Multiperturbation approach to potential energy surfaces for polyatomic molecules

Ab initio calculations including electron correlation are reported for the water and methylene molecules as a function of geometry. A large contracted gaussian basis set is used and the multiconfiguration wave functions, optimized by the iterative natural orbital procedure, include 277 and 617 configurations for H2O and CH2 respectively. The method of selecting configurations, yielding “first-order” wave functions, is discussed in some detail. For H2O, the SCF geometry is r=0,942 A, θ=105,8°, the correlated result is r=0,968 A, θ=103,2°, and the experimental r=0,957 A, θ=104,5°. The water stretching force constants, in millidynes/A, are 8,72 (SCF), 8,75 (CI), and 8,4 (experiment). Bending force constants are 0,88 (SCF), 0,83 (CI), and 0,76 (experiment). For methylene the SCF geometry is r=1,072 A, θ=129,5°, while the result from first-order wave functions is r=1,088 A, θ=134°. The predicted CH2 force constants are 6,16 (SCF) and 6,13 (CI) for stretching and 0,44 (SCF) and 0,33 (CI) for bending.

A systematic way of simultaneously handling relativistic and many-body effects for electric dipole transition probabilities is introduced. Relativistic many-body wave functions are generated using a relativistic configuration-interaction (RCI) approach, where the virtual space is represented by screened hydrogenic functions whose effective charges are determined during the RCI process. It is shown that the number of ``parents'' that must be kept in a first-order wave function may be minimized, using a procedure called reduce. The relativistic form of the first-order theory of oscillator strengths is used to determine which configurations are crucial. Application is made to the ${\mathrm{Tl}}^{+}$ 6${s}^{2}$\ensuremath{\rightarrow}6s6p $^{1}$,3${\mathrm{P}}_{1}$ transitions for which both nonorthonormality and core excitation effects are found to be crucial. For the allowed transition, our results (length and velocity) are in excellent agreement with experiment.

A moving interpolation technique which provides an accurate representation of potential energy surfaces for polyatomic molecules is presented. The method uses the ab initio energy, energy gradient, and second derivatives calculated at dynamically important configurations. The interpolant of the energy and its derivatives converges to the exact value with increasing number of data. A procedure is given for finding the optimum configurations at which ab initio calculations are performed. The method is demonstrated by application to the six-dimensional surface of a diatomic plus diatomic reaction.

We study a many-body system consisting of $N$ identical anyons in an external harmonic-oscillator potential. A partial set of exact solutions is obtained by using Jacobi coordinates. For completing the full investigation, we employ a perturbative method to compute those spectra, which have not been analytically obtained. Near the boson limit, we point out that the requirement of the boson being hard core is needed for performing the perturbative calculations, and the first-order $N$-anyon ground-state energies are explicitly presented by using a proper regulation procedure. Up to third perturbative order from the fermion limit, the three-anyon ground-state energy corrections are explicitly presented. Finally we compute the first-order three-anyon ground-state wave function near the fermion limit.

A post-VBSCF method, called valence bond second-order perturbation theory (VBPT2), is developed in this paper and is shown to be (i) economical and (ii) at par with more sophisticated VB and MO-based methods. The VBPT2 method starts with VBSCF using a minimal structure set. Subsequently, the Møller-Plesset (MP) partition of the zeroth-order Hamiltonian is obtained by introducing a generalized Fock matrix constructed from the VBSCF density matrix. The first-order wave function is expressed in terms of singly and doubly excited VB structures, which are generated by replacing occupied orbitals by virtual orbitals, the latter being defined as orthogonal to the occupied orbitals. The VBPT2 method retains the simplicity of a VB presentation by condensing contributions from the excited structures into the minimal number of fundamental structures that are involved in the VBSCF calculation. The method is tested by calculating the bond energies of H(2), F(2), N(2), O(2), the barrier of identity hydrogen abstraction reaction, the atomization energy and a potential energy curve for the water molecule and the structural weights and covalent-ionic resonance energy of F(2). It is shown that the VBPT2 method gives results in good agreement with those of the VBCI method and molecular-orbital based methods such as MRPT and MRCI at the same truncation levels. However, the computational effort is greatly reduced, compared to that of VBCI. Future potential directions for the development of the VBPT2 method are outlined.

