Isotope effect of hydrogen and lithium hydride molecules. Application of the dynamic extended molecular orbital method and energy component analysis

In order to explore the isotope effect including the nuclear–electronic coupling and nuclear quantum effects under the one-particle approximation, we apply the dynamic extended molecular orbital (DEMO) method and energy component analysis to the hydrogen and lithium hydride isotope molecules. Since the DEMO method determines both electronic and nuclear wave functions simultaneously by variationally optimizing all parameters embedded in the basis sets, the virial theorem is completely satisfied and guarantees the relation of the kinetic and potential energies. We confirm the isotope effect on internuclear distances, nuclear and electronic wave functions, dipole moment, the polarizability, and each energy component. In the case of isotopic species of the hydrogen molecule, the total energy decreases from the H₂ to the T₂ molecule due to the stabilization of the nuclear–electronic potential component, as well as the nuclear kinetic one. In the case of the lithium hydride molecule, the energy lowering by replacing ⁶Li with ⁷Li is calculated to be greater than that by replacing H with D. This is mainly caused by the small destabilization of electron–electron and nuclear–nuclear repulsion in ⁷LiH compared to ⁶LiH, while the change in the repulsive components from ⁶LiH to ⁶LiD increases. Received: 24 March 1999 / Accepted: 5 August 1999 / Published online: 15 December 1999     

Ab initio calculation and quasi‐classical dynamics study of the two lowest potential energy surfaces of the O(1D)+HBr system*

The lowest singlet 1¹A′ and 1¹A″ potential energy surfaces (PES) of the O(¹D)+HBr system have been ab initio computed. The complete active space self‐consistent field (CASSCF) method was used in most of the calculations, considering all the valence orbitals as active. The calculations were complemented with both analytical gradient calculations to characterize the stationary points and multireference configuration interaction (MRCI) calculations at selected nuclear geometries to improve the determination of the barrier heights and of the energetics. Electronic energy values for both PESs were then independently fitted by polynomial expansions in bond order coordinates. On the fitted surfaces quasi‐classical trajectories were separately run. Single‐surface calculations behave qualitatively different for the ground and the excited PES at low collision energies. A satisfactory agreement with existing experimental data was obtained by using the ground PES while calculations performed on the excited 1¹A″ PES worsened the agreement. However, when collision energy is increased, detailed experimental distributions are less well reproduced by calculations on the ground PES. This may imply the participation via nonadiabatic transitions of the 2¹A′ PES at higher energies while the adiabatic ground singlet PES well describes reactive scattering at low collision energy. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

On the role of dynamical barriers in barrierless reactions at low energies: S(1D) + H2

Reaction probabilities as a function of total angular momentum (opacity functions) and the resulting reaction cross sections for the collision of open shell S((1)D) atoms with para-hydrogen have been calculated in the kinetic energy range 0.09-10 meV (1-120 K). The quantum mechanical hyperspherical reactive scattering method and quasi-classical trajectory and statistical quasi-classical trajectory approaches were used. Two different ab initio potential energy surfaces (PESs) have been considered. The widely used reproducing kernel Hilbert space (RKHS) PES by Ho et al. [T.-S. Ho, T. Hollebeek, H. Rabitz, S. D. Chao, R. T. Skodje, A. S. Zyubin, and A. M. Mebel, J. Chem. Phys 116, 4124 (2002)] and the recently published accurate double many-body expansion (DMBE)/complete basis set (CBS) PES by Song and Varandas [Y. Z. Song and A. J. C. Varandas, J. Chem. Phys. 130, 134317 (2009)]. The calculations at low collision energies reveal very different dynamical behaviors on the two PESs. The reactivity on the RKHS PES is found to be considerably larger than that on the DMBE/CBS PES as a result of larger reaction probabilities at low total (here also orbital) angular momentum values and to opacity functions which extend to significantly larger total angular momentum values. The observed differences have their origin in two major distinct topographic features. Although both PESs are essentially barrierless for equilibrium H-H distances, when the H-H bond is compressed the DMBE/CBS PES gives rise to a dynamical barrier which limits the reactivity of the system. This barrier is completely absent in the RHKS PES. In addition, the latter PES exhibits a van der Walls well in the entrance channel which reduces the height of the centrifugal barrier and is able to support resonances. As a result, a significant larger cross section is found on this PES, with marked oscillations attributable to shape resonances and/or to the opening of partial wave contributions. The comparison of the results on both PESs is illustrative of the wealth of the dynamics at low collision energy. It is also illuminating about the difficulties encountered in modeling an all-purpose global potential energy surface.     

