Potential Hypersurface Research Articles

Quantum chemical calculation of normal vibration frequencies of polyatomic molecules

Quantum calculation of molecular vibrational frequency is important in investigating infrared spectrum and Raman spectrum. In this work, a low computational cost method of calculating the quantum chemistry of vibrational frequencies for large molecules is proposed. Usually, the calculation of vibrational frequency of a molecule containing <i>N</i> atoms needs to deal with the Hessian matrix, which consists of second derivatives of the 3<i>N</i>-dimensional potential hypersurface, and then solve secular equations of the matrix to obtain normal vibration modes and the corresponding frequencies. Larger <i>N</i> implies higher computational cost. Therefore, for a limited computational hardware condition, higher-level computations for large <i>N</i> atomic molecule’s vibrational frequencies cannot be implemented in practice. Here we solve this problem by calculating the vibrational frequency for only one vibrational mode each time instead of calculating the Hessian matrix to obtain all vibrational frequencies. When only one vibrational mode is taken into consideration, the molecular potential hypersurface can be transformed into one-dimensional curve. Hence, we can calculate the curve with high-level computational method, then deduce the expression of one-dimensional curve by using harmonic oscillating approximation and obtain the vibrational frequency by using the expression to fit the curve. It should be noted that this method is applied to vibrational modes whose vibrational coordinates can be completely determined by equilibrium geometry and the molecular symmetry and be independent of the molecular force constants. It requires that there exists no other vibrational mode with the same symmetry but with different frequencies. The lower computational cost for a one-dimensional potential curve than that for 3<i>N</i>-dimensional potential hypersurface’s second derivatives permits us to use higher-level method and larger basis set for a given computational hardware condition to achieve more accurate results. In this paper we take the calculation of<i> B</i><sub>2</sub> vibrational frequency of water molecule for example to illustrate the feasibility of this method. Furthermore, we use this method to deal with the SF<sub>6</sub> molecule. It has 7 atoms and 70 electrons, hence there exists a large amount of electronic correlation energy to be calculated. The MRCI is an effective method to calculate the correlation energy. But by now no MRCI result of SF<sub>6</sub> vibrational frequencies has been reported. So here we use MRCI/6-311G* to calculate the potential curves of A<sub>1g</sub>, E<sub>g</sub>, T<sub>2g</sub> and T<sub>2u</sub> vibrational modes separately, deduce their expressions, then use the expressions to fit the curves, and finally obtain the vibrational frequencies. The results are then compared with those obtained by other theoretical methods including HF, MP2, CISD, CCSD(T) and B3LYP methods through using the same 6-311G* basis set. It is shown that the relative error to experimental result of the MRCI method is the least in the results from all these methods.

Theoretical investigations of structural, thermal properties and stability of the group 12 metal M(XH) isomers in atmosphere: M = (Zn, Cd, Hg) and XH = (OH, SH)

Electronic structure calculations have been performed of the group 12 metal (Zn, Cd, Hg) reaction between hydroxyl OH and hydrosulfide SH to understand the processes of transformation in the atmosphere. DFT/B3LYP methods are employed to calculate the structure of reactants, intermediates, transition states and products as well as their equilibrium geometries, electronic properties, dissociation energy. The scalar relativistic effects have been accurately included by making use of the relativistic effective potentials. The computing results obtained at B3LYP/MWB level of M(OH) and M(SH) for doublet and quartet (2,4∑+, 2A′, 4A″ and 2,4∏) state suggest that the doublet states are most stable than the quartet. The computed potential hypersurface 2A′ indicates four stationary points; two of them correspond to the stable structures with symmetries: MOH/MSH(2A′) and OMH/SMH(2∏), and two points correspond to transition states with the symmetries: MOH/MSH(2∑+) and MOH/MSH(2A′). The isomerization process MXH(2A′) → XMH(2∏) via the transition state and the atmospheric stability of M(XH) are also discussed. Examination of dissociation energy, enthalpy of reaction and wavelength from linear form OMH/SMH(2∏) estimate that the molecule has appreciable stability. As for the angled form MOH/MSH(2A′), the values obtained suggest that it is easily dissociable in the presence of solar radiation. Our results are compared with previous work, when available.

Insights into Geometric and Electronic Structures of VGe3-/0 Clusters from Anion Photoelectron Spectrum Assignment.

The global minima of both neutral and anionic clusters of VGe3-/0 were determined using different quantum chemical methods (DFT, RCCSD(T), CASSCF/CASPT2). On the basis of the ground states identified, most excited bands in the anion photoelectron spectrum of VGe3- were assigned. The tetrahedral isomers of both charged states are the most stable ones. A singlet state (Cs,1A') of the tetrahedral isomer has the globally lowest energy on the potential hypersurface of VGe3-. Two states 12A' and 12A″ of the neutral tetrahedral isomer are nearly degenerate and identified as the competing ground state of VGe3. From the anionic ground state, four of five bands in the anion photoelectron spectrum of VGe3- were determined to be the consequences of one-electron transitions starting from the anionic ground state 1A'. Both nearly degenerate neutral ground states are responsible for generation of the first band. Two different transitions from the anionic ground state 1A' to the first two nearly degenerate excited states (22A' and 22A″) of the neutral underlie the second lowest ionization band. Two higher levels of ionization recorded in the spectrum were assigned to the two higher excited states 42A' and 52A' of the neutral. Franck-Condon factor simulations of the first band were performed to obtain more insights into the experimental bands of the spectrum.

Breadth versus depth: Interactions that stabilize particle assemblies to changes in density or temperature.

We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic, convex-repulsive pair potentials that maximize the density range for which a two-dimensional square lattice is the stable ground state subject to a constraint on the chemical potential advantage it exhibits over competing structures (i.e., "depth" of the associated minimum on the chemical potential hypersurface). We formulate the design problem as a nonlinear program, which we solve numerically. This allows us to efficiently find optimized interactions for a wide range of possible chemical potential constraints. We find that assemblies designed to exhibit a large chemical potential advantage at a specified density have a smaller overall range of densities for which they are stable. This trend can be understood by considering the separation-dependent features of the pair potential and its gradient required to enhance the stability of the target structure relative to competitors. Using molecular dynamics simulations, we further show that potentials designed with larger chemical potential advantages exhibit higher melting temperatures.

An improved fast local level set method for three-dimensional inverse gravimetry

We propose an improved fast local level set method for the inverse problem ofgravimetry by developing two novel algorithms: one is of linear complexitydesigned for computing the Frechet derivative of the nonlinear domain inverseproblem, and the other is designed for carrying out numerical continuationrapidly so as to obtain fictitious full measurement data from partialmeasurement. Since the Laplacian kernel is symmetric and translationally invariant, wedesign certain affine transformations to speed up the computational process inevaluating the Frechet derivative; since it decays rapidly away from diagonal,we carry out low-rank matrix approximation to reduce storage requirements. Theseproperties are eventually translated into an algorithm of linear complexity andlinear storage requirement for computing the derivative. Since the single layerdensity function, used in representing the potential, is smooth and periodic onan artificial hypersurface enclosing the target domain, the spectral expansionis allowed to approximate this density function, which eventually leads to rapidalgorithms for carrying out the numerical continuation in both 2-D and 3-Dcases. 2-D and 3-D numerical examples illustrate that this improved level-setmethod is capable of computing high-resolution inversions and handling 3-Dlarge-scale inverse gravimetry problems.

Ultrafast electronic relaxation and vibrational dynamics in a polyacetylene derivative

Real-time vibrational spectra in a polyacetylene derivative, poly[o-TFMPA([o-(trifluoromethyl) phenyl]acetylene)] in a broad electronic spectral region were observed using a sub-7-fs laser. Using the frequencies and initial phases of vibrational modes obtained by the spectroscopy, the assignment of the wavepackets was made. From the first moment, Huang–Rhys parameters were determined for six most prominent modes, which characterize the potential hypersurface composed of multi-dimensional vibrational mode spaces.

D 3h Al3N: a novel promising ligand for coordination chemistry

Several prior experimental and theoretical studies have been reported on Al3N and have shown that the D3h isomer is the global minimum. In this work, we attempt to theoretically design new molecular materials containing the D3h Al3N as unit. A novel series of metal complexes with the Al3N ligand, including [(Al3N)K(Al3N)]+ (traditional homo-decked sandwich), [(Al3N)ZnZn(Al3N)]2+ (binuclear metallocene), and [(Al3N)Zn(C5H5)]+ (hetero-decked sandwich), are predicted to be local minima on their corresponding potential hyper surfaces at the B3LYP, B3PW91, and BP86 levels of theory with the 6–311+G(d) basis set. Natural bond orbital and AOMix analyses indicate that the interaction between the metal ions and the Al3N ligands is mostly electrostatic. This fact suggests that the Al3N is a promising ligand for coordination chemistry.

Evolution of cluster size-distributions in nucleation-growth and spinodal decomposition processes in a regular solution

Nucleation-growth and spinodal decomposition processes are two of the basic mechanisms first-order phase transitions – like condensation and boiling, segregation or crystallization and melting – may proceed. Their adequate theoretical description is essential in order to understand the basis mechanisms of self-structuring of matter at nano-scale dimensions. The basic features of evolution of cluster size-distributions are discussed in detail both for meta-stable (nucleation) and unstable (spinodal decomposition) initial states for a simple model of a binary mixture. The results are obtained by the numerical solution of a set of kinetic equations where the thermodynamics of cluster formation is formulated based on the generalized Gibbs' method. It is shown, that nucleation will not proceed, in general (especially in meta-stable initial states near to the spinodal curve), via the saddle point but in trajectories of evolution by-passing the saddle point. For systems in unstable initial states, spinodal decomposition can proceed similarly to nucleation forming clusters evolving to the new phase via the ridge of the thermodynamic potential hyper-surface.

High resolution infrared spectroscopy and global vibrational analysis for the CH3D and CHD3 isotopomers of methane

We report infrared spectra of CH3D and CHD3 in the range 2900 to 9000 cm−1 measured with the Zürich high resolution Fourier transform infrared (FTIR) interferometer Bruker IFS 125 prototype (ZP 2001) at 80 K in a collisional-cooling cell with optical paths ranging from 5 to 10 m. In all, 57 new ro-vibrational bands of CH3D and 40 for CHD3 were assigned and analysed. Using a strategy of the direct assignment of the J = 0 states of excited vibrational levels, precise experimental values of the band centres with uncertainties in the range of about 0.0001 to 0.0003 cm−1 were obtained. Including 15 previously known band centres of CH3D and 12 previously known band centres of CHD3, these data were used as the initial information for the determination of the harmonic frequencies, anharmonic coefficients, and vibrational resonance interaction parameters in an effective hamiltonian. A joint set of 64 parameters reproduces the 124 experimental vibrational energies of both molecules up to 6500 cm−1 with a root mean deviation of d rms = 0.73 cm−1. The results are discussed in relation to intramolecular dynamics on a global potential hypersurface of methane, intramolecular vibrational redistribution, and the spectroscopy of the atmospheres of the earth and planetary systems.

Preliminary observations on a new water-water potential

A new potential formula for water–water interactions has been proposed. It includes a polarization term to take many-body effects explicitly into account. The potential parameters have been obtained by fitting about 250 ab initio calculated water trimer energies and about 350 water dimer energies. Two fittings are obtained: one with the basis set superposition error corrected, the other uncorrected. Molecular dynamics calculations for both potentials have been carried out for liquid water in order to compare the properties obtained from the potentials with each other and with experimental data where possible. Internal energy, pressure and some dynamical properties are found to be very sensitive to the potential hypersurface in use. Experimental data are generally enclosed between the two potentials.

High-Resolution Near Infrared Spectroscopy and Vibrational Dynamics of Dideuteromethane (CH2D2)

We report the infrared spectrum of CH(2)D(2) measured in the range from 2800 to 6600 cm(-1) with the Zurich high-resolution Fourier transform interferometer Bruker IFS 125 prototype (ZP 2001, with instrumental bandwidth less than 10(-3) cm(-1)) at 78 K in a collisional enclosive flow cooling cell used in the static mode. Precise experimental values (with uncertainties between 0.0001 and 0.001 cm(-1)) were obtained for the band centers by specific assignment of transitions to the J = 0 level of 71 vibrational levels. In combination with 22 previously known band centers, these new results were used as the initial information for the determination of the harmonic frequencies, force constant parameters F(ij), anharmonic coefficients, and vibrational resonance interaction parameters. A set of 47 fitted parameters for an effective Hamiltonian reproduces the vibrational level structure of the CH(2)D(2) molecule up to 6600 cm(-1) with a root-mean-square deviation d(rms) = 0.67 cm(-1). The results are discussed in relation to the multidimensional potential hypersurface of methane and its vibrational dynamics.

STUDY OF THEORETICAL VIBRATIONAL SPECTRA AND THEIR ASSIGNMENTS FOR VINYLPHOSPHONIC AND VINYLTHIOPHOSPHONIC ACIDS

The structures and conformational stability of vinylphosphonic and vinylthiophosphonic acids were investigated using calculations mostly at DFT/6-311G** level and ab initio ones at MP2/6-311G** level. From the calculations the molecules were predicted to exist in a nonplanar near-cis (nc) to trans -gauche (tg) conformational equilibrium with nc (phosphonic oxygen or sulfur nearly eclipses the vinyl group) being the predominant conformer at ambient temperature, at least on the basis of Gibbs free energy (in the case of the thio compound the potential energy of tg is slightly lower than that of nc). The antisymmetric potential function for the internal rotation was determined for each one of the molecules. However, when starting optimizations from a structure too close to the full cis symmetry, the cis form results as an extremum on the potential hyper-surface. Consequently cis was reported in the literature several times as minimum. However, when we calculated the vibrational frequencies the cis form turned out to have an imaginary frequency, and thus cis is a local maximum along one of the normal coordinates. The true minimum, with only real frequencies, actually is an nc one with a very low barrier to rotation. The rotational angle out of cis is rather small; however, HOPX dihedral angles are quite away from real cis. This holds true not only with DFT but also with MP2. The vibrational frequencies were computed and the spectra were plotted as a prediction. Normal coordinate calculations were carried out and potential energy distributions were calculated for the molecules in the nc and the tg conformations. From our results and their analysis, we conclude, in agreement with results from the literature based on localized orbitals, that conjugation effects are absent – or at least negligible – as compared with electrostatic or steric ones in determining the structures of the stable conformers in the vinyl derivatives.

Boron rings containing planar octa-and enneacoordinate cobalt, iron and nickel metal elements

For a series of boron rings with planar hyper-coordinate 8th group transition metal atoms, singlet 1FeB 8 −2 , multiplet k FeB 9 n (n = −1, k = 1; n = 0, k = 2), singlet 1CoB 8 n (n = −1, +1, +3), multiplet k CoB 9 n (n = +1, k = 2; n = 0, k = 1) and singlet 1NiB 9 + , the geometry structures have been optimized to be local minima on corresponding potential hyper-surfaces. The electron structures are discussed by orbital analysis and the aromaticity is predicted by nucleus-independent chemical shifts calculation at both the B3LYP/6-311+G* and BP86/6-311+G* levels of theory, respectively. The results suggest that all these structures with high symmetry planar geometries are stable and have aromatic properties with six π valence electrons.

Correlations of instantaneous transition energy and intensity of absorption peaks during molecular vibration: toward potential hyper-surface

Time-resolved spectrum after ultrashort pulse excitation revealed fine structure of instantaneous vibronic absorption spectra in a thiophene derivative. The probe photon energy-dependent amplitudes of molecular vibration coupled to the induced absorption were composed of several peaks. An absorbance-change peak-tracking method revealed four vibronic transitions buried in the time-integrated spectra over several vibrational periods of typical molecular vibration. Four vibronic transitions located at 2.024, 1.921, 1.818 and 1.731 eV were found to be correlated among themselves with respect to the photon energies and intensities of the peaks in the difference absorbance change spectra. From the size and sign of the correlation strengths the mechanism of the vibronic coupling was related to non-Condon mechanism and Herzberg–Teller vibronic coupling.

A spline for your saddle

Pinpointing extrema on a multidimensional hypersurface is an important generic problem with a broad scope of application in statistical mechanics, biophysics, chemical reaction dynamics, and quantum chemistry. Local minima of the hypersurface correspond to metastable structures and are usually the most important points to look for. They are relatively easy to find using standard minimizing algorithms. A considerably more difficult task is the location of saddle points. The saddle points most sought for are those which form the lowest barriers between given minima and are usually required for determining rates of rare events. We formulate a path functional minimum principle for the saddle point. We then develop a cubic spline method for applying this principle and locating the saddle point(s) separating two local minima on a potential hypersurface. A quasi-Newton algorithm is used for minimization. The algorithm does not involve second derivatives of the hypersurface and the number of potential gradients evaluated is usually less than 10% of the number of potential evaluations. We demonstrate the performance of the method on several standard examples and on a concerted exchange mechanism for self-diffusion in diamond. Finally, we show that the method may be used for solving large constrained minimization problems which are relevant for self-consistent field iterations in large systems.

Analysis of the CH-chromophore spectra and dynamics in dideutero-methyliodide CHD2I1

We report the infrared spectra of dideutero-methyliodide CHD2I in the range from 500 to 12 000 cm−1. Twenty two vibrational bands were assigned to the coupled CH-stretching and bending vibrations of the CH-chromophore. They were analysed in terms of an effective Hamiltonian including strong anharmonic resonances up to the polyad N = 4 corresponding to a maximum of four quanta of stretching excitation. The ab initio potential hypersurface for the three-dimensional CH-chromophore subspace was calculated at the full MP2 level. This surface was finally scaled to fit experiment with vibrational energy levels being calculated by an adiabatic successive truncation technique. The resulting spectrum was represented by the same effective Hamiltonian as used for the experimental data, the results from both approaches agreeing well. The time-dependent quantum dynamics were obtained from this Hamiltonian adjusted to experiment. It showed very fast but incomplete energy transfer from pure CH-stretching excitation with four or five quanta to partial CH-bending excitation in about 100 fs. These results are discussed in terms of a doorway to further excitation transfer to the lower frequency modes measured before by femtosecond pump–probe experiments in our group. 1Dedicated to Hubert van den Bergh on the occasion of his 65th birthday.

Vibrational fine structures revealed by the real-time vibrational phase and amplitude in MEH-PPV using few cycle pulses

It was found that the vibronic transition peaks hidden in a featureless spectrum of induced absorption could be clearly revealed by utilizing the spectra of phases and amplitudes of the molecular vibrational modes. Some of the peaks were also found in a second derivative of a transition spectrum integrated over a delay time from 100 to 700 fs. This is because of the localization of a wave packet in a limited region along the potential multimode hypersurfaces. The transition energy of an induced absorption or an induced emission corresponds to some localized point (space) on the potential hypersurface to which the wave packets visit with some fixed phases.

Stereomutation dynamics in hydrogen peroxide

Hydrogen peroxide (H–O–O–H) is among the simplest prototype molecules showing a chiral equilibrium geometry with the possibility of fast quantum stereomutation in the low barrier limit. We report full dimensional quantum dynamical tunneling calculations on a semi-global fully six-dimensional empirically adjusted potential hypersurface for H 2O 2, which is realistically close to spectroscopic and thermochemical accuracy (B. Kuhn, T.R. Rizzo, D. Luckhaus, M. Quack, M.A. Suhm, J. Chem. Phys. 111 (1999) 2565). Solutions of the time independent Schrödinger equation lead to levels of well defined parity (but undefined chirality), which compare well with available spectroscopic results and provide numerous predictions. Solutions of the time dependent Schrödinger equation with initial conditions of well defined chirality for P and M enantiomers show the time dependent wavepacket motion and periodic change of chirality for time scales between picoseconds and hundreds of picoseconds. Complete six-dimensional dynamics and adiabatic separation of the torsional mode from the high-frequency modes leads to essentially identical results for the stereomutation dynamics in terms of the relevant time dependence. Mode selective inhibition and catalysis of stereomutation by exciting various vibrationally excited levels are reported and discussed in relation to the concept of quasiadiabatic above barrier tunneling. The transition to relaxation behaviour and racemisation is demonstrated with quasithermal wavepackets and analysed in terms of a simple statistical model. At 3000 K the racemisation relaxation time is calculated to be 30 fs. We also discuss the results in the context of recent results on hydrogen peroxide as a prototype system for parity violation in chiral molecules.

Infrared Spectra of the Complexes of Trifluoroethene with Dimethyl Ether, Acetone, and Oxirane: A Cryosolution Study

Infrared spectra of solutions of trifluoroethene and dimethyl ether, acetone, or oxirane in liquid krypton and liquid argon have been studied. For each Lewis base the formation of a 1:1 complex with the Lewis acid was observed. The C-H stretching of trifluoroethene being perturbed by a strong Fermi resonance, the complexes with trifuloroethene-d were also investigated and showed that in each case the hydrogen bond between the acid and base is of the traditional, red-shifting type. The structures of the complexes were investigated using ab initio calculations. These indicate that with dimethyl ether and acetone two different isomeres can be formed, but with a single one detected in the solution in each case. The Fermi resonance in the complex with unlabeled trifluoroethene is discussed using data derived form ab initio potential and dipole hypersurface calculations. The complexation enthalpies of the complexes were obtained from temperature dependent studies of the solutions and are discussed in relation to the ab initio complexation energies and Monte Carlo free energy perturbation calculations of solvent effects.

Mode selective tunneling dynamics observed by high resolution spectroscopy of the bending fundamentals of N14H2D and N14D2H

High resolution (0.004 and 0.01 cm(-1) instrumental bandwidth) interferometric Fourier transform infrared spectra of (14)NH2D and (14)ND2H were measured on a Bomem DA002 spectrometer in a supersonic jet expansion and at room temperature. We report the analysis of the bending fundamentals of (14)NH2D with term values Tv(s)=1389.9063(2) cm(-1) and Tv(a)=1390.4953(2) cm(-1) for the nu(4b) fundamental and Tv(s)=1605.6404(7) cm(-1) and Tv(a)=1591.0019(7) cm(-1) for the nu(4a) fundamental, and of (14)ND2H with term values of Tv(s)=1233.3740(2) cm(-1) and Tv(a)=1235.8904(2) cm(-1) for the nu(4a) fundamental and Tv(s)=1461.7941(9) cm(-1) and Tv(a)=1461.9918(19) cm(-1) for the nu(4b) fundamental. In all cases Tv(s) gives the position of the symmetric inversion sublevel (with positive parity) and Tv(a) the position of the antisymmetric inversion sublevel (with negative parity). The notation for the fundamentals nu(4a) and nu(4b) is chosen by correlation with the degenerate nu(4) mode in the C(3v) symmetric molecules NH3 and ND3. The degeneracy is lifted in Cs symmetry and a indicates the symmetric, b the antisymmetric normal mode with respect to the Cs symmetry plane in NH2D and ND2H. Assignments were established with certainty by means of ground state combination differences. About 20 molecular parameters of the effective S-reduced Hamiltonian could be determined accurately for each fundamental. In particular, the effect of Fermi resonances of the 2nu(2) overtone with the nu(4a) bending mode was observed, leading to an increased inversion splitting in the case of ND2H and to a strongly increased inversion splitting and an inverted order of the two inversion levels in NH2D. Rotational perturbations observed with the nu(4b) bending fundamentals are probably due to Coriolis interactions with the inversion overtone 2nu(2). The results are important for understanding isotope effects on the inversion in ammonia as well as its selective catalysis and inhibition by excitation of different vibrational modes, as treated by quantum dynamics on high dimensional potential hypersurfaces of this molecule.