Using two different extended basis sets of Slater-type orbitals, we have carried out a study of the correlation energy and hyperfine structure of the $^{4}S$ ground state of the nitrogen atom. Symmetry-adapted pair correlations were evaluated with respect to a multiconfiguration reference state, the first-order wave function. It was found that each symmetry-adapted pair correlation energy could be rather accurately (to about 3%) approximated as a sum of effects due to symmetry-determined classes of configurations. Using the larger of the two basis sets, the effects of 1633 configurations, constructed from 19 530 distinct Slater determinants, were considered. With this basis set the correlation energy obtained was 0.181 75 hartree, compared to the estimated correlation energy 0.186 hartree. It was found that pair correlations had large canceling effects on the hyperfine structure, the net result of which was a spin density 77% of experiment, and only slightly larger than the first-order spin density, which includes core polarization effects. Several points in common are found in a comparison with the many-body perturbation theory results of Dutta, Matsubara, Pu, and Das. The most useful and interesting result of the present work is a clear picture of the different effects which contribute to the correlation energy and hyperfine structure of $^{4}S$ N.

In ultrasmall systems such as nanoscale metallic grains, the discrete energy spectrum together with electron correlations may give dramatic properties at low temperatures. Among others, the Kondo effect has attracted considerable attention recently. In particular, parity effects should emerge depending on the number of total electrons: e.g., the Kondo effect appears (disappears) at low temperatures for an even (odd) number of electrons, yielding a finite (divergent) susceptibility when the Kondo temperature is smaller than the level spacing. More remarkable parity effects were pointed out by Thimm et al. in dynamical as well as transport properties when the mean level spacing is nearly equal to (or even smaller than) the Kondo temperature. They found that the Kondo resonance is discretized into a series of subpeaks with one main peak (two split peaks) at the Fermi level for an even (odd) number of electrons. They claimed that this behavior characterizes the Kondo effect in a metallic grain, which also leads to the oscillation behavior in the conductance. Although such parity effects are naturally expected, it is not clear how a single (double) peak structure is developed in the Kondo resonance depending on whether the electron count is even or odd. More generally we ask which aspect is universal in the parity effects. In this note we revisit this question about the Kondo effect in a metallic grain. Using the self-consistent second-order perturbation expansion, we demonstrate that although the parity effect indeed appears generically, the shape of the spectrum exhibits nonuniversal properties depending on a model system employed, in contrast to the claim of Thimm et al. In the nonequilibrium case, we find the oscillation behavior possessing the parity effect in the differential conductance. We consider a small metallic grain including a magnetic impurity described by the Anderson Hamiltonian,

The computation of the spin–orbit interaction is discussed for electronic wave functions expressed in the new nonlinear expansion form. This form is based on spin eigenfunctions using the graphical unitary group approach (GUGA). The nodes of a Shavitt graph in GUGA are connected by arcs, and a Configuration State Function (CSF) is represented as a walk along arcs from the vacuum node to a head node. The wave function is a linear combination of product functions each of which is a linear combination of all CSFs, wherein each CSF coefficient is a product of nonlinear arc factors. When the spin–orbit interaction is included the Shavitt graph is a union of single‐headed Shavitt graphs each with the same total number of electrons and orbitals. Thus spin–orbit Shavitt graphs are multiheaded. For full‐CI multiheaded Shavitt graphs, analytic expressions are presented for the number of walks, the number of nodes, the number of arcs, and the number of node pairs in the associated auxiliary pair graph. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

where the biological activity is expressed as the reciprocal of the concentration that elicit a given biological, pharmacological or toxicological endpoint such as ED 50 (effective dose 50%), IC 50 (inhibitory concentration 50%) or LD 50 (lethal dose 50%), and where x i is the i predictor (from a set of n predictors) raised to the powers from 1 to m and weighted by its coefficients a ij obtained from a multivariate statistical fitting [4,5]. Usually, most of the coefficients a ij can be zero, leading to much simpler looking QSAR models than the general form in Equation 1, as in the example below. Often, other functions of x i are used in the QSAR model such as the logarithmic or exponential function instead of a simple power expansion as in Equation 1. As a simple illustration of the operation of Equation 1 is the following example of a QSAR model to predict the inhibitory effect of 3-nitroflavones (3NF) based on a single predictor, x (the energy of the highest occupied molecular orbital, E HOMO ) raised to the power 1 (see also [6]). Invasive tumor growth and metastasis are sustained by angiogenesis (the formation of new blood vessels [7,8]), which led Folkman to suggest anticancer therapies by the use of antiangiogenic agents [9,10]. Lichtenberg et al. have shown that the antiangiogenicity of six 3NF is correlated with the energies of the highest occupied molecular orbital, E HOMO, the lower the oxidation potential the greater the inhibitory effects on several biomarkers of angiogenesis [11,12]. These authors report the following correlation between the E HOMO and the IC 50 of six 3NF for inhibition of proliferation of microvascular endothelial HMEC-1 cells after 72 h of incubation:

