A comparative quantum mechanical study of bond separation energies as a measure of cyclic conjugation

Restricted Hartree-Fock (RHF), second-order Møller-Plesset (MP2), and density functional calculations [using the Becke/Lee-Yang-Parr (B-LYP) exchange/correlation gradient-corrected functionals] employing the 6-311G(d, p) and 6-311 + + G(d, p) basis sets have been carried out to calculate isodesmic bond separation energies for reactions involving a number of representative five- and six-membered ring organic compounds. The MP2 and density functional approaches yield reasonably good energies; the density functional method agrees particularly well with experiment, exhibiting a root-mean-square error of only 2.5 kcal/mol. Ring geometries are calculated satisfactorily in all approaches but are given particularly accurately by the MP2 approach. A comparison of the B-LYP bond separation energies with several other definitions of resonance energy shows that these different approaches correlate with each other in a reasonable fashion. © 1995 John Wiley & Sons, Inc.     

On the calculation of Auger energies

“Frozen-orbital” expressions within an average-energy formalism are presented for the calculation of Auger transition energies based on the orbitals determined for the initial state. Trial calculations at the minimal-basis level are reported for the K-LL transition in Ne, Na and Mg. We also discuss an ambiguity in the use of certain models for the calculation of both semi-empirical and ab initio Auguer energies. For illustration we give some numerical data on the atoms Ne, Na, Mg and S.     

On the calculation of surface energies

A simple formalism based on response theory is used to evaluate expressions for the surface energy of a uniform dielectric or metallic medium and the change in surface energy of a dielectric solvent when a dilute electrolyte is dissolved in it. The latter result coincides with the result of Onsager and Samaras.     

Effect of benzo-annelation on cyclic conjugation

Abstract  

Earlier studies revealed that the effect of benzo-annelation on cyclic conjugation in the central ring of a polycyclic conjugated molecule obeys certain general regularities. We now elaborate quantitative models of this effect, showing that the main factors that need to be taken into account are the numbers of angularly, linearly, and geminally annelated rings.     

A calculation of the relative protonation energies of amines in solution

Relative protonation energies in the primary, secondary and tertiary aliphatic series of amines are calculated by a semiempirical method employing the virtual charge model. The method accounts quite well for the observed differences between the gas-phase protonation affinities and the protonation enthalpies in solution, but when allowance is made for steric shielding from the bulk solvent for “non-edge” atoms, some anomalies in the uncorrected model are removed. The calculated solute-solvent interactions are related to experimental enthalpies of solution and to trends expected from the Born model.     

Some aspects of the calculation of lattice energies

Some relations between lattice energies calculated from various simple equations are pointed out. It is found that these equations give values of the variation of compressibility with pressure that agree poorly with experiments, at least for sodium and cesium chloride, bromide, and iodide. Equations which take this variation into account are developed, and it is found that calculated values of the lattice energy vary very little with the exact equation used. On the whole these extended equations give better agreement between the calculated and observed lattice energies.     

PCILO calculation of intermolecular energies: The water dimer

The PCILO (perturbative configuration interaction using localized orbitals) method for approximating the electronic structure of molecules has been used with some success for calculating intramolecular interactions in large molecules where intramolecular hydrogen bonding is involved. In this note we show that the PCILO method may be used to calculate the energy of interaction between two water molecules in selected configurations.     

On the calculation of energies of excited states

We reformulate a scheme for calculation of the energies of excited states which, unlike the variation method, does not require that the trial function be orthogonalized to the wavefunctions for lower excited states. The possibility of obtaining wavefunctions as well as energies is discussed, and an example of the scheme's application is made to the harmonic oscillator.

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Zusammenfassung Es wird eine neue Form für eine Methode zur Berechnung von angeregten Zuständen gegeben. Die Probefunktion braucht nicht wie bei der Variationsmethode orthogonal zu den Wellenfunktionen der tiefer liegenden Zuständen zu sein. Es wird die Möglichkeit diskutiert, Wellenfunktionen ebenso wie Energien zu erhalten. Das Schema wird auf den harmonischen Oszillator angewandt.

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Resume On donne une nouvelle forme pour une methode de calcul des niveaux excités. La methode ne demande pas l'orthogonalisation de la fonction d'essai par rapport aux fonctions d'onde correspondant aux niveaux inférieurs, ce qui montre un avantage auprès de la methode variationnelle. La possibilité d'obtenir les fonctions d'onde elles-mêmes est discutée, et on donne un exemple de l'application de cette nouvelle methode.

