Quantum mechanical model for the dissociative adsorption of diatomic molecules on metal surfaces

A quantum mechanical nonadiabatic theory of dissociative adsorption of diatomic molecules X2 on metal surface is presented. The following reaction coordinates are used to construct crossing diabatic potential energy surfaces (PES): the distance y between the atoms of the X2 molecule, the distance x of the X2 molecular axis from the surface, the set of coordinates describing possible displacements of metal atoms under adsorption. Expression for the rate constant is derived using the model potentials describing vibrations along these coordinates. The calculated dependency of the rate constant W on the reaction heat DeltaE is compared with that in classical approximation. It is shown that quantum effects lead to a weaker dependence of W on DeltaE as compared to that for classical one.     

Vibrational spectra and normal coordinate analysis for cis-diamminetetrachloroplatinum

The normal coordinate analysis of cis-diamminetetrachloroplatinum has been carried out by using a modified Urey—Bradley force field. According to the molecular structure, 45 internal coordinates were established and 33 theoretical vibrational frequencies were calculated. Due to considering the interaction between non-neighbouring stretching vibrations and between bending vibrations and introducing an appropriate set of internal coordinates in the course of calculation, the calculated frequencies agree well with the observed values, with an average difference 3.61 cm⁻¹ between them. The rationality and the reliability of the results are discussed and the questionable empirical assignment of ν(PtCl) in the literature is corrected.     

Molecular dynamics integration and molecular vibrational theory. I. New symplectic integrators

New symplectic integrators have been developed by combining molecular dynamics integration with the standard theory of molecular vibrations to solve the Hamiltonian equations of motion. The presented integrators analytically resolve the internal high-frequency molecular vibrations by introducing a translating and rotating internal coordinate system of a molecule and calculating normal modes of an isolated molecule only. The translation and rotation of a molecule are treated as vibrational motions with the vibrational frequency zero. All types of motion are thus described in terms of the normal coordinates. The method's time reversibility requirement was used to determine the equations of motion for internal coordinate system of a molecule. The calculation of long-range forces is performed numerically within the generalized second-order leap-frog scheme, in the same way as in standard second-order symplectic methods. The new methods for integrating classical equations of motion using normal mode analysis allow us to use a long integration step and are applicable to any system of molecules with one equilibrium configuration.     

Kinetic energy operators in linearized internal coordinates

It is customary to describe molecular vibrations using as exact kinetic energy operators and as accurate potentials as possible. It has become a standard approach to express Hamiltonians in curvilinear internal displacement coordinates, because they offer a simple and physical picture of vibrational motions, including large amplitude changes in the shape. In the older normal mode model of molecular vibrations, the nuclei are thought to vibrate infinitesimally about the reference configuration, and the shape of the molecule is described using linearized approximations of the true geometrically defined internal displacement coordinates. It is natural to ask how the two approaches are related. In this work, I present a general yet practical way to obtain curvilinear displacement coordinates as closed function of their linearized counterparts, and vice versa. In contrast to the conventional power series approach, the body-frame dependency is explicitly taken into account, and the relations are valid for any value of the coordinates. The present approach also allows one to obtain easily exact kinetic energy operators in linearized shape coordinates.     

Theoretical modeling of the interaction of phenylacetylene and styrene molecules with Pd{111}

The DFT-PBE method was used to calculate the structural and energy characteristics of all possible adsorption complexes of phenylacetylene (PA) and styrene (St) molecules with the Pd{111} surface. According to the calculations, the acetylene group of the PA molecule in the energetically preferred complexes is bound to three or four Pd atoms and the plane of the phenyl ring is parallel to the Pd surface. In the case of deficiency of fcc sites, the phenyl ring of the PA molecule is displaced from the Pd{111} surface. The number of Pd atoms required for the compact adsorption of two PA molecules is the same as that for the adsorption of one St molecule.     

