Patrick Duffy

Comparison of local‐density and Hartree–Fock calculations of molecular polarizabilities and hyperpolarizabilities

This paper presents a comparison between density functional theory local density approximation (LDA) and Hartree–Fock approximation (HFA) calculations of dipole moments, polarizabilities, and first hyperpolarizabilities, using ‘‘comparable’’ basis sets, in order to assess the relative quality of the LDA and the HFA for calculating these properties. Specifically, calculations were done using basis sets of roughly double or triple zeta plus polarization quality, with and without added field‐induced polarization (FIP) functions, for the seven small molecules H2, N2, CO, CH4, NH3, H2O, and HF, using the HFA option in the program HONDO8 and the LDA options in the programs DMol and deMon. For the calculations without FIP functions, the results from HONDO8 HFA and deMon LDA, both of which use Gaussian basis sets, are very similar, while DMol, which uses a LDA numerical atomic orbital basis set, gives substantially better results. Adding FIP functions does much to alleviate these observed basis set artifacts and ...

Assessment of Gaussian-weighted angular resolution functions in the comparison of quantum-mechanically calculated electron momentum distributions with experiment

Abstract A critical assessment is made of the recently proposed momentum-averaged Gaussian-weighted (MAGW) method [A.O. Bawagan and C.E. Brion, Chem. Phys. 144 (1990) 167] of incorporating angular (or momentum) resolution into quantum-mechanically calculated momentum distributions for comparison with EMS measurements. In particular, the general efficacy of the proposed, semi-emperically based Gaussian angular (θ and ϕ) resolution functions as dimensioned in the MAGW method is tested by systematic application to high-level (essentially Hartree-Fock limit and/or configuration interaction) calculations of the momentum distributions of the outermost orbitals of a wide range of target species including Ne, Ar, Kr, Xe, H2O, and H2S. The folded calculations are compared with recent measurements. New highly accurate analytical mathematical procedures have been developed and confirm the adequacy of the previous Monte Carlo method for resolution folding. However, the new procedures result in substantial improvements over use of the Monte Carlo method for the graphical representation of the variation of the momentum resolution function with azimuthal angle. The respective merits of comparing folded theory and experiment as a function of nominal relative azimuthal angle (ϕ0) or of momentum are discussed. In the momentum representation, the question of whether it is preferable to use average or nominal momentum is further considered. Either choice is found to afford a reasonable basis for detailed comparison of folded theory and experiment. In all cases, the folded theory is found to be in good agreement with experiment when the Gaussian-weighted angular resolution functions are used, whereas less satisfactory overall agreement is obtained when the calculations are folded with earlier types of resolution-folding procedure. It is concluded that the Gaussian-weighted angular resolution functions, appropriately dimensioned, provide a satisfactory accounting for the experimental angular (or momentum) resolutions effects and that they can be used with reasonable confidence in future studies for the evaluation of molecular wavefunctions.

Accurate density-functional calculation of core-electron binding energies with a scaled polarized triple-zeta basis set. Twelve test cases and application to three C2H4O2 isomers

Abstract A scaling procedure based on Clementi and Raimondis rules for atomic screening was proposed for atomic orbital basis sets in the unrestricted generalized transition state (uGTS) model of density functional calculation of core-electron binding energies (CEBEs). The exchange-correlation potential is based on a combined functional of Beckes exchange (B88) and Perdews correlation (P86). This proposal was tested on CEBEs of twelve small molecules, including F 2 , N 2 and H 2 O, and applied to the computation of CEBEs of three isomers of C 2 H 4 O 2 : acetic acid (CH 3 COOH), methyl formate (HCOOCH 3 ), and glycolic aldehyde (CH 2 OHCHO). In all cases, the new scaled pVTZ basis performs almost as well as the much larger cc-pV5Z and the average absolute difference between the results from the scaled pVTZ and estimated complete basis set limits is 0.04 eV.

Evaluation of patients with pain following total hip replacement.

Ongoing pain after total hip replacement is a source of frustration to both the patient and the surgeon. A structured approach to the evaluation of patients with postoperative pain is essential. The key to such an approach is a meticulous patient history and physical examination. The results of relevant investigations allow an effective treatment plan to be quickly implemented.

One‐electron properties of several small molecules calculated using the local density approximation within density functional theory

Density functional theory (DFT) is a field enjoying a tremendous recent surge in popularity among theoretical and practical chemists alike because of its ability to more easily handle larger molecular systems than conventional ab initio methods. Until recently, however, assessment of the quality of the properties predicted (and therefore the charge density) from DFT had been limited mainly to dipole moments and their nuclear coordinate and electric field derivatives. This paper presents the calculated results for some of the one‐electron properties of the eight small molecules (NH3, PH3, H2O, H2S, HF, HCl, CO, and N2). The properties chosen weight different regions of the charge density, from either very close in or at the nucleus (e.g., δ, the electron density at the nucleus) to regions farther out from the nucleus (e.g., the diamagnetic susceptibility 〈r2〉). It is found that properties which depend on an accurate knowledge of the electron density near to the nucleus are predicted poorly by the local den...

Electron momentum spectroscopy of the valence orbitals of acetylene: Quantitative comparisons using near Hartree-Fock limit and correlated wavefunctions

Abstract Measurements of the complete valence shell binding energy spectrum (8–55 eV) and the corresponding orbital electron momentum distributions have been obtained using electron momentum spectroscopy. The measured momentum distributions are compared with SCF calculations using basis sets ranging from minimum basis set to very near Hartree-Fock limit in quality. The effects of relaxation and electron correlation are investigated using second-order Greens function calculations and also using configuration interaction (CI) methods. The CI calculations recover up to 66% of the estimated total parent correlation energy. In the case of acetylene all SCF calculations at the double zeta level and above give a reasonable description of the shapes of the momentum distributions and only minor differences result from inclusion of correlation and relaxation. This contrasts sharply with the situation for row two hydrides where inclusion of correlation has been found to be crucial. The calculated position and momentum density maps for the oriented C 2 H 2 molecule are compared with the experimental results. Detailed studies of the binding energy spectrum and momentum distributions in the inner valence region demonstrate that the satellite intensity overwhelmingly arises from 2σ g ionization with only a very small satellitec contribution expected from 2σ u ionization. The inner valence results are compared with earlier findings from photoelectron spectroscopy measurements and a range of theoretical calculations.

An investigation of the outermost orbital momentum distributions of formaldehyde, acetaldehyde and acetone, by electron momentum spectroscopy and quantum chemical calculations at the SCF and MRSD-CI levels

Abstract The outermost valence electron momentum profiles have been obtained at high-momentum resolution for acetone (5b 2 ) and acetaldehyde (10a′). These are compared with calculated profiles of wide ranging quality from minimal basis STO-3G to near Hartree-Fock limit SCF treatments, together with the outermost momentum profile of formaldehyde (2b 2 ) measured previously by Bawagan et al. (Chem. Phys. 128 (1988) 439). The effects of the addition of diffuse functions to the basis sets are examined for a number of properties. Many-body corrections to the independent particle SCF model are evaluated by multi-reference singles and doubles configuration interaction calculations of all three molecules. These are found to give large improvements for calculated total energy but only modest gains in agreement with the observed momentum profiles. The implications for the nature of chemical bonding in these orbitals is discussed in the context of the theoretical and experimental results.