Alternative expressions for energies and forces due to angle bending and torsional energy

We have derived alternative expressions for computing the energies and forces associated with angle bending and torsional energy terms commonly used in molecular mechanics and molecular dynamics computer programs. Our expressions address the problems of singularities that are intrinsic in popular angle energy functions and that occur from other chain rule derivations of force expressions. Most chain rule derivations of expressions for Cartesian forces due to angle energies make use of relations such as where ? is a bond or torsion angle, E(?) is energy, and ?/?x represents a derivative with respect to some Cartesian coordinate. This expression leads to singularities from the middle term, ?1/sin ?, when ? is 0 or π. This is a problem that prevents the use of torsional energy expressions that have phase angles, ?°, other than 0 or π, such as in E(?) = κ[1 + cos(n? ? phsi;°)]. Our derivations make use of a different, but equivalent, form of the chain rule: This form still possesses singularities for the bond angle forces since the last factor is undefined when ? is 0 or π. However, the alternate form may be used to great advantage for the torsional angle forces where no such problem arises. The new expressions are necessary if one desires the use of torsional energy expressions with general phase angles. Even for energy expressions in common use, i.e., with phase angles of 0 or π, our force expressions are as computationally efficient as the standard ones. The new expressions are applicable to all molecular simulations that employ restrained, or phase-shifted, torsional angle energy expressions.     

Internal axis molecular parameters, torsional energies and matrix elements of methyl mercaptan-D2

In this paper an internal axis method Hamiltonian model has been applied to evaluate the torsional rotational molecular parameters of asymmetrically substituted methyl mercaptan (CHD2SH) using previously observed microwave transitions. The torsional potential barrier function V2 has been obtained. The pure torsional energies and matrix elements between various torsional sub-levels up to the fourth excited torsional state in the ground vibrational state have been determined. The matrix elements and the torsional energies will be of great value to researchers seeking the spectrum of this molecule.     

Coupling of bending and stretching deformations in vesicle membranes

Biomimetic membranes are fluid and can undergo two different elastic deformations, bending and stretching. The bending of a membrane is primarily governed by two elastic parameters: its spontaneous (or preferred) curvature m and its bending rigidity κ. These two parameters define an intrinsic tension scale, the spontaneous tension 2 κm². Membrane stretching and compression, on the other hand, are determined by the mechanical tension acting within the membrane. For vesicle membranes, the two elastic deformations are coupled via the enclosed vesicle volume even in the absence of mechanical forces as shown here by minimizing the combined bending and stretching energy with respect to membrane area for fixed vesicle volume. As a consequence, the mechanical tension within a vesicle membrane depends on the spontaneous curvature and on the bending rigidity. This interdependence, which is difficult to grasp intuitively, is then illustrated for a variety of simple vesicle shapes. Depending on the vesicle morphology, the magnitude of the mechanical tension can be comparable to or can be much smaller than the spontaneous tension.     

First and second order derivative spectrophotometric determination of benzyl alcohol and diclofenac in pharmaceutical forms

Diclofenac sodium is a drug with analgesic, antipyretic and anti-inflammatory properties. It is present in numerous pharmaceutical preparations. In injectable forms, it is usually accompanied by benzyl alcohol as an excipient, which is used as a blocking anesthetic (4%) and an antiseptic (4-10%). In this work spectrophotometric methodology was used in order to determine diclofenac and benzyl alcohol in injectable formulations by applying, on the one hand, the first-derivative method of crossing zero for diclofenac sodium and on the other, second derivative for benzyl alcohol. The results obtained show that this method has a significant advantage over other techniques and it is appropriate for routine pharmaceutical analysis.     

Ab initio calculation of the potential energy surface for the large-amplitude bending and symmetric stretching vibration in the electronic ground state of XeF2

A two-dimensional symmetric stretching-bending potential surface for the electronic ground state of the XeF₂ molecule has been computed by means of self-consistent field and multi-reference configuration interaction methods. At the correlated level of treatment it is found that the linear nuclear arrangement of XeF₂ with XeF bond distances close to 200 pm corresponds only to a local minimum on the potential energy surface separated from the dissociation products Xe + 2F by a high energy barrier. The results of a vibrational analysis study enable a reliable reproduction and interpretation of available experimental data concerning the infrared spectrum of the molecule.     

Method of computer algebraic calculation of the matrix elements in the second quantization language

An automated method by the algebraic programming language REDUCE3 for specifying the matrix elements expressed in second quantization language is presented and then applied to the case of the matrix elements in the TDHF theory. This program works in a very straightforward way by commuting the electron creation and annihilation operators (a^? and a) until these operators have completely vanished from the expression of the matrix element under the appropriate elimination conditions. An improved method using singlet generators of unitary transformations in the place of the electron creation and annihilation operators is also presented. This improvement reduces the time and memory required for the calculation. These methods will make programming in the field of quantum chemistry much easier. © 1995 John Wiley & Sons, Inc.     