A nine-dimensional calculation of the vibrational OH stretching and HOH bending spectrum of the water trimer

We have studied the vibrational high-frequency spectrum of the water trimer computationally. We expand an earlier study [J. Chem. Phys. A 2009, 113, 9124-9132] where we approximated the water trimer as three individually vibrating water monomer units. Some intramolecular potential energy coupling terms are now included in the previous model. The six OH bond lengths and the three HOH bending angles are used as the internal coordinates. The kinetic energy operator is a sum of the kinetic energy operators of the monomer units. We use the coupled cluster method with single, double, and perturbative triple excitations method [CCSD(T)] with augmented correlation consistent polarized valence triple-ζ (aug-cc-pVTZ) basis set to calculate the potential energy surface (PES). The counterpoise correction is included in the one-dimensional part of the PES. We calculate the vibrational energy eigenvalues using the variational method. The corresponding eigenfunctions are used to obtain the absorption intensities.     

Efficiency considerations in the construction of interpolated potential energy surfaces for the calculation of quantum observables by diffusion Monte Carlo

A modified Shepard interpolation scheme is used to construct global potential energy surfaces (PES) in order to calculate quantum observables--vibrationally averaged internal coordinates, fully anharmonic zero-point energies and nuclear radial distribution functions--for a prototypical loosely bound molecular system, the water dimer. The efficiency of PES construction is examined with respect to (a) the method used to sample configurational space, (b) the method used to choose which points to add to the PES data set, and (c) the use of either a one- or two-part weight function. The most efficient method for constructing the PES is found to require a quantum sampling regime, a combination of both h-weight and rms methods for choosing data points and use of the two-part weight function in the interpolation. Using this regime, the quantum diffusion Monte Carlo zero-point energy converges to the exact result within addition of 50 data points. The vibrationally averaged O-O distance and O-O radial distribution function, however, converge more slowly and require addition of over 500 data points. The methods presented here are expected to be applicable to both other loosely bound complexes as well as tightly bound molecular species. When combined with high quality ab initio calculations, these methods should be able to accurately characterize the PES of such species.     

Accurate time-dependent wave packet study of the Li + H₂⁺ reaction and its isotopic variants

The dynamics and kinetics of the Li + H?? reaction and its isotopic variants (D?? and T??) have been studied by using a time-dependent wave packet (TDWP) coupled-channel (CC) method on the ab initio potential energy surface (PES) of Martinazzo et al. [J. Chem. Phys. 2003, 119, 21]. Total initial v = 0, j = 0 state-selected reaction probabilities for the Li + H?? reaction and its isotopic variants have been calculated from the threshold up to 1 eV for total angular momenta J from 0 to 90. Integral cross sections have been evaluated from the reaction probabilities at collision energies from threshold (≈0.2 eV) up to 1.0 eV collision. The calculated rate constants as a function of temperature show an Arrhenius type behavior in the 200 ≤ T ≤ 1000 K temperature interval. It has been found to be a considerable large intermolecular kinetic isotope effect. The TDWP-CC results are in overall good agreement with those obtained applying the TDWP Centrifugal-Sudden (CS) approximation, showing that the CS approximation is rather accurate for the title reaction.     

