VB calculations with orthogonal basis functions

As a first step in the development of a semiempirical VB method,ab initio VB calculations were performed to obtain potential energy curves for the molecules HF and BeH₂ and the energy profile of the collinear exchange reaction F + H₂ HF + H. The applicability of the method is discussed with particular emphasis on the calculation of integrals over OAO's, the choice of valence structures to be included in the CI scheme and the interpretation of the wave function in terms of OAO's.     

Nature of the Transition State in Peroxyl Radical Recombination

We have carried out an ab initio calculation of the potential surface for the reaction CH₃O₄H CH₂=O + O₂ + H₂O. We have established the structure of the transition state and studied the dependence of the energy barrier on the size of the basis and whether electron correlation is taken into account. We have studied the electronically excited terms for the participants in this reaction and we have established the mechanism for the formation of chemiluminescence emitters in this reaction.     

Generalized-molecular-orbital theory: Simple multiconfiguration self-consistent-field method

Even after completing a multiconfiguration self-consistent-field (MCSCF ) calculation, one must often include additional configuration interaction (CI ) to obtain quantitative or semiquantitative results. There is some question of whether the prior MCSCF calculation is worthwhile, if additional CI is needed later. We have developed a new MCSCF computational method, which, because of our assumptions about the nature of the configurations, yields one Fock-like operator for all the “filled” orbitals (high occupation numbers) and a second Fock-like operator for all the “virtual” orbitals (low occupation numbers). Since there are only two matrices to build, our method is considerably faster than other MCSCF approaches. Because of these similarities to standard molecular-orbital (MO ) calculations, we have termed our approach generalized-molecular-orbital (GMO ) theory. However, the “virtual” orbitals, unlike those of standard MO theory, are optimized to correlate the “filled” ones and can he used in a subsequent CI calculation. Results are presented for the correlation energy of H₂O, the spectroscopic constants of N₂, the singlet–triplet energy separations in CH₂, and the nature of the chromium–chromium quadruple bond. Although these results are at a very low level of CI , the GMO approach appears to correct for the gross deficiencies of the single-determinant SCF procedure.     

The ground state of MoCr(O2CH)4 at theab initio SCF and CI levels. A symmetry adapted RHF energy functional with an artificial double minimum

Ab initio restricted Hartree-Fock (RHF) calculations carried out on the ground state of MoCr(O₂CH)₄ lead to two distinct energy minima according to the initial guess made for the set of trial vectors. It is shown that these two symmetry-adapted wavefunctions can be correlated with a twofold degenerate broken-symmetry solution previously characterized for the related system of higher symmetry Cr₂(O₂CH)₄. Complete CI expansions have been carried out from either RHF polarized wavefunction using as a basis the set of eight frontier MO's with high metal character. These expansions yield poorly resymmetrized wavefunctions. A similar CI expansion has finally been carried out from a wavefunction resymmetrized at the SCF level and corresponding to a saddle point of the RHF energy hypersurface. The total energy associated with this latter expansion is the lowest obtained in the present work. The natural orbital analysis corresponds to ()^1.86()^3.58()^1.54()^0.46()^0.42 (^*)^0.14 and shows that this resymmetrized CI expansion is in many respects similar to the correlated wavefunctions obtained for the homobinuclear parent systems.     

MCSCF reaction-path energetics and thermal rate-constants for the reaction of3NH with H2

Summary The intrinsic reaction-path, reactants, transition state and products for the reaction of NH (^3–)+H₂ (¹ _g ⁺ ) NH₂ (²B₁)+H (²S) involving the lowest triplet electronic state of NH₃ were calculated using multi-configuration (MC) SCF methods. The calculated change of internal energy for the reaction of 11.0 kcal mol^–1 agrees with the experimental value within 2 kcal mol^–1. The barrier to reaction is 23.4 kcal mol^–1 high. The harmonic MCSCF reaction-path potential was calculated and canonical variational transition state theory calculations of the rate constants performed over a temperature range from 400 to 2500 K. The computed rate constants are generally two orders of magnitude smaller than those of the comparable reaction of OH with H₂, whereas those of the reverse reaction are by a factor of 20 larger than those of OH₂ with H.     

The formaldehyde decomposition chain mechanism

A kinetic mechanism for the chain decomposition of formaldehyde consistent with recent theoretical and experimental results is presented. This includes new calculations and measurements of the rate constant for the abstraction reaction The calculation uses a multi-reference configuration interaction wavefunction to construct the potential energy surface which is used in a tunneling-corrected TST calculation of the rate constant. The rate constant for the bond fission at high temperatures was determined by an RRKM extrapolation of direct low temperature measurements. This mechanism has been successfully tested against laser-schlieren measurements covering the temperature range 2200–3200 K. These measurements are insensitive to all but the above two reactions and they confirm the large, non-Arrhenius rate for the abstraction reaction derived here from theory. Modeling of previous experiments using IR emission, ARAS, and CO laser absorption with this mechanism is quite satisfactory. The branching ratio of the rate of the faster molecular dissociation (CH₂O + (M) → CO + H₂ + (M)), to that of the bond fission reaction, was estimated to be no more than 2 or 3 over 2000 to 3000 K. Such a ratio is consistent with one recent theoretical estimate and most of the experimental observations. © 1993 John Wiley & Sons, Inc.     

Is GVB-CI superior to CASSCF?

Presently the most reliable approach for the study of reaction pathways where chemical bonds are broken and formed is to carry out CASSCF calculations followed by corresponding multireference perturbation or CI treatments. The latter step generally relaxes the “antibonding character” of the CASSCF results. In this study we demonstrate that similar results can be well approximated by using a less optimized MCSCF method and not performing the multireference perturbation or CI step at all. This is accomplished by performing a complete CI calculation within the active orbital space of the generalized valence bond perfect pairing (GVB-PP) model. The local bond/antibond character of the orbital space of the GVB-PP method also allows development of a fast, but robust, Bethe–Goldstone algorithm, which reconstructs the CI energy to an accuracy of a few tenths of a millihartree for most types of bond breaking cases found in chemical reactions. This algorithm executes at a speed proportional to N where N_p is the number of localized electron pairs in the active space. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 999–1008, 1999     

Theoretical study of hydrogen abstraction reactions CH4 + R → CH3 + HR,geometrical, energetical and kinetical aspects

Five hydrogen abstraction reactions, CH₄ + R CH₃ + HR have been studied usingab initio SCF and CI methods. R was successively chosen as H, CH₃, NH₂, OH and F. Geometries were fully optimized at SCF level and energies were computed at CI level for products, reactants and transition states. Quadratic hypersurfaces were fitted in the neighborhood of the most important points of the potential energy hypersurfaces and vibrational analysis were performed thereupon. Wigner's and Christov's approximations were used to obtain an idea of the importance of tunneling of H atoms through the reaction barrier, and this effect was shown to be non-negligible. Finally, rate constant calculation were carried out at different temperatures.Chercheur Qualifié au Fonds National Belge de la Recherche Scientifique.     

A fully ab initio potential energy surface for ClH2 reactive system

Anab initio analytical potential energy surface called BW3 for the ClH₂ reactive system is presented. The fit of this surface is based on about 1 200ab initio energy points, computed with multi-reference configuration interaction(MRCI) and scaling external correlation (SEC) method and a very large basis set. The precision in the fit is very high. The BW3 surface could reproduce correctly the dissociation energy of H₂ and HCl, and the endothermicity of the Cl + H₂ abstraction reaction. For the Cl + H₂ abstraction reaction, the saddle point of BW3 