Correlation energy of two electrons in the high-density limit

We consider the high-density-limit correlation energy \Ec in $D \ge 2$ dimensions for the $^1S$ ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the \Ec values are strikingly similar, depending strongly on $D$ but only weakly on the external potential. We conjecture that, for large $D$, the limiting correlation energy \Ec \sim -\delta^2/8 in any confining external potential, where $\delta = 1/(D-1)$.Comment: 4 pages, 0 figur

Excitation Gap from Optimized Correlation Functions in Quantum Monte Carlo Simulations

We give a prescription for finding optimized correlation functions for the extraction of the gap to the first excited state within quantum Monte Carlo simulations. We demonstrate that optimized correlation functions provide a more accurate reading of the gap when compared to other `non-optimized' correlation functions and are generally characterized by considerably larger signal-to-noise ratios. We also analyze the cost of the procedure and show that it is not computationally demanding. We illustrate the effectiveness of the proposed procedure by analyzing several exemplary many-body systems of interacting spin-1/2 particles.Comment: 11 pages, 5 figure

Ab-initio-MO-Studie Methyl- und Phenyl-substituierter Allenyl-Kationen

An den Methyl- und Phenyl-substituierten Allenyl-Kationen 3 - 12 (Tab. 1) wurden ab-initio-MO-Berechnungen unter Verwendung des STO-3G Basissatzes durchgeführt. Die berechneten Bindungslängen und Ladungsverteilungen zeigen Delokalisierung der positiven Ladung an, wie in Formel 1 gezeigt. Mit Hilfe isodesmischer Reaktionen werden Stabilisierungsenergien von Substituenten in 1- und 3-Position ermittelt. Diese Werte ermöglichen in Kombination mit der experimentell bekannten Bildungswärme des Stammkörpers 2 die Bestimmung von H sämtlicher Allenyl-Kationen 3 - 12. Der Vergleich dieser Daten mit einigen experimentell bestimmten Bildungswärmen zeigt Übereinstimmung innerhalb von 2 kcal/mol. Es werden Voraussagen für das Reaktionsverhalten gegenüber n-Nucleophilen und -Systemen gemacht

Representations of molecular force fields. I. Ethane: Ab initio and model, harmonic and anharmonic

The quadratic and selected cubic force constants for ethane have been computed, using single determinant molecular orbital wavefunctions at the 4‐31G level, with a view to testing and extending model consistent force fields (CFF) for ’’molecular mechanics’’ calculations. Results agree semiquantitatively with experiment, but experimental force constants of sufficient reliability to provide a definitive comparison are not yet available. In a comparison with the most rational general CFF available, that of Ermer and Lifson, the most significant discrepancies found to occur are those for certain stretch–bend couplings assumed to be zero in the CFF but shown to be appreciable by quantum calculation. It is observed that these couplings, but not the stretch–stretch couplings, are well accounted for by a steric interaction model. The ab initio cubic constants examined display the same pattern of conformity with a steric model. Bend–bend–bend and bend–bend–stretch but not all stretch–stretch–stretch interactions agree with those of the steric model. The partial success of the steric model shows that it is possible to represent a large number of interaction constants, quadratic and higher order, by a small number of parameters in molecular mechanics. The failure of the steric model to account for predominantly stretching interactions confirms that ’’classical’’ nonbonded interactions as embodied in conventional Urey–Bradley fields are not the only major contributors to off‐diagonal force constants. An alternative model, the anharmonic model of Warshel, as modified by Kirtman et al., was found to account well for pure stretches but not for bends or stretch–bend interactions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70643/2/JCPSA6-63-11-4750-1.pd