Normal Coordinate Analysis in Cartesian Space III. The Symmetric Nonplanar XYn Type Molecules

The normal vibrations of tetrahedral hydride and octahedral hexafluoride have been studied in the Cartesian coordinates. Equations relating the force constants with the vibrational frequencies are derived by using symmetry coordinates. Numerical values of the force constants and normal coordinates of these molecules are tabulated.     

Ab initio calculations of the ultraviolet resonance Raman spectra of uracil

An equation been derived to calculate, ab initio, the frequencies and intensities of a resonant Raman spectrum from the transform theory of resonance Raman scattering. This equation has been used to calculate the intensities of the ultraviolet resonance Raman spectra from the first π-π* excited state of uracil and 1,3-dideuterouracil. The protocol for this calculation is as follows: (1) The force constant matrix elements in Cartesian coordinate space, the vibrational frequencies, and the minimum energy ground and excited state geometries of the molecule are calculated ab initio using the molecular orbital program Gaussian 92, (2) the force constants in Cartesian coordinates are transformed into force constants in the space of a set of 3N – 6 nonredundant symmetrized internal coordinates, (3) the G matrix is constructed from the energy minimized ground state Cartesian coordinates and the GFL = LΛ eigenvalue equation is solved in internal coordinate space, (4) the elements of the L and L^?1 matrices are calculated, (5) the changes in all of the internal coordinates in going from the ground to the excited state are calculated, and (6) these results are used in combination with the transform theory of resonance Raman scattering to calculate the relative intensities of each of the 3N – 6 vibrations as a function of the exciting laser frequency. There are no adjustable parameters in this calculation, which reproduces the experimental frequencies and intensities with remarkable fidelity. This indicates that the Dushinsky rotation of the modes in the excited state of these molecules is not important and that the simplest form of the transform theory is adequate. © 1995 John Wiley & Sons, Inc.     

Normal coordinate analysis of H8Si8O12

Normal coordinate analysis of the fundamental vibrations of H₈Si₈O₁₂ has been carried out. Because of the octahedral symmetry, the 78 vibrational degrees of freedom lead to 33 different vibrations, six of which are infrared active, 13 are Raman active and 14 are inactive. From the internal coordinates one gets 116 symmetry coordinates. We describe a straightforward method for determining the internal symmetry coordinates of any molecular system. Internal coordinates, symmetry force constants, the full set of orthonormal symmetry coordinates as well as the 38 redundant orthonormal symmetry coordinates of H₈Si₈O₁₂ are tabulated. The potential energy distribution analysis shows that most of the fundamental vibrations can be very well interpreted in terms of the internal vibrations ν(SiH), ν(SiO), δ(SiH), δ(OSiO) and δ(SiOSi) which makes it easy to compare them with vibrations observed in other silsesquioxanes and similar silicon compounds.     

A reaction surface Hamiltonian study of malonaldehyde

We report calculations using a reaction surface Hamiltonian for which the vibrations of a molecule are represented by 3N-8 normal coordinates, Q, and two large amplitude motions, s(1) and s(2). The exact form of the kinetic energy operator is derived in these coordinates. The potential surface is first represented as a quadratic in Q, the coefficients of which depend upon the values of s(1),s(2) and then extended to include up to Q(6) diagonal anharmonic terms. The vibrational energy levels are evaluated by solving the variational secular equations, using a basis of products of Hermite polynomials and appropriate functions of s(1),s(2). Our selected example is malonaldehyde (N=9) and we choose as surface parameters two OH distances of the migrating H in the internal hydrogen transfer. The reaction surface Hamiltonian is ideally suited to the study of the kind of tunneling dynamics present in malonaldehyde. Our results are in good agreement with previous calculations of the zero point tunneling splitting and in general agreement with observed data. Interpretation of our two-dimensional reaction surface states suggests that the OH stretching fundamental is incorrectly assigned in the infrared spectrum. This mode appears at a much lower frequency in our calculations due to substantial transition state character.     

