Canonical force field theory in terms of curvilinear internal coordinates: Application to the methane molecule

This Letter generalizes the Kuczera’s theory of the vibrational canonical force field in order to obtain an unambiguous and uniquely defined expression for the anharmonic force field in terms of curvilinear internal coordinates. By using this generalization it has been shown mathematically that the canonical force constants could be transferred between molecules with the same geometrical structure. As illustration, the theory is used to obtain the expressions for the quadratic and cubic canonical force constants of the methane molecule.     

Generalized inverse method for computation of molecular force field

The generalized inverse method is applied to the force constants calculation problem having a nearly singular Jacobian matrix, and by substituting it by one of lower rank which is near to it and well conditioned it is possible to eliminate the convergence difficulties of the least squares iteration process. A further significant advantage of the method is that certain matrix theoretical considerations give the possibility of deciding at the end of the iteration which force constants are determined by the available observations. Numerical results for the dimethylmercury molecule are given.     

On formulas in closed form for Van Vleck expansions

Canonical transformations have been widely used to simplify Hamiltonians and other operators. In molecular and in solid state theory, the so-called Van Vieck expansion is usually employed for this purpose while in theories of particles interacting with fields a combination of canonical transformations in closed form with Van Vleck type expansions has been found effective. For some of the transformations used in applications formulas in closed form are well known. It will be shown here that such formulas can be derived whenever the transformation function is bilinear in the canonical variables, and further that the use of matrix operators makes it possible to simplify these derivations substantially. The Cayley-Hamilton theorem is then used to express the expansions for the matrix operators in closed form. The number of separate operator terms appearing in the formulas thus obtained is the same as the rank of the matrices used. To calculate the coefficients of these operator terms a new type of special functions is introduced. The resulting linear canonical transformations include generalized rotations in both ordinary and phase-space. Explicit results have been obtained for several two- to four-dimensional problems.     

Degeneracy of some matrix graph invariants

New matrices associated with graphs and induced global and local topological indices of molecular graphs were proposed recently by Diudea, Minailiuc and Balaban. These matrices in canonical form are matrix graph invariants. A combined degeneracy of such invariants is considered. For every case of degeneracy corresponding graphs are presented.     

Preparation of Losartan Potassium Controlled Release Matrices and In-Vitro Investigation Using Rate Controlling Agents

Controlled release matrices have predictable drug release kinetics, provide drugs for an extended period of time, and reduce dosing frequency with improved patient compliance as compared with conventional tablet dosage forms. In the current research work, losartan potassium controlled release matrix tablets were fabricated and prepared with rate altering agents; that is, Ethocel grade 100 combined with Carbopol 934PNF. Various drug to polymer ratios were used. HPMC, CMC, and starch were incorporated in some of the matrices by replacing some amount of filler (5%). The direct compression method was adopted for the preparation of matrices. In phosphate buffer (pH 6.8), the dissolution study was conducted by adopting the USP method-I as the specified method. Drug release kinetics was determined and dissolution profiles were also compared with the reference standard. Prolonged release was observed for all matrices, but those with Ethocel 100FP Premium showed more extended release. The co-excipient (HPMC, CMC, and starch) exhibited enhancement in the drug release rates, while all controlled release matrices released the drug by anamolous non-Fickian diffusion mechanism. This combination of polymers (Ethocel grade 100 with Carbopol 934PNF) efficiently extended the drug release rates up to 24 h. It is suggested that these matrix tablets can be given in once a day dosage, which might improve patient compliance, and the polymeric blend of Ethocel grade 100 with Carbopol 934PNF might be used in the development of prolonged release matrices of other water-soluble drugs.     

Matrix formulation of the generalized Hartree-Fock methods

Spin-projected one-particle density and spin density matrices are presented as polynomials of suitable unprojected quantities with generalized Sasaki-Ohno coefficients. Thus an explicit form of Harriman's theorems is given. For the two-particle spatial density matrix an expansion in direct products of powers of unprojected residual electron and spin density matrices is given. For these basic matrices of the scheme the variational spin-extended equations are formulated.     

