[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

The relatively small diffuse function-augmented basis set, 3-21+G, is shown to describe anion geometries and proton affinities adequately. The diffuse sp orbital exponents are recommended for general use to augment larger basis sets.

Efficient diffuse function‐augmented basis sets for anion calculations. III. The 3‐21+G basis set for first‐row elements, Li–F

A new algorithm is presented for obtaining points on a steepest descent path from the transition state of the reactants and products. In mass‐weighted coordinates, this path corresponds to the intrinsic reaction coordinate. Points on the reaction path are found by constrained optimizations involving all internal degrees of freedom of the molecule. The points are optimized so that the segment of the reaction path between any two adjacent points is given by an arc of a circle, and so that the gradient at each point is tangent to the path. Only the transition vector and the energy gradients are needed to construct the path. The resulting path is continuous, differentiable and piecewise quadratic. In the limit of small step size, the present algorithm is shown to take a step with the correct tangent vector and curvature vector; hence, it is a second order algorithm. The method has been tested on the following reactions: HCN→CNH, SiH2+H2→SiH4, CH4+H→CH3+H2, F−+CH3F→FCH3+F−, and C2H5F→C2H4+HF. Reaction paths calculated with a step size of 0.4 a.u. are almost identical to those computed with a step size of 0.1 a.u. or smaller.

An improved algorithm for reaction path following

https://www.tddft.org/TDDFT2004/PracticalSessions/papers/ahlrichs_casida.pdf

Treatment of electronic excitations within the adiabatic approximation of time dependent density functional theory

Time-dependent density-functional (TDDFT) methods are applied within the adiabatic approximation to a series of molecules including C70. Our implementation provides an efficient approach for treating frequency-dependent response properties and electronic excitation spectra of large molecules. We also present a new algorithm for the diagonalization of large non-Hermitian matrices which is needed for hybrid functionals and is also faster than the widely used Davidson algorithm when employed for the Hermitian case appearing in excited energy calculations. Results for a few selected molecules using local, gradient-corrected, and hybrid functionals are discussed. We find that for molecules with low lying excited states TDDFT constitutes a considerable improvement over Hartree–Fock based methods (like the random phase approximation) which require comparable computational effort.

An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules

Algorithms for finding local minima, maxima, and saddle points on surfaces, starting from an arbitrary point are presented. These algorithms are based on making a local approximation to the surface in the form of a rational function constructed from the local first and second derivatives of the surface. All parameters of these algorithms required for stepping across the surface are determined in nonarbitrary ways. The convergence of these procedures to the desired stationary point is shown to be quadratic. Applications for stationary-point searches on two model surfaces are also given for illustrative purposes. 12 references, 4 figures.

Search for stationary points on surfaces

Developpement d'un algorithme pour la marche automatisee sur une surface, en combinant l'approximation quadratique locale a la surface d'energie potentielle et une mise a l'echelle d'une coordonnee active

Walking on potential energy surfaces

Second Quantization-based Methods in Quantum Chemistry

Passing the one-billion limit in full configuration-interaction (FCI) calculations

In characterizing anion states either experimentally or theoretically different techniques are required for bound and temporary or metastable anions. Anions that lie energetically above the ground state of the neutral molecule (or atom) are called temporary anions since they are unstable with respect to electron detachment. Temporary anions generally have lifetimes in the range of 10-13-10-16 s and thus are difficult to study by using optical spectroscopic methods. Various types of electron-impact spectroscopy have proven particularly valuable for characterizing temporary anions.’I2 Some of these experimental methods are discussed in the accompanying paper3 of Jordan and Burrow. Because temporary anion states lie in the continuum of the neutral species plus free electron, they cannot be treated in general by means of a straightforward variational calculation. Techniques designed for their study are discussed later in this paper. Bound or stable anions lie energetically below the ground state of their parent neutral and can be studied by a variety of experimental methods including photodetachment spectroscopy* and laser photoelectron spectro~copy.~ The contribution by Wetzel and Brauman in this issue covers many of these experimental techniques. Theoretically they can be characterized by using traditional quantum chemical methods such as the self-consistent field (SCF), configuration interaction (CI), multiconfiguration self-consistent field (MCSCF), and manybody techniques, although extra care must be exercised for reasons outlined below. The ab initio theoretical study of stable atomic and molecular negative ions involves complications not encountered in analogous studies of neutral or cationic species. In particular, the diffuse spatial extent of the outermost orbitals of anions places additional requirements on any quantum chemical calculation. Within the conventional LCAO-MO finite atomic basis approach, adequate description of diffuse charge densities requires that diffuse atomic orbitals be added to the core-and-valence atomic basis sets. Because computational expense varies as a high power of the size of the atomic orbital basis set, this greatly increases the computer-time requirements for negative ion calculations. Diffuse charge densities correspond to weak binding energies and low average values of kinetic energy. The weak binding energies imply that any method used to compute the electron affinities (EA) must be very reliable. The low classical kinetic energies suggest that energy transfer from vibrational and rotational degrees of freedom to the electronic degrees of freedom may be more facile than in neutral or cationic species where the more rapidly moving electrons readily “track” the motion of the underlying nuclei. Thus, the neglect of nonadiabatic interactions, which is the cornerstone upon which the concept of the potential energy surface is predicated, is less likely to be reasonable for anions. For most classes of molecules, the calculation of accurate EA’S requires that the molecular orbital picture be corrected by including so-called electron correlation effeds. In the self-consistent field (SCF) Hartree-Fock molecular orbital model of electronic structure, each electron is allowed to “feel” the other electrons only via an average interaction potential. This potential consists of the averaged Coulomb and exchange interaction

Jack Simons

Papers

Search for stationary points on surfaces

Walking on potential energy surfaces

Second Quantization-based Methods in Quantum Chemistry

Passing the one-billion limit in full configuration-interaction (FCI) calculations

Ab initio electronic structure of anions