Calculation of Chlorin IR Spectrum by Density Functional Theory

The structure, frequencies of normal vibrations, and absolute intensities of bands in the IR spectra of chlorin and four of its symmetric isotopomers were calculated using DFT/B3LYP with the 6-31G(d) basis set. The force field was scaled by the Pulay method in independent and dependent natural coordinates. A method for obtaining effective force fields without using experimental data for the frequencies of fundamental vibrations was proposed. It has been demonstrated that most vibrations of the porphyrin macrocycle have characteristic frequencies upon hydrogenation of the pyrrolenine ring and only 12 vibrations differed significantly. The IR spectra of chlorin and its isotopomers were modelled. Frequencies were assigned and normal vibrations were interpreted for the examined molecules.     

Normal coordinate analysis and DFT calculations of the vibrational spectra for lanthanide(III) complexes with 3-bromo-4-methoxy-2,6-lutidine N-oxide: LnCl3(3Br4CH3OC7H7NO)3 (Ln=Pr, Nd, Sm, Eu, Gd, Dy)

The results of the FT-Raman and FT-IR studies of the LnCl₃(LNO)₃ type complexes (where Ln=Pr, Nd, Sm, Eu, Gd, Dy and LNO=3-Br-4-CH₃OC₇H₇NO) are presented. The spectral contours observed in the regions of the lanthanide-oxygen, lanthanide-chlorine and nitrogen-oxygen vibrations are employed in the discussion of the molecular structure of the complex ions and the local symmetry of the LnCl₃(ON)₃ polyhedron. The discussion of the vibrational spectra is based on the classical normal coordinate analysis and its results are compared to the results of DFT quantum chemical calculations performed for complete molecule. The normal coordinate analysis has been performed for PrCl₃(ON)₃ and DyCl₃(ON)₃ molecular systems, which have been treated as a different ‘isotopic units’. Basing on the predominant PED contributions of the respective internal coordinates the assignment of the normal vibrations has been proposed.     

Internal vibrations of the Li(NH3)4+ complex analyzed from ab initio, density functional theory, and the classical spring network model

We report our theoretical findings regarding internal vibrations of the Li(NH 3) 4 (+) complex which have been studied using three different methods, namely, a classical spring network model, density functional theory, and ab initio Hartree-Fock plus M?ller-Plesset correlation energy correction truncated at second-order. The equilibrium Li...N and N...N distances are found to be 2.12 and 3.47 A, respectively, in good agreement with the experimental data. The theoretically determined vibrational frequencies of the lowest modes are in good agreement with those extracted from inelastic X-ray scattering measurements. From group theory considerations, the internal vibrations of Li(NH 3) 4 (+) complexes resemble those of a tetrahedral object. Further experimental investigation is suggested.     

IR Spectra of N,N′-Ethylene-Bis(salicylaldiminates) and N,N′-ethylene-Bis(acetylacetoniminates) of Ni(II), Cu(II), and Zn(II)

Vibrational spectra of N,N′-ethylene-Bis(salicylaldiminaates) and N,N′-ethylene-Bis(acetylacetoniminates) of nickel (II), copper (II), and zinc (II) are studied experimentally (IR spectroscopy, 400–4000 cm⁻¹) and theoretically (B3LYP), band assignment is given, and the distribution of potential energy of normal vibrations in internal coordinates is studied. Differences between vibrational spectra of the complexes are discussed. Thermodynamic functions of gas-phase complexes corresponding to temperatures of 298 and 800 K are calculated.     

Investigation into the nature of intermolecular and ion—molecular interactions in H-groups of hydroxyl-containing compounds and calculation of vibration frequencies for A-H and H⋯X bonds using the anharmonic approach

Quantum chemistry calculation methods are used to study the H-bond formation in ion—molecular and molecular complexes of hydroxyl-containing compounds. The effect of electrostatic fields of electron donors and acceptors on the H-bond stability and the frequency of OH valence vibrations is studied. Charge transfer effects are analyzed. Potential surface parameters for complexes are calculated and the results used to calculate vibration frequencies for fundamental transitions and the first overtones for valence A-H and H?X vibrations in multiatomic models using the anharmonic approximation.     