Cross sections of the O+ + H2 --> OH+ + H ion-molecule reaction and isotopic variants (D2, HD): quasiclassical trajectory study and comparison with experiments

A dynamics study [cross section and microscopic mechanism versus collision energy (E(T))] of the reaction O+ + H2 --> OH+ + H, which plays an important role in Earth's ionosphere and interstellar chemistry, was conducted using the quasiclassical trajectory method, employing an analytical potential energy surface (PES) recently derived by our group [R. Martinez et al., J. Chem. Phys. 120, 4705 (2004)]. Experimental excitation functions for the title reaction, as well as its isotopic variants with D2 and HD, were near-quantitatively reproduced in the calculations in the very broad collision energy range explored (E(T) = 0.01-6.0 eV). Intramolecular and intermolecular isotopic effects were also examined, yielding data in good agreement with experimental results. The reaction occurs via two microscopic mechanisms (direct and nondirect abstraction). The results were satisfactorily interpreted based on the reaction probability and the maximum impact parameter dependences with E(T), and considering the influence of the collinear [OHH]+ absolute minimum of the PES on the evolution from reactants to products. The agreement between theory and experiment suggests that the reaction mainly occurs through the lowest energy PES and nonadiabatic processes are not very important in the wide collision energy range analyzed. Hence, the PES used to describe this reaction is suitable for both kinetics and dynamics studies.     

Kinetics of model energy landscapes: an approach to complex systems

An idealized potential energy surface (PES), simply a PES-like network of stationary points, is demonstrated to be a useful tool to study kinetic relaxation of complex energy landscapes. Combined with a master equation, we show that if constructed with proper regularity, the kinetics of the PES is easy to predict and understand by carefully examining the eigenmodes of the master equation. By modifying the idealized PES model to make it more and more complicated, we demonstrate a systematic method to study the complex kinetics on large PES. The idealized PES model is used to explore the feasibility and the robustness of statistical sampling of large PES. We develop several sampling strategies, such as the "rough topography sampling" and the "low barrier saddle sampling" in the idealized PES model and find they are also applicable to a realistic PES of the 13-atom Morse cluster with range parameter rho= 6. To measure the robustness of the sampling methods, we compare the eigenvalue spectra, the eigenvector similarity and the relaxation times of the total energy of the full and sample PESs.     

A global potential energy surface and time‐dependent quantum wave packet calculation of Au + H2 reaction

A global potential energy surface (PES) corresponding to the ground state of AuH₂ system has been constructed based on 22 853 ab initio energies calculated by the multireference configuration interaction method with a Davidson correction. The neural network method is used to fit the PES, and the root mean square error is only 1.87 meV. The topographical features of the novel global PES are compared with previous PES which is constructed by Zanchet et al. (Zanchet PES). The global minimum energy reaction paths on the two PESs both have a well and a barrier. Relative to the Au + H₂ reactants, the energy of well is 0.316 eV on the new PES, which is 0.421 eV deeper than Zanchet PES. The calculation of Au(²S) + H₂(X¹Σ_g⁺) → AuH(X¹Σ⁺) + H(²S) dynamical reaction is carried out on new PES, by the time‐dependent quantum wave packet method (TDWP) with second order split operator. The reaction probabilities, integral cross‐sections (ICSs) and differential cross‐sections are obtained from the dynamics calculation. The threshold in the reaction is about 1.46 eV, which is 0.07 eV smaller than Zanchet PES due to the different endothermic energies on the two PESs. At low collision energy (<2.3 eV), the total ICS is larger than the result obtained on Zanchet PES, which can be attributed to the difference of the wells and endothermic energies.     

Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water

An integrated Feynman path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method has been used to investigate the kinetic isotope effects (KIEs) in the proton transfer reaction between nitroethane and acetate ion in water. In the present study, both nuclear and electronic quantum effects are explicitly treated for the reacting system. The nuclear quantum effects are represented by bisection sampling centroid path integral simulations, while the potential energy surface is described by a combined quantum mechanical and molecular mechanical (QM/MM) potential. The accuracy essential for computing KIEs is achieved by a FEP technique that transforms the mass of a light isotope into a heavy one, which is equivalent to the perturbation of the coordinates for the path integral quasiparticle in the bisection sampling scheme. The PI-FEP/UM method is applied to the proton abstraction of nitroethane by acetate ion in water through molecular dynamics simulations. The rule of the geometric mean and the Swain-Schaad exponents for various isotopic substitutions at the primary and secondary sites have been examined. The computed total deuterium KIEs are in accord with experiments. It is found that the mixed isotopic Swain-Schaad exponents are very close to the semiclassical limits, suggesting that tunneling effects do not significantly affect this property for the reaction between nitroethane and acetate ion in aqueous solution.     

Substituent effects on the photophysical properties of 2,9-substituted phenanthroline copper(I) complexes: a theoretical investigation

The electronic and nuclear structures of a series of [Cu(2,9-(X)₂-phen)₂]⁺ copper(I) complexes (phen=1,10-phenanthroline; X=H, F, Cl, Br, I, Me, CN) in their ground and excited states are investigated by means of density functional theory (DFT) and time-dependent (TD-DFT) methods. Subsequent Born-Oppenheimer molecular dynamics is used for exploring the T₁ potential energy surface (PES). The T₁ and S₁ energy profiles, which connect the degenerate minima induced by ligand flattening and Cu−N bond symmetry breaking when exciting the molecule are calculated as well as transition state (TS) structures and related energy barriers. Three nuclear motions drive the photophysics, namely the coordination sphere asymmetric breathing, the well-documented pseudo Jahn-Teller (PJT) distortion and the bending of the phen ligands. This theoretical study reveals the limit of the static picture based on potential energy surfaces minima and transition states for interpreting the luminescent and TADF properties of this class of molecules. Whereas minor asymmetric Cu−N bonds breathing accompanies the metal-to-ligand-charge-transfer re-localization over one or the other phen ligand, the three nuclear movements participate to the flattening of the electronically excited complexes. This leads to negligible energy barriers whatever the ligand X for the first process and significant ligand dependent energy barriers for the formation of the flattened conformers. Born-Oppenheimer (BO) dynamics simulation of the structural evolution on the T₁ PES over 11 ps at 300 K confirms the fast backwards and forwards motion of the phenanthroline within 200–300 fs period and corroborates the presence of metastable C₂ structures.     

The Role of High Excitations in Constructing Sub-spectroscopic Accuracy Intermolecular Potential of He-HCN: Critically Examined by the High-Resolution Spectra with Resonance States

Interpreting high-resolution rovibrational spectra of weakly bound complexes commonly requires spectroscopic accuracy (<1 cm^-1) potential energy surfaces (PES). Constructing high-accuracy ab initio PES relies on the high-level electronic structure approaches and the accurate physical models to represent the potentials. The coupled cluster approaches including single and double excitations with a perturbational estimate of triple excitations (CCSD(T)) have been termed the "gold standard" of electronic structure theory, and widely used in generating intermolecular interaction energies for most van der Waals complexes. However, for HCN-He complex, the observed millimeter-wave spectroscopy with high-excited resonance states has not been assigned and interpreted even on the ab initio PES computed at CCSD(T) level of theory with the complete basis set (CBS) limit. In this work, an effective three-dimensional ab initio PES for HCN-He, which explicitly incorporates dependence on the Q₁ (C-H) normal-mode coordinate of the HCN monomer has been calculated at the CCSD(T)/CBS level. The post-CCSD(T) interaction energy has been examined and included in our PES. Analytic two-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for v₁(C-H)=0, and 1 to the Morse/Long-Range potential function form with root-mean-square deviations (RMSD) smaller than 0.011 cm^-1. The role and significance of the post-CCSD(T) interaction energy contribution are clearly illustrated by comparison with the predicted rovibrational energy levels. With or without post-CCSD(T) corrections, the value of dissociation limit (D₀) is 8.919 or 9.403 cm^-1, respectively. The predicted millimeter-wave transitions and intensities from the PES with post-CCSD(T) excitation corrections are in good agreement with the available experimental data with RMS discrepancy of 0.072 cm^-1. Moreover, the infrared spectrum for HCN-He complex is predicted for the first time. These results will serve as a good starting point and provide reliable guidance for future infrared studies of HCN doped in (He)_n clusters.     

