Robert C. Morrison

Variational principles for describing chemical reactions: Condensed reactivity indices

Two recent papers [P. W. Ayers and R. G. Parr, J. Am. Chem. Soc. 122, 2010 (2000); 123, 2007 (2001)] have shown how variational principles for the energy may be used to derive and elucidate the significance of the chemical reactivity indices of density-functional theory. Here, similar ideas are applied, yielding a systematic, mathematically rigorous, and physically sound approach to condensed reactivity indices. First, we use the variational principle for the energy to derive an expression for the condensed Fukui function index in terms of the condensed hardness kernel. Next, we address an important open problem pertaining to condensed reactivity indices: when (if ever) is the condensed Fukui function for an atom in a molecule negative? In particular, our analysis confirms the observation, hitherto based only on computational evidence, that the Hirshfeld partitioning is optimal for obtaining non-negative Fukui functions. We also hypothesize that the strong diagonal dominance of the condensed hardness kern...

Extension of Koopmans’ theorem. II. Accurate ionization energies from correlated wavefunctions for closed‐shell atoms

Extended Koopmans’ theorem ionization energies are presented for MC−SCF wavefunctions of the 1s2 2s2 (1S) ground state isoelectronic series, Li− through O4+, and also for some larger CI wavefunctions of Be and B+. Correlation in these reference states reduces the error in the Koopmans’ ionization energy for the 2s electron to approximately 0.01−0.08 eV (1/100−1/20 the SCF Koopmans’ error) in all states except the negative ion, for which the MC−SCF extended Koopmans’ error of 0.25 eV was of the same magnitude but of opposite sign to the SCF error. Our extended Koopmans’ energies for 1s ionization were only slightly better than the corresponding SCF values. Koopmans’ theorem does not yield a 2p ionization energy (1s2 2s2 → 1s2 2p), but the extended Koopmans’ theorem yields an ionization energy whose error is about one−third the SCF 2s error.

Fermi-Amaldi model for exchange-correlation: atomic excitation energies from orbital energy differences

Motivated by recent work on asymptotic correct exchange-correlation potentials, this paper investigates properties of the Fermi-Amaldi model for the exchange-correlation potential. It compares atomic excitation energies for Hydrogen through Argon to orbital energy differences computed using the exact Kohn-Sham potential and the Fermi-Amaldi approximation to the Kohn-Sham potential. While the Fermi-Amaldi model is not a particularly good model for the exchange-correlation energy, its eigenvalue spectrum is semi-quantitatively correct for alkali metals and alkaline earths. However, it is not accurate for p-block atoms, which suggests that the Fermi-Amaldi model may not be a superior choice for asymptotically correcting exchange-correlation potentials. It is suggested that asymptotic correction involving the Fukui function would give better results.

The extended Koopmans’ theorem and its exactness

The extended Koopmans’ theorem (EKT) is shown to give accurate and potentially exact values for the lowest ionization potential (IP). Accurate results are reported for LiH, H+5, He2, and Li2. Results obtained for the lowest IP’s of LiH and He2 are nearly identical with those obtained by taking the difference of the total energies from separate, full configuration interaction calculations on the N‐electron and the (N−1)‐electron systems. The differences between the two IP calculations for a series of increasingly larger basis sets are 0.0017, 0.0004, and 0.0001 eV for LiH and are 0.0154, 0.0018, and 0.0007 eV for He2. The implication is that the lowest IP can be calculated to arbitrary accuracy. The EKT method is easily implemented as part of a multiconfigurational self‐consistent‐field calculation by diagonalizing the matrix of Lagrange multipliers with the first‐order reduced density matrix as the metric.

Electron correlation and noninteracting v-representability in density functional theory: The Be isoelectronic series

Reference densities from accurate configuration interaction wave functions for the beryllium isoelectronic series were used to solve the Kohn–Sham equations using a constrained search that minimizes the kinetic energy. For Z<25 in the series, a single Kohn–Sham determinant is sufficient to give the minimum kinetic energy. For higher Z a single Kohn–Sham determinant produces 2p eigenvalues that are lower than the 2s eigenvalues, and a kinetic energy that is not the minimum that can be obtained from an antisymmetric wave function that produces the reference density. Fractional occupation numbers are required to obtain the minimum kinetic energy, and at the minimum kinetic energy the 2s and 2p eigenvalues become equal. Values of the optimal 2p occupation numbers approach 0.09 for high Z.

Auditory presentation of experimental data

Our research group has been working for several years on the development of auditory alternatives to visual graphs, primarily in order to give blind science students and scientists access to instrumental measurements. In the course of this work we have tried several modes for auditory presentation of data: synthetic speech, tones of varying pitch, complex waveforms, electronic music, and various non-musical sounds. Our most successful translation of data into sound has been presentation of infrared spectra as musical patterns. We have found that if the stick spectra of two compounds are visibly different, their musical patterns will be audibly different. Other possibilities for auditory presentation of data are also described, among them listening to Fourier transforms of spectra, and encoding data in complex waveforms (including synthetic speech).

Extension of Koopmans’ theorem. IV. Ionization potentials from correlated wavefunctions for molecular fluorine

Uncorrelated (Hartree–Fock) ab initio calculations have proven unable to predict the energy ordering of 3σg and 1πu molecular orbitals as observed in electron spectroscopy experiments on fluorine (F2). The correct ordering was obtained, however, by applying an extension of Koopmans’ theorem [J. Chem. Phys. 62, 113 (1975)] to an MC–SCF correlated wavefunction for F2 which contained only one configuration beyond the one used in Hartree–Fock. With the addition of still further configurations to the wavefunction for the neutral molecule, the ordering of the extended Koopmans’ valence orbital energies was maintained and the correspondence improved between those and the experimental values.

A Microcomputer-Based Laboratory Aid for Visually Impaired Students

Built with high-performance industrial boards, this portable microcomputer functions both as a CP/M-based data acquisition and analysis system with voice output and as a talking scientific calculator.

Approximate scaling properties of the density functional theory Tc for atoms

Revealed are scaling properties for T(c)[rho], the kinetic-energy component of the correlation energy density functional for atoms, in terms of the total number of electrons N, the nuclear charge Z, and the total electron density at the nucleus rho(0). T(c) scales well as Nrho(0)/Z(8/3) for both neutral atoms up to Z=18 and the four-electron Be-like cationic species. A model is given that describes these findings, involving a density encoding the cusp information and an effective potential going like r(-4/3).

Comment on ‘‘The exactness of the extended Koopmans’ theorem: A numerical study’’ [J. Chem. Phys. 98, 3999 (1993)]

Recent systematic, numerical calculations by Sundholm and Olsen [J. Chem. Phys. 98, 3999 (1993)] support the proof that the lowest ionization potential can in principle be obtained exactly using the extended Koopmans’ theorem. Because of the nature of their calculations it cannot be concluded that only the lowest ionization potential could be obtained exactly using the extended Koopmans’ theorem.