The use of internal cartesian coordinates for describing molecular vibrations

An analysis of the influence of isotope substitution on the system of electronic-nuclear equations for an arbitrary molecular system was used as a basis for formulating invariance conditions with respect to isotope substitution of the potential energy surface written in the Cartesian coordinates rigidly bound with the center of mass of the molecule (internal Cartesian coordinates). This property of the potential function obviates the necessity of using curvilinear natural coordinates, which can be replaced by Cartesian coordinates, in theoretical studies of the vibrational spectra of molecules and their isotopomers and in solving the direct and inverse anharmonic problems. An equation for the quantum-mechanical Hamiltonian of a normal molecule in internal Cartesian coordinates was obtained.     

The molecular structure and vibrational spectra of corrolazine metal complexes (CzM) by density functional theory

The ground-state geometries, electronic structures and vibrational frequencies of metal corrolazine complexes, CzM (M=Mn, Co, Ni and Fe) have been studied using B3LYP/6-311 g(d) method. The molecular geometries are sensitive to the species of the metal, and the bond length of the MN is increase with the metal atom radii. The ground-state electronic structures indicate that there are strong interactions between dx2-y2 of the metal fragments and the corrolazine fragments. The calculations also indicate that the CzNi is the stabilest among the four metal corrolazine complexes. Vibrational frequencies of these metal corrolazine complexes were also calculated and were assigned to the local coordinates of the corrolazine ring, which reveals the some common feature of the molecular vibrations of the metal corrolazine complexes as four-coordination metallocorrolazines.     

Quantum chemical calculation of infrared spectra of acidic groups in chabazite in the presence of water

The changes in the spectra of the acidic group in chabazite are studied by quantum chemical calculations. The zeolite is modeled by two clusters consisting of eight tetrahedral atoms arranged in a ring and seven tetrahedral atoms coordinated around the zeolite OH group. The potential energy and dipole surfaces were constructed from the zeolite OH stretch, in-plane and out-of-plane bending coordinates, and the intermolecular stretch coordinate that corresponds to a movement of the water molecule as a whole. Both the anharmonicities of the potential energy and dipole were taken into account by calculation of the frequencies and intensities. The matrix elements of the vibrational Hamiltonian were calculated within the discrete variable representation basis set. We have assigned the experimentally observed frequencies at approximately 2900, approximately 2400, and approximately 1700 cm(-1) to the strongly perturbed zeolite OH vibrations caused by the hydrogen bonding with the water molecule. The ABC triplet is a Fermi resonance of the zeolite OH stretch mode with the overtone of the in-plane bending (the A band) and the overtone of the out-of-plane bending (the C band). In the B band the stretch is also coupled with the second overtone of the out-of-plane bending. The frequencies at approximately 3700 and approximately 3550 cm(-1) we have assigned to the OH stretch frequencies of a slightly perturbed water molecule.     

A five-dimensional potential energy surface and predicted infrared spectra for the N2O-hydrogen complexes

We present a five-dimensional potential energy surface for the N(2)O-hydrogen complex using supermolecular approach with the full counterpoise correction at the coupled-cluster singles and doubles with noniterative inclusion of connected triple level. The normal mode Q(3) for the nu(3) antisymmetric stretching vibration of the N(2)O molecule was included in the calculations of the potential energies. The radial discrete variable representation/angular finite basis representation method and Lanczos algorithm were employed to calculate the rovibrational energy levels for four species of N(2)O-hydrogen complexes (N(2)O-para-H(2), -ortho-H(2), -ortho-D(2), and -para-D(2)) without separating the inter- and intramolecular vibrations. The calculated band origins are all blueshifted relative to the isolated N(2)O molecule and in good agreement with the experimental values. The calculated rotational spectroscopic constants and molecular structures agree well with the available experimental results. The frequencies and line intensities of the rovibrational transitions in the nu(3) region of N(2)O for the van der Waals ground vibrational state were calculated and compared with the observed spectra. The predicted infrared spectra are consistent with the observed spectra and show that the N(2)O-H(2) complexes are mostly a-type transitions while both a-type and b-type transitions are significant for the N(2)O-D(2) complexes.