucleus A (and B ) , E> ; the electronic component of the electric field gradient at nucleus A (and B ) , -qX; the nuclearelectronic repulsion energy, -V,, ; the one-electron contribution to the total energy, T + V,, ; and the total Hellmann-Feynrnan force F. Nucleus A (F, C, or Li) is the coordinate origin and nucleus B (H or 0) is at Re along the positive x axis. "Exact" expectation values for these properties were from experimental and theoretical data [ 1-31. The constrained calculations used the secantparametrization method [4]. * Owing to symmetry there are only seven nontrivial constraints for N2. t

Comparison of the RHF, NDDO, and MOM molecular one‐electron expectation values calculated using minimum basis sets with Slater, Burns, Clementi, and BLMO exponents

“…The difference between the Slater and BLMO values of -0; is small compared with the estimated error in the value. 42 The BLMO value of -0; is very close to the result obtained by Bender and David~on.~' For both -0; and r," the values using Burns exponents are too large.…”

“…Exponent optimization also builds up charge density in the internuclear region,17J8*44 giving more attractive E i and E i and reduces the size (r,") and asymmetry (-0,") of the overall charge density distribution, while energy-related properties, T, ri', -V, , , and T + V, , are relatively i n s e n~i t i v e ?~-~~'~~ For energy related properties the expectation values with Slater exponents agree as well with the experimental and theoretical values, as the corresponding BLMO values. 42 For FH, LiH, and CO, exponent optimization improves the electric field and field gradient at each nucleus; the electric field gradient is particularly sensitive to exponent optimization,'% 2o and the improvement is usually substantial and reflects the greater quadrupolar polarization of the charge density distribution near each nucleus due to contraction and expansion of the 2pa and 2pn AOS, respectively, which is not taken into account in the well-known theories of molecular nuclear quadrupole coupling constants of Townes and D a i l e~,~~ and Cotton and Harris.48…”

A possible resurrection of the abinitio maximum overlap (MOM) method

“…Of the procedures for maximum overlap (7,8,(15)(16)(17)(18)(19)(20)(21)(22), that of Lykos and Schmeising (20) was most suitable for the present study, because their MOM wavefunctions can be directly compared with RHF (21,22) and NDDO' wavefunctions. Secondly, the secant-parameterization method used in the constrained RHF calculations (21) is easily adapted to this version of the MOM method.…”