A quartic force field coordinate substitution scheme using hyperbolic sine coordinates

Quartic force fields (QFF) are currently the most cost‐effective method for the approximation of potential energy surfaces for the calculation of anharmonic vibrational energies. It is known, although, that its performance can be less than satisfactory due to limitations related to slow convergence of the series. In this article, we present a coordinate substitution scheme using a combination of Morse and sinh coordinates, well adapted for its use with cartesian normal coordinates. We derive expressions for analytical integrals for use in VSCF and VCI calculations and show that the simultaneous substitution of symmetric and antisymmetric normal coordinates by Morse and sinh coordinates, respectively, significantly improves the vibrational transition frequencies for these modes in a well‐balanced fashion. The accuracy of this substitution scheme is demonstrated by comparing one and two‐dimensional sections of substituted and unsubstituted QFF with ab initio potential energy grids, as well as with vibrational energy calculations using as test cases two well‐studied benchmark molecules: water and formaldehyde. We conclude that the coordinate substitution scheme presented constitutes a very attractive alternative to simple QFFs in the context of cartesian normal coordinates.     

The rotation–vibration coupling equations for polyatomic molecules in internal coordinates

An exact vibration–rotation kinetic energy operator for polyatomic molecules has been obtained on the basis of Sutcliffe's method, in terms of curvilinear internal coordinates and rotational angular moment operators. This operator is derived from the kinetic energy operator in Cartesian coordinates by the successive transformations using the chain rule. This kinetic energy operator can be used not only for the system of any triatomic and tetraatomic molecules and common polyatomic molecules in chemistry, but also for the investigation of the collision problems between two molecules after some modifications. Finally, using this Hamiltonian, the rotation–vibration coupling equations of polyatomic molecules have been derived and discussed. © 1992 John Wiley & Sons, Inc.     

An adaptive potential energy surface generation method using curvilinear valence coordinates

An automatic Born-Oppenheimer potential energy surface (PES) generation method AGAPES is presented designed for the calculation of vibrational spectra of large rigid and semi-rigid polyatomic molecules within the mid-infrared energy range. An adaptive approach guided by information from intermediate vibrational calculations in connection with a multi-mode expansion of the PES in internal valence coordinates is used and its versatility is tested for a selection of molecules: HNO, HClCO, and formaldoxime. Significant computational savings are reported. The possibility of linear scaling of the sampling grid size with the molecular size due to decrease of correlation of remote coordinates in large molecules is examined and finally, possible improvements are suggested.     

Gyration- and inertia-tensor-based collective coordinates for metadynamics. Application on the conformational behavior of polyalanine peptides and Trp-cage folding

Effective simulations of proteins, their complexes, and other amino-acid polymers such as peptides or peptoids are critically dependent on the performance of the simulation methods and their ability to map the conformational space of the molecule in question. The most important step in this process is the choice of the coordinates in which the conformational sampling will be executed and their uniqueness regarding the capability to unambiguously determine the energy minimum on the free-energy hypersurface. In the presented study, we show that metadynamics and chosen collective coordinates-the principal moments of the tensors of gyration and inertia, the principal radii of gyration around the principal axes, asphericity, acylindricity, and anisotropy-can be used as a powerful combination to map the conformational space of peptides and proteins. We show that the combination of these coordinates with metadynamics produces a powerful tool for the study of biologically relevant molecules.     

Partial optimization of large molecules and clusters

By examining the displacement coordinate metric three modes of constrained optimization for large molecules and clusters are suggested. The first method corresponds to a conventional optimization using internal coordinates. The second mode has applications with respect to both internal and cartesian coordinates. The final mode is particularly interesting because it can result in computational savings. A mixture of both internal and cartesian coordinates is specified where these coordinates are usually a subset of the molecules or clusters total coordinate set. In the optimization only a subset of the energy derivatives need be evaluated reducing the computational effort associated with the gradient calculation.     

Shape and spin state in four-coordinate transition-metal complexes: the case of the d(6) configuration

Generalized polyhedral interconversion coordinates are defined within the framework of Avnir's continuous shape measures. The application of such interconversion coordinates to the study of the potential energy surfaces that define the stereochemical choice in four-coordinate transition metal complexes with different spin states is presented, and the correlation between potential energy curves and distribution of experimental structures along the tetrahedron to square interconversion path is shown for the case of the d(6) transition-metal complexes.     