A laser-induced fluorescence study of energy transfer between the symmetric stretching and bending modes of CO2

The equilibration of the lower laser levels in CO₂, 10^O0 and 02^O0, has been studied via a laser-induced fluorescence technique. We conclude that the coupling between these levels is rapid, ?1100 ms^?1 Torr^?1, and that these levels are also coupled though at a somewhat slower rate of 387 ± 75 ms^?1 Torr^?1 to the bending modes of CO₂.     

A novel decomposition of torsional potentials into pairwise interactions: A study of energy second derivatives

A general method of analyzing intramolecular torsional potentials in terms of energy second derivatives that couple the rotating atoms is presented. The method offers a rigorous decomposition of the total torsional potential into pairwise (dihedral) interactions and enables one to derive nonbonded torsional interactions between 1–4 atoms as well as between more distant atoms and sites. The method is demonstrated on ethane, propane and acetaldehyde. It is shown that the 1–4 H…H dihedral potentials in ethane and propane are very similar, thereby supporting the notion of transferable force field potential functions. However, the dihedral potentials that are obtained differ from 1–4 potentials that are used in current force fields. Intramolecular three body effects are clearly seen in this method and are found to be relatively large for the dihedral interactions, although in the one case studied (propane) the overall effect on the methyl-methyl interaction is negligible due to cancellation of terms. The analysis explicitly shows that the barrier in acetaldehyde is due mainly to the dihedral H…H interaction.     

Explicit formulas for the Hamiltonian matrix elements

The explicit formulas for the evaluation of the Hamiltonian matrix elements are presented. The calculation of the integral coefficients is independent of both the nature of the orbitals and th spin coupling schemes. It is fully automatic and only dependent on the number of doubly and singly occupied orbitals. Further-more, the symmetric group representation matrices are not needed, and the N! problem can be avoided.     

Reaction of HOD+ with NO2: effects of OD and OH stretching, bending, and collision energy on reactions on the singlet and triplet potential surfaces

Integral cross sections and product recoil velocity distributions were measured for the reaction of HOD(+) with NO(2), in which the HOD(+) reactant was prepared in its ground state and with mode-selective excitation in the 001 (OH stretch), 100 (OD stretch), and 010 (bend) modes. In addition, we measured the 300 K thermal kinetics in a selected ion flow tube reactor and report product branching ratios different from previous measurements. Reaction is found to occur on both the singlet and triplet surfaces with near-unit efficiency. At 300 K, the product branching indicates that triplet → singlet transitions occur in about 60% of triplet-coupled collisions, which we attribute to long interaction times mediated by complexes on the triplet surface. Because the collision times are much shorter in the beam experiments, the product distributions show no signs of such transitions. The dominant product on the singlet surface is charge transfer. Reactions on the triplet surface lead to NO(+), NO(2)H(+), and NO(2)D(+). There is also charge transfer, producing NO(2)(+) (a(3)B(2)); however, this triplet NO(2)(+) mostly predissociates. The NO(2)H(+)/NO(2)D(+) cross sections peak at low collision energies and are insignificant above ~1 eV due to OH/OD loss from the nascent product ions. The effects of HOD(+) vibration are mode-specific. Vibration inhibits charge transfer, with the largest effect from the bend. The NO(2)H(+)/NO(2)D(+) channels are also vibrationally inhibited, and the mode dependence reveals how energy in different reactant modes couples to the internal energy of the product ions.     

Efficient parallelization of the energy,surface, and derivative calculations for internal coordinate mechanics

An efficient algorithm for parallelization of a molecular mechanics program operating in the space of internal coordinates such as dihedral angles, bond angles, and bond lengths is described. The iterative procedure to calculate analytical energy derivatives with respect to the internal coordinates was modified to allow parallelization. Computationally intensive modules that calculate energy and its derivatives, solvent-accessible surface, electrostatic polarization energy and that update lists of interactions were parallelized with nearly 100% efficiency. The proposed strategy for the shared-memory computer architecture is easily scalable and requires minimum changes in a program code. The overall speedup for a realistic calculation minimizing the energy of a myoglobin reaches a factor of 3 for 4 processors. © 1994 by John Wiley & Sons, Inc.     

Hypervirial theorem and matrix elements for the Coulomb potential

It is well known that hydrogen like atoms may be represented as Morse oscillators. Our aim in this article was to show how this result and the hypervirial theorem lead to a computational method with which the matrix elements for the Coulomb potential can be easily calculated. Also, a closed analytical expression for 〈n₂l₂|r^k|n₁l₁〉 is obtained. © 1995 John Wiley & Sons, Inc.     

On the interrelation between frequencies of stretching and bending vibrations in liquid water

The problem is investigated whether the distributions of bending frequencies P(vbend,T) of H2O molecules in the liquid could be calculated from statistical distributions P(vOH,T) of stretching frequencies on the basis of the empirical correlation established for their mean values. It is found that correlations of different kinds fail to reproduce real spectra. They result in a bending band that is too narrow and give rise to an Evans hole in the stretching band. This provides evidence of the strong intermolecular coupling of bending modes, which makes their frequencies statistically independent from stretching frequencies.     

One-center expansion for pseudopotential matrix elements

Semilocal pseudopotential operators can be expressed as a linear combination of nonlocal (projection) operators. Pseudopotential operator integrals over a molecular basis set are therefore reduced to linear combinations of overlap integrals products. Molecular calculations indicate that sufficient precision can be achieved with a limited number of nonlocal operators. Analytic derivatives of pseudopotential integrals are easily deduced and implemented in a standard quantum chemistry program.     

Generating function for rotation matrix elements

The rotation matrix elements are expressed in terms of the Jacobi, Hypergeometric, and Legendre polynomials in the literature. In this study, the generating function is presented for rotation matrix elements by using properties of Jacobi polynomials. In addition, some special values and Rodrigues' formula of rotation matrix elements are obtained by using the generating function. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Generating functions for oscillator matrix elements

Two general harmonic oscillator elements \documentclass{article}\pagestyle{empty}\begin{document}$$ \left\langle m \right|\hat x^s \hat p\left| n \right\rangle $$\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$$ \left\langle m \right|\exp \left[ { - \alpha \left( {\hbar /m*\omega } \right)\hat x^2 } \right]\exp \left( {\beta \hat x} \right)\left| n \right\rangle $$\end{document} are derived by a generating function method using operator techniques which contain practically all one- and two-centre integrals with equal frequencies of chemical physics.     

CH bond dissociation energies,isolated stretching frequencies,and radical stabilization energy

An earlier correlation between isolated CH stretching frequencies, v, and experimental CH bond dissociation energies, in hydrocarbons, fluorocarbons, and CHO compounds, is updated. A stabilization energy, E, which reflects only the properties of the radical, is defined by the deviation of a point from the above correlation. E values for a variety of radicals are listed and discussed. In H? C? N and H? C? O compounds E is low or negligible, due to the low v found in these compounds. The conventional definition of E_S then represents a serious misnomer, which distracts attention from the probable source of discrepancies between experimental and ab initio values of DH°(C? H), namely, the parent molecules. Stereo electronic effects concerned with the breaking of CH bonds are predicted in a variety of situations. Some experimental determinations of DH°(C? H), viz., in C₂H₄, HCOOH, CH₃CHO, CH₃NH₂, are considered to be probably in error. Schemes for partitioning energies of atomization into ‘standard’ or ‘intrinsic’ bond energies are criticized.     

Effect of bending and stretching of polyethylene strips on the adsorption of surface-active substances

The adsorption of tritium-labeled sodium stearate and ³⁵S-labeled sodium dodecylsulfate from aqueous solution on bent and on stretched polyethylene strips was directly measured. The amount of adsorption increased from 2.5 to 4.5 times on surfaces of various polyethylene samples stretched from 5.2 to 5.3 times the original length. For one sample, adsorption increased 8 and 2.5 times, respectively, on the convex and concave surfaces of a bent strip. Autoradiographs of the strips taken after adsorption revealed the appearance of both homogeneous and heterogeneous adsorption on the stretched surface of the polyethylene. The electron micrographs of the strips showed that many small fissures, about 1–5μ in length, formed on their surfaces after the strips were bent or stretched. Enhanced adsorption of the surface-active substance along these fissures was suggested. On the basis of these observations, it is proposed that in stretching or bending, fissures increase adsorption of the detergent, and the adsorption in turn promotes further development of fissures. Thus, bending and adsorption mutually promote the growth of fissures which finally result in failure of the polyethylene.     

Energy-adjustedab initio pseudopotentials for the second and third row transition elements

Summary Nonrelativistic and quasirelativisticab initio pseudopotentials substituting the M^(Z–28)+-core orbitals of the second row transition elements and the M^(Z–60)+-core orbitals of the third row transition elements, respectively, and optimized (8s7p6d)/[6s5p3d]-GTO valence basis sets for use in molecular calculations have been generated. Additionally, corresponding spin-orbit operators have also been derived. Atomic excitation and ionization energies from numerical HF as well as from SCF pseudopotential calculations using the derived basis sets differ in most cases by less than 0.1 eV from corresponding numerical all-electron results. Spin-orbit splittings for lowlying states are in reasonable agreement with corresponding all-electron Dirac-Fock (DF) results.     

Intermolecular coupling of the NH stretching and bending vibrations in the amide - electrolyte solutions

The polarized Raman scattering by the amide - electrolyte solutions have been investigated in the NH stretching and NH₂ bending vibration regions. The differences between the frequencies of the isotropic and anisotropic components are interpreted in terms of hydrogen bonding and intermolecular coupling of the NH vibrators.