     

Efficient calculation of short-range Coulomb energies

An efficient algorithm for the calculation of short-range Coulomb energies is examined. The algorithm uses a boxing scheme and a prescreening for negligible integrals to evaluate the short-range Coulomb energy via computational work that scales only linearly with the size of the system. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 921–927, 1999     

Accurate calculation of core-electron binding energies: multireference perturbation treatment

Multireference perturbation theory (MRPT) with multiconfigurational self-consistent field (MCSCF) reference functions is applied to the calculations of core-electron binding energies (CEBEs) of atoms and molecules. Orbital relaxations in a core-ionized state and electron correlation are both taken into account in a conventional MCSCF-MRPT procedure. In the MCSCF calculation, the target core ionized state is directly optimized as an excited state and this treatment can completely prevent a variational collapse. Multireference Moller-Plesset perturbation theory and multiconfigurational self-consistent field reference quasidegenerated perturbation theory were used to treat electron correlation. The present method quite accurately reproduced the 1s CEBEs of CH4, NH3, H2O, and FH; the average deviation from the experimental data is 0.11 eV using Ahlrichs' VTZ basis set. The C 1s and O 1s CEBEs of formic acid and acetic acid were calculated and the results are consistent with the bonding characters of the atoms in these molecules. The present procedure can also be applied to CEBEs of higher angular momentum orbitals by including spin-orbit coupling. The calculated CEBEs of Ar 2p, HCl 2p, Kr 3d, and HBr 3d are in reasonable agreement with the available experimental values. In the calculation of the 3d CEBEs, a relativistic correction significantly improves the agreements. The effect of polarization functions is also discussed.     

A water-swap reaction coordinate for the calculation of absolute protein-ligand binding free energies

The accurate prediction of absolute protein-ligand binding free energies is one of the grand challenge problems of computational science. Binding free energy measures the strength of binding between a ligand and a protein, and an algorithm that would allow its accurate prediction would be a powerful tool for rational drug design. Here we present the development of a new method that allows for the absolute binding free energy of a protein-ligand complex to be calculated from first principles, using a single simulation. Our method involves the use of a novel reaction coordinate that swaps a ligand bound to a protein with an equivalent volume of bulk water. This water-swap reaction coordinate is built using an identity constraint, which identifies a cluster of water molecules from bulk water that occupies the same volume as the ligand in the protein active site. A dual topology algorithm is then used to swap the ligand from the active site with the identified water cluster from bulk water. The free energy is then calculated using replica exchange thermodynamic integration. This returns the free energy change of simultaneously transferring the ligand to bulk water, as an equivalent volume of bulk water is transferred back to the protein active site. This, directly, is the absolute binding free energy. It should be noted that while this reaction coordinate models the binding process directly, an accurate force field and sufficient sampling are still required to allow for the binding free energy to be predicted correctly. In this paper we present the details and development of this method, and demonstrate how the potential of mean force along the water-swap coordinate can be improved by calibrating the soft-core Coulomb and Lennard-Jones parameters used for the dual topology calculation. The optimal parameters were applied to calculations of protein-ligand binding free energies of a neuraminidase inhibitor (oseltamivir), with these results compared to experiment. These results demonstrate that the water-swap coordinate provides a viable and potentially powerful new route for the prediction of protein-ligand binding free energies.     

Perturbation-graph theory—I: Resonance energies of heteroannulene π systems

Perturbation theory and the graph-theoretical definition of resonance energy are combined and applied to π systems substituted with heteroatoms and external substituents. The systems investigated are monocyclic and contain 3–6 atoms with 2–8 π electrons. In general, heteroatoms are calculated to exert their effects on resonance energy through two separable mechanisms, due either to the electronegativity (h parameter) or the conjugative ability (k parameter) of the substituent atom. There is no first-order effect of electronegativity in species containing 4n+2 (n= integer) π electrons. All electronegative or electropositive substituents are predicted to stabilize 4n π electron systems. Enhanced conjugation stabilizes 4n+2 systems and destabilizes 4n systems. Several examples of ions and molecules are given that qualitatively conform to these rules.     

A Hartree-Fock SCF calculation of the activation energies for two SN2 reactions

Roothaan Hartree-Fock SCF calculations for points on the F⁻ + CH₃F and CN⁻ + CH₃F minimum potential energy surfaces are reported. Considerable care has been taken in the choice of basis sets used to describe these systems.     

A comparative calculation on excited state energies of some conjugated hydrocarbons

The energies of the single-configuration lowest π – π* singlet and triplet states of some conjugated hydrocarbons have been calculated by the MC-SCF method using the conjugate-gradient technique of minimisation. The results are compared with those calculated by other methods currently in use, like (a) single-configuration calculation with V_N?1 potential for virtual orbitals; (b) CI calculation involving singly excited states; and (c) TDHF method. It has been concluded that the results for the MC-SCF method are very good, considering that only a single open-shell configuration is involved.     

Resonance energies of fullerenes with 4-membered rings

We report the resonance energies (REs ) of several fullerenes with 4-membered rings and their isomers with only 5- and 6-membered rings computed using the conjugated-circuit model [RE (CC )] and the topological resonance energy (TRE ) model. Both aromaticity indices were normalized by dividing by the size of the considered fullerene [RE (CC )/e and TRE /e]. The results parallel the predictions by Gao and Herndon using the much more advanced SCF –UHF π-electron approach. A good linear correlation is found between the topologically defined indices [RE (CC )/e and TRE /e] and normalized SCF –UHF π-electron energy. © 1995 John Wiley & Sons, Inc.