On the use of optimal internal vibrational coordinates for symmetrical bent triatomic molecules

The use of generalized internal coordinates for the variational calculation of excited vibrational states of symmetrical bent triatomic molecules is considered with applications to the SO2, O3, NO2, and H2O molecules. These coordinates depend on two external parameters which can be properly optimized. We propose a simple analytical method to determine the optimal internal coordinates for this kind of molecules based on the minimization with respect to the external parameters of the zero-point energy, assuming only quadratic terms in the Hamiltonian and no quadratic coupling between the optimal coordinates. The optimal values of the parameters thus obtained are shown to agree quite well with those that minimize the sum of a number of unconverged energies of the lowest vibrational states, computed variationally using a small basis function set. The unconverged variational calculation uses a basis set consisting of the eigenfunctions of the uncoupled anharmonic internal coordinate Hamiltonian. Variational calculations of the excited vibrational states for the four molecules considered carried out with an increasing number of basis functions, also evidence the excellent convergence properties of the optimal internal coordinates versus those provided by other normal and local coordinate systems.     

Geometry optimization of molecular clusters and complexes using scaled internal coordinates

Scaled internal coordinates are introduced for use in the geometry optimization of systems composed of multiple fragments, such as solvated molecules, clusters, and biomolecular complexes. The new coordinates are related to bond lengths, bond angles and torsion angles by geometry-dependent scaling factors. The scaling factors serve to expedite the optimization of complexes containing outlying fragments, without hindering the optimization of the intramolecular degrees of freedom. Trial calculations indicate that, at asymptotic separations, the scaling factors improve the rate of convergence by a factor of 4 to 5.     

Analysis on solvated molecules with a new energy partitioning scheme for intra- and intermolecular interactions

A new partitioning scheme for the total energy of molecules is presented. In the scheme, the Hartree-Fock total energy of a molecular system is represented as the sum of one- and two-center terms exactly. The present method provides physically reasonable behavior for a wide range of interactions, and intermolecular interaction is treated equivalently with intramolecular interaction. The method is applied to analysis on the inter- and intramolecular interactions of molecular complexes both in gas phase and in aqueous solution. The results strongly indicate that the present method is a powerful tool to understand not only the bonding nature of molecules but also interaction between molecules.     

An extended version of boyd''s force field method applicable to heteroatomic molecules Part 3. Glycine, -isoleucine, -norleucine

The force field method developed by Boyd is extended to include molecules containing atoms other than C and H (e.g., N, O, P, S, Cl, Br, …). A new set of force field parameters is determined in order to redefine the potential energy functions that govern the dynamics of the internal (valence coordinates) degrees of freedom of a molecule. It is shown that the minimum of the partial potential energy surface is significantly affected by electrostatic intramolecular interactions. In this regard the non-bonded interactions appear to be less important than the dipole—dipole type interactions for a given interatomic distance when heteroatoms are present in the molecular framework. The reliability of the extended method as regards minimized structure, vibrational spectra and thermodynamic properties has been checked for more than 20 polyatomic molecules. From the correlation between calculated and experimental properties it is concluded that the method has good potential for further applications on polyatomic molecules with increasing size and topological compexities such as adenine and uracil.     

Potential energy functions of polyatomic molecules

A direct method is proposed for determining polyatomic potential energy functions, expressed in terms of normal coordinates, which yield a given set of vibrational excitation energies. The method is a modification of the semiclassical technique for computing vibrational energy levels of Percival and Pomphrey. The technique is used to derive potential functions for the NO₂, SO₂ and ClO₂ molecules. With these potentials twenty two higher vibrational excitations energies have been predicted for these molecules and these results differ from the experimental values by at most 3 cm^?1. The computed potential functions are not unique despite the apparent accuracy of the vibrational energy levels. Comparison with the RKR method indicates that the present method must be extended to include rotational perturbations.     