Projection method, cranking condition and collective energy

The streamer zone of positive leader during the breakthrough phase of long sparks was experimentally investigated with two methods. One of the methods is the analysis of streamer‐zone images obtained with a high‐speed framing camera with image enhancement. This method allowed us to estimate the spatial distribution of streamer density and low‐frequency conductivity in the streamer zone. The other method is the microwave probing, which we applied for the first time to long sparks. The attenuation of microwave beam in the streamer zone in our experiments is proportional to the total number of free electrons inside the microwave beam. Experimental data on the microwave attenuation combined with the streamer density found using the first method allowed us to estimate the total number of free electrons in one streamer. The following parameters were obtained. The streamer density in the center of the streamer zone is (0.6–1) · 105 m−3, and the total number of streamers in the streamer zone is 4 · 105–106. The average total number of free electrons in one streamer is about 3 · 1010. Low‐frequency conductivity on the axis of streamer zone was estimated to be typically 2 · 10−5 S/m, which is similar to that estimated for corona sheath in lightning. Both methods are based on the assumption of constancy of electric field and similarity of all streamers inside the streamer zone. The overall results of this study are generally consistent with this assumption.

By considering the particular case of the 2s21S state of helium, it is shown that in the Hartree–Fock approximation autoionizing states of atoms have square-integrable wave functions and are, therefore, bound states. It follows that autoionization is a correlation effect. The autoionizing states must have non-square-integrable wave functions. The origin of the breakdown of the square integrability is studied with the help of a spectral analysis of the first-order wave function.

We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body Hamiltonian is relativistically covariant. It can be easily separated in terms of the center-of-mass and the relative motion of any two-body subsystem. It can also be separated into an unperturbed Hamiltonian with a residual interaction. In a system of two-body composite particles, the solutions of the unperturbed Hamiltonian are relativistic two-body internal states, each of which can be obtained by solving a relativistic Schr\"odinger-like equation. The resultant two-body wave functions can be used as basis states to evaluate reaction matrix elements in the general N-body problem. We prove a relativistic version of the post-prior equivalence which guarantees a unique evaluation of the reaction matrix element, independent of the ways of separating the Hamiltonian into unperturbed and residual interactions. Since an arbitrary reaction matrix element involves composite particles in motion, we show explicitly how such matrix elements can be evaluated in terms of the wave functions of the composite particles and the relevant Lorentz transformations.

A highly optimized code for calculating atomic data at neutron star magnetic field strengths using a doubly self-consistent Hartree–Fock–Roothaan method

We present a detailed study of persistent current and low-field magnetic susceptibility insingle isolated normal metal mesoscopic rings and cylinders in the tight-binding model withhigher-order hopping integral in the Hamiltonian. Our exact calculations show that order ofmagnitude enhancement of persistent current takes place even in the presenceof disorder if we include the higher-order hopping integral in the Hamiltonian.In strictly one-channel mesoscopic rings the sign of the low-field currents canbe predicted exactly even in the presence of impurity. We observe that perfectrings with both odd and even numbers of electrons support only diamagneticcurrents. On the other hand in the disordered rings, irrespective of realization ofthe disordered configurations of the ring, we always get diamagnetic currentswith odd numbers of electrons and paramagnetic currents with even numbersof electrons. In mesoscopic cylinders the sign of the low-field currents cannotbe predicted exactly since it strongly depends on the total number of electrons,Ne, and also on the disordered configurations of the system. From the variation of persistentcurrent amplitude with system size for constant electron density, we conclude that theenhancement of persistent current due to additional higher-order hopping integrals isvisible only in the mesoscopic regime.