Potential surfaces and nonadiabatic couplings in ionic systems: A study of the (O2H)+ interactions

The adiabatic potential energy surfaces (PES ) which are most likely to be involved in the elementary mechanism presiding over charge-exchange and direct inelastic collisions between O₂ molecules and collimated beams of protons are discussed. The general behavior of Diatomics-in-molecule (DIM ) model interactions is analyzed in great detail as a function of the molecular vibrational coordinate and of the other internal nuclear coordinates. The general features of the lower two PES are discussed, and the corresponding nonadiabatic coupling terms between these surfaces are also computed and analyzed. These model results turn out to provide very useful indications on the specific dynamical features that are to be considered responsible for the inelastic, vibronic transitions observed in the target molecule during collisional experiments.     

Dissociative double ionization of CO2: dynamics, energy levels, and lifetime

In a kinematically complete experiment on the dissociative double ionization of CO2 by electron impact, spontaneous and metastable decay have been observed via the channel CO2(2+) --> CO+ + O+. The metastable decay shows a lifetime of 5.8 +/- 1.5 micros. The measured kinetic energy release spectrum of the dissociation shows one broad peak. To understand the observed features, ab initio potential energy surface (PES) for the ground electronic state of CO2(2+) was computed using a multireference configuration interaction method and a correlation-consistent polarized-valence quadruple-zeta basis set, for a range of internuclear distances and O-C-O bond angles, and an analytic fit of the PES was obtained. The computed PES clearly indicates the metastability of the dication and yields a barrier height and an asymptotic limit in fair agreement with the reported data. A time-dependent quantum mechanical approach was used to compute the ground vibrational state wave function of CO2 in its ground electronic state. Assuming a Franck-Condon transition, the same function was taken to be the initial wave function at time t = 0 for the time evolution on the fitted PES for the ground electronic state of CO2(2+). The autocorrelation function was computed and Fourier transformed to obtain the excitation spectrum. Upon convolution with the instrument resolution function, the kinetic energy release spectrum was obtained, in good agreement with the experimental results, particularly at lower energies. The discrepancies at higher energies are attributed to the noninclusion of the excited states of CO2(2+) in the dynamical study.     

Intrinsic self-calibration of non-destructive gamma spectrometric measurements determination of U,Pu and241Am isotopic ratios

The intrinsic consistency and discrete character of high resolution gamma spectrometric measurements are used in order to make self-calibration of these measurements. Both energy and overall relative efficiency (including all geometrical self-attenuation and attenuation factors as well as the detector efficiency) can be performed using the same measured spectrum. The method is particularly useful for non-destructive gamma spectrometric measurements of isotopic ratios on different nuclear material samples. As an illustration, a complete isotopic analysis of U/Pu mixed oxide rods is given. The accuracy of the isotopic measurements depends strongly on the accuracy of the available nuclear data and comparison with destructive analysis when possible facilitates the process of obtaining more accurate nuclear data for the isotopes involved. The attainable accuracy is estimated to be better than 0.5% for²³⁹Pu and²⁴¹Pu measurements.     

On a possible mechanism for Ar 4 + fragmentation

The full potential energy surface (PES) for the collinear Ar ₄ ⁺ cluster as a function of the three internuclear distances is computed at the post-Hartree-Fock level using Density Functional Theory (DFT) methods to treat dynamic correlation effects. The behaviour of the overall configuration energy minima as the central Ar ₂ ⁺ bond stretches is analysed as a function of the fragmentation coordinates of the wing atoms. The coupling between the stretching coordinate and the fragmentation coordinates is also analysed over the whole PES. The calculations suggest that large vibrational energy content in the core dimer ion causes localization of the coupling with either wing atoms which could in turn favour energetically the sequential fragmentation, while Ar ₄ ⁺ with a vibrationally cold core markedly lowers any energy barrier to fragment in a concerted fashion. Such suggestions provide further useful information for what has been found in some of the experimental studies on this ionic system (and on larger ionized argon clusters) and underline the possible role which the internal vibrational energy content of the ionic cluster can play in the fragmentation.     