Energy Landscape of Aptamer/Protein Complexes Studied by Single‐Molecule Force Spectroscopy

Aptamers are single‐stranded nucleic acid molecules selected in vitro to bind to a variety of target molecules. Aptamers bound to proteins are emerging as a new class of molecules that rival commonly used antibodies in both therapeutic and diagnostic applications. With the increasing application of aptamers as molecular probes for protein recognition, it is important to understand the molecular mechanism of aptamer–protein interaction. Recently, we developed a method of using atomic force microscopy (AFM) to study the single‐molecule rupture force of aptamer/protein complexes. In this work, we investigate further the unbinding dynamics of aptamer/protein complexes and their dissociation‐energy landscape by AFM. The dependence of single‐molecule force on the AFM loading rate was plotted for three aptamer/protein complexes and their dissociation rate constants, and other parameters characterizing their dissociation pathways were obtained. Furthermore, the single‐molecule force spectra of three aptamer/protein complexes were compared to those of the corresponding antibody/protein complexes in the same loading‐rate range. The results revealed two activation barriers and one intermediate state in the unbinding process of aptamer/protein complexes, which is different from the energy landscape of antibody/protein complexes. The results provide new information for the study of aptamer–protein interaction at the molecular level.     

Separation of the vibrational,rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates

A new method is suggested for separating the vibrational, rotational, and translational motions of polyatomic molecules using curvilinear vibrational coordinates that are linear with respect to the natural vibrational coordinates. It is shown that, in this case, Coriolis interactions between the vibrational and rotational motions are absent. The solutions of the anharmonic vibrational-rotational problems in the curvilinear and linear vibrational coordinates are compared. The absence of Coriolis interactions between the vibrational and rotational motions in the curvilinear vibrational coordinates is proved numerically. The same conclusion is additionally supported by calculations of the anharmonic vibrational energy levels for the H₂O, H₂S, NO₂, SO₂, and ClO₂ molecules in the linear and curvilinear vibrational coordinates using the Hamiltonian designed in the curvilinear vibrational coordinates with and without Coriolis vibrational-rotational interactions. Volgograd Pedagogical University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 239–254, March–April, 1995. Translated by I. Izvekova     

A method for the calculation of normal-mode vibrational frequencies using symmetry coordinates. Application to the calculation of secondary deuterium isotope effects on carbocations

A method is introduced for the calculation of normal-mode vibrational frequencies of polyatomic molecules based on numerical differencing of analytical gradients in symmetry coordinates. This procedure requires a number of gradient evaluations equal to the largest number of symmetry coordinates belonging to any single irreducible representation of the molecular point group (plus a single gradient evaluation at the equilibrium configuration), which is fewer than the 3N-6 (N atoms) gradient evaluations needed for schemes based on Cartesian or internal coordinates. While the proposed method will not generally be as efficient as procedures which involve the direct calculation of energy second derivatives analytically (as are now available for single-determinant wavefunctions) it appears to be equally accurate, and it should be the method of choice for frequency calculations involving multideterminant wavefunctions for which analytical second-derivative algorithms have yet to be developed. The method is illustrated by the calculation of equilibrium secondary deuterium-isotope effects on a number of reactions involving simple carbocations.     

Theoretical aspects of IR-laser induced dissociation and desorption processes

A theoretical approach to IR-laser induced dissociation and desorption is described which is based on the generally recognized fact that vibrational energy is mainly transferred on the short range repulsive core of the interaction potential. Because of the shortness of the range, it may be assumed that the motion relevant for the vibrational energy transfer takes place on an element dS of the potential surface which is of small dimensions as compared to those of molecules. The Hamiltonian can be transformed into the form which enables elimination of coordinates which are nearly cyclic on dS and to derive the equation of motion for the distance perpendicular to dS which may be regarded as the relevant generalized coordinate for the problem. Its motion is quantized, and the quantum mechanical transition probabilities must be averaged over different surface elements dS. The theory readily reproduces the most striking features of the vibrational predissociation of complexes like Ar.HCl and Ar.HD. It allows physical insight and can also be implemented on more complex systems where presently no other theoretical methods are available.     