Explicit form of determinants and inverse matrices of Tribonacci <Emphasis Type="Italic">r</Emphasis>-circulant type matrices

The determinants and inverses of Tribonacci r-circulant type matrices are discussed in the paper. Firstly, Tribonacci r-circulant type matrices are defined. In addition, we show the invertibility of the Tribonacci r-circulant matrix and present the determinant and the inverse matrix based on constructing the transformation matrices. By utilizing the relation between r-circulant and r-left circulant, the invertibility of the Tribonacci r-left circulant matrix are also discussed. Finally, the determinants and the inverse matrices of the these matrices are given, respectively.     

A generalized graph-theoretical matrix of heterosystems and its application to the VMV procedure

The extensions of generalized (molecular) graph-theoretical matrix and vector-matrix-vector procedure are considered. The elements of the generalized matrix are redefined in order to describe molecules containing heteroatoms and multiple bonds. The adjacency, distance, detour and reciprocal distance matrices of heterosystems, and corresponding vectors are derived from newly defined generalized graph matrix. The topological indices, which are most widely used in predicting physicochemical and biological properties/activities of various compounds, can be calculated from the new generalized vector-matrix-vector invariant.     

Instanton rate constant calculations close to and above the crossover temperature

Canonical instanton theory is known to overestimate the rate constant close to a system‐dependent crossover temperature and is inapplicable above that temperature. We compare the accuracy of the reaction rate constants calculated using recent semi‐classical rate expressions to those from canonical instanton theory. We show that rate constants calculated purely from solving the stability matrix for the action in degrees of freedom orthogonal to the instanton path is not applicable at arbitrarily low temperatures and use two methods to overcome this. Furthermore, as a by‐product of the developed methods, we derive a simple correction to canonical instanton theory that can alleviate this known overestimation of rate constants close to the crossover temperature. The combined methods accurately reproduce the rate constants of the canonical theory along the whole temperature range without the spurious overestimation near the crossover temperature. We calculate and compare rate constants on three different reactions: H in the Müller–Brown potential, methylhydroxycarbene → acetaldehyde and H₂ + OH → H + H₂O. © 2017 Wiley Periodicals, Inc.     

The mechanical moduli of lamellar semicrystalline polymers

Bounds on the elastic constants are derived for semicrystalline polymers whose local morphology is lamellar. Local response matrices (stiffness and compliance) are formulated in three dimensions that simultaneously incorporate uniform in-plane strain and additive forces from layer to layer of crystalline and amorphous phases and uniform stress and additive displacements normal to the lamellar surfaces. Spatial averaging of the stiffness and compliance matrices under the assumption of axially symmetric orientation gives the upper and lower bounds on the longitudinal and transverse tensile moduli and the axial and transverse shear moduli as functions of the separate phase elastic constants, the volume percent crystallinity, and the moments of the orientation 〈cos²θ〉 and 〈cos⁴θ〉. The bounds are much tighter than the Voight upper and Reuss lower bounds that do not recognize phase geometry. Using the known crystal elastic constants of polyethylene, sample calculations on isotropic unoriented materials show that the divergence of bounds at high crystallinity necessitated by the extreme crystal anisotropy shows up only at very high crystallinity. At low temperature the bounds are tight enough to specify G₁, the amorphous modulus, from the measured G and the known crystal elastic constants. At higher temperatures and lower G, the bounds are not tight enough for this purpose but the shear modulus versus crystallinity and temperature data are well fitted by the lamellar lower bound using a temperature-dependent, crystallinity-independent G₁.     

Reversed headspace analysis for characterization, identification, and analysis of solid and liquid matrices: Part I

This paper offers a methodology of an experimentally simple reversed headspace (RHS) analysis for measuring of matrix effects and their use for identification and characterization of condensed matrices such as pharmaceuticals, polymers, chromatographic packing, etc. applicable for both quality control monitoring and research and development investigation. In RHS methods, the matrix is spiked and equilibrated with a mixture of volatile chemicals containing various functional groups (molecular sensor array or MSA mixture). Headspace chromatograms of the same spikes of a sample and an empty vial are compared. Examination of basic headspace theory shows that matrix specific constants (M), rather than partition coefficients (K), can be calculated from the headspace chromatograms and M=(K-1)xbeta, where beta is a degree of matrix volume change during equilibration. Matrix specific constants can be plotted against any property of chemicals (polarity, dielectric constant, solubility parameter, vapor pressure, etc.) or just against a set of consecutive numbers, each representing a chemical in MSA. This plot is, in a sense, a molecular affinity spectrum (MAS) specific for a given matrix at a given temperature and is independent of an instrument. Changes in MAS that correspond to chemicals with a particular functional group give an insight to the type of differences between matrices and may quantitatively define them.     

Calculation of intramolecular force fields from second-derivative tensors

A practical procedure (FUERZA) to obtain internal force constants from Cartesian second derivatives (Hessians) is presented and discussed. It allows a systematic analysis of pair atomic interactions in a molecular system, and it is fully invariant to the choice of internal coordinates of the molecule. Force constants for bonds or for any pair of atoms in general are defined by means of the eigenanalysis of their pair interaction matrix. Force constants for the angles are obtained from their corresponding two-pair interaction matrices of the two bonds or distances forming the angle, and the dihedral force constants are similarly obtained using their corresponding three-pair interaction matrices. © 1996 John Wiley & Sons, Inc.     

New conditions for validity of the centroid molecular dynamics and ring polymer molecular dynamics

Validity of the centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) in quantum liquids is studied on an assumption that momenta of liquid particles relax fast. The projection operator method allows one to derive the generalized Langevin equation including a memory effect for the full-quantum canonical (Kubo-transformed) correlation function. Similar equations for the CMD and RPMD correlation functions can be derived too. The comparison of these equations leads to conditions under which the RPMD and CMD correlation functions agree approximately with the full-quantum canonical correlation function. The condition for the RPMD is that the memory effects of the full-quantum and RPMD equations vanish quickly with the same time constants. The CMD correlation function requires additional conditions concerning static correlation.     

NMR偶合常数的从头算级别自然杂化轨道研究

为了研究自然杂化轨道计算结果与核自旋偶合常数的相关性,本文进行了从头算级别的自然杂化轨道计算。采用STO－3G基组,利用Lowdin正交化原子轨道基组下的密度矩阵,得到了分子中各原子的杂化轨道、净电荷与^13C-H、^13C-^13C键自旋偶合常数^1Jcn和^1Jcc之间关系式。利用这些式子计算得到的结果与实验数据非常一致。     

Measurement of aroma compound self-diffusion in food models by DOSY

Self-diffusion measurement of solutes in polymer gels has been investigated using pulsed gradient spin echo NMR spectroscopy. However, few data are available on the self-diffusion of small solutes in natural polysaccharide polymers used as thickeners in the food industry. Since aroma diffusion in food matrices could have an impact on flavor release, this is an interesting and economic challenge. Diffusion ordered spectroscopy (DOSY) resolves diffusion data for each component in complex mixtures. We used DOSY with the inverse Laplace transform approach with the maximum entropy algorithm to investigate diffusion of two aroma compounds, ethyl butanoate and linalool, in an iota-carrageenan matrix as the food model. We showed that the self-diffusion coefficient values of small molecules in a polysaccharide matrix could be easily extracted using this method. We then investigated the impact of the gelling state of iota-carrageenan matrices on the self-diffusion of ethyl butanoate.     

Vibrational spectroscopy at high pressure of the permanganate anion trapped in potassium bromide and potassium perchlorate matrices

The effect of high pressure on the resonance Raman spectra of the permanganate ion isolated in potassium bromide and potassium perchlorate matrices has been investigated at room temperature for pressures up to 50 kbar. The pressure dependences of the anharmonicity constants and harmonic frequencies have been determined from the overtones of the totally symmetric nu1(A1) mode of the permanganate ion. For both matrices, as the pressure increases, the anharmonicity constants decrease slightly, while the harmonic frequencies increase steadily. The effect of the potassium bromide phase transition from a face-centered to a body-centered structure was observed on the permanganate ion Raman spectrum at approximately 24 kbar. The perchlorate matrix does not exhibit any phase transition under the experimental conditions used in this study.