A sensitivity analysis of a diatomics-in-molecules model of the 1A′ states of H2O

A method for computing the sensitivity of diatomics-in-molecules (DIM) potential energy surfaces (PES) to variations in the parameters characterizing the diatomic fragment matrices is applied to the ¹A′ states of H₂O. The analysis, presented explicitly for 2 × 2 and 3 × 3 fragment matrices, identifies those parameters having the largest influence on local features of the PES. Estimates of the parameter alterations necessary to effect specific changes in the PES are easily provided, allowing manipulation of the DIM model so as to obtain a good overall representation of the PES. Local regions of the PES turn out to be sensitive to only a few parameters and are largely unaffected by the rest. This supports the notion, customary in reaction dynamics, that processes may be discussed qualitatively in terms of the local properties of a PES such as the position of a barrier or the type of energy release.     

Analytical fitting of potential energy surfaces for the Hxy systems

Use of the London-Eyring-Polanyi + 3-Center + power-series (LEP -3C -PS ) analytical potential as a fit to potential energy surfaces (PES ) which are known numerically only are suggested. This analytical fit was performed for the diatomics-in-molecules + 3 Center (DIM -3C ) PES of HCl₂ and HI₂ systems. The HCl₂ analytical LEP -3C-PS potential was used for classical trajectory calculations of the Cl' + HCl → HCl' + Cl reaction. The rate constant obtained from these calculations for T = 358° K is 1.95 X 10⁹ cm³/mol sec which is close to the experimental value of 2.5 10⁹ cm³/mol sec.     

Kinetic isotope effects for the H2 + C2H ↔ C2H2 + H reaction based on the ab initio calculations and a global potential energy surface

In the present paper, kinetic isotope effects of the title reaction are studied with canonical variational transition state theory on the modified Wang Bowman (MWB) potential energy surface (PES) (Chem Phys Lett 2005, 409, 249) and the ab initio calculations at the quadratic configuration interaction (QCISD (T, full))/aug‐cc‐pVTZ//QCISD (full)/cc‐pVTZ level. The calculated rate constants for the isotopic variants of this title reaction on the MWB PES have good agreement with those of the present ab initio calculations over the temperature range of 20–5000 K for the forward reactions and 800–5000 K for the reverse reactions, respectively. In particular, the forward rate constants for the title reaction and its isotopically substituted reactions have negative temperature dependences at about 40 K. Rate expressions are presented for all the studied reactions. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 289–298, 2010     

The Influence of the Exchange-Correlation Functional on the Non-Interacting Kinetic Energy and Its Implications for Orbital-Free Density Functional ApproximationsSCI北大核心CSCD

In this work it is shown that the kinetic energy and the exchange-correlation energy are mutual dependent on each other.This aspect is first derived in an orbital-free context.It is shown that the total Fermi potential depends on the density only,the individual parts,the Pauli kinetic energy and the exchange-correlation energy,however,are orbital dependent and as such mutually influence each other.The numerical investigation is performed for the orbital-based non-interacting Kohn-Sham system in order to avoid additional effects due to further approximations of the kinetic energy.The numerical influence of the exchange-correlation functional on the non-interacting kinetic energy is shown to be of the orderof a few Hartrees.For chemical purposes,however,the energetic performance as a function of the nuclear coordinates is much more important than total energies.Therefore,the effect on the bond dissociation curve was studied exemplarily for the carbon monoxide.The data reveals that,the mutual influence between the exchange-correlation functional and the kinetic energy has a significant influence on bond dissociation energies and bond distances.Therefore,the effect of the exchange-correlation treatment must be considered in the design of orbital-free density functional approximations for the kinetic energy.