苝二酸酐与嘧啶衍生物的氢键组装

Semi-empirical AM1 method was used to study 1:1 and 1:2 hydrogen bond complexes formed with perylene dianhydride and pyridine derivatives. The weak interaction energy become bigger as the number of hydrogen bonds increases. The donor groups on the host and electron-withdrawing groups on the guest molecules favor hydrogen bonding interactions, and the formation of hydrogen bonding leads to electron density flow from the host to the guest molecules. Electronic spectra of these complexes were computed using INDO/SCI method. Blue-shift of the electronic absorption spectra for the complexes, comparing that of the host,takes place, and the first peaks for different complexes changed slightly. These are in agreement with the experimental results. The cause of blue-shift was discussed, and the electronic transitions were assigned based on theoretical calculations. The potential curve of double proton transfer in the complex was calculated, and the transition state and activated energy relative to the N-H bond were obtained.     

Interplay of bonding and geometry of the adsorption complexes of light alkanes within cationic faujasites. Combined spectroscopic and computational study

A FT-IR spectroscopic study of methane, ethane, and propane adsorption on magnesium and calcium forms of zeolite Y reveals different vibrational properties of the adsorbed molecules depending on the exchanged cation. This is attributed to different adsorption conformations of the hydrocarbons. Two-fold eta(2) coordination of light alkanes is realized for MgY, whereas in case of CaY zeolite quite different adsorption modes are found, involving more C-H bonds in the interaction with the cation. The topological analysis of the electron density distribution function of the adsorption complexes shows that when a hydrocarbon coordinates to the exchanged Mg(2+) ions, van der Waals bonds between H atoms of the alkane and basic zeolitic oxygens significantly contribute to the overall adsorption energy, whereas in case of CaY zeolite such interactions play only an indirect role. It is found that, due to the much smaller ionic radius of the Mg(2+) ion as compared to that of Ca(2+), the former ions are significantly shielded with the surrounding oxygens of the zeolitic cation site. This results in a small electrostatic contribution to the stabilization of the adsorbed molecules. In contrast, for CaY zeolite the stabilization of alkanes in the electrostatic field of the partially shielded Ca(2+) cation significantly contributes to the adsorption energy. This is in agreement with the experimentally observed lower overall absorption of C-H stretching vibrations of alkanes loaded to MgY as compared to those for CaY zeolite. The preferred conformation of the adsorbed alkanes is controlled by the bonding within the adsorption complexes that, in turn, strongly depends on the size and location of the cations in the zeolite cavity.     

Standard free energy of releasing a localized water molecule from the binding pockets of proteins: double-decoupling method

Localized water molecules in the binding pockets of proteins play an important role in noncovalent association of proteins and small drug compounds. At times, the dominant contribution to the binding free energy comes from the release of localized water molecules in the binding pockets of biomolecules. Therefore, to quantify the energetic importance of these water molecules for drug design purposes, we have used the double-decoupling approach to calculate the standard free energy of tying up a water molecule in the binding pockets of two protein complexes. The double-decoupling approach is based on the underlying principle of statistical thermodynamics. We have calculated the standard free energies of tying up the water molecule in the binding pockets of these complexes to be favorable. These water molecules stabilize the protein-drug complexes by interacting with the ligands and binding pockets. Our results offer ideas that could be used in optimizing protein-drug interactions, by designing ligands that are capable of targeting localized water molecules in protein binding sites. The resulting free energy of ligand binding could benefit from the potential free energy gain accompanying the release of these water molecules. Furthermore, we have examined the theoretical background of the double-decoupling method and its connection to the molecular dynamics thermodynamic integration techniques.     

Noble gas-transition-metal complexes: coordination of VO2 and VO4 by Ar and Xe atoms in solid noble gas matrixes

The matrix isolation infrared spectroscopic and quantum chemical calculation results indicate that vanadium oxides, VO2 and VO4, coordinate noble gas atoms in forming noble gas complexes. The results showed that VO2 coordinates two Ar or Xe atoms and that VO4 coordinates one Ar or Xe atom in solid noble gas matrixes. Hence, the VO2 and VO4 molecules trapped in solid noble gas matrixes should be regarded as the VO2(Ng)2 and VO4(Ng) (Ng = Ar or Xe) complexes. The total V-Ng binding energies were predicted to be 12.8, 18.2, 5.0, and 7.3 kcal/mol, respectively, for the VO2(Ar)2, VO2(Xe)2, VO4(Ar), and VO4(Xe) complexes at the CCSD(T)//B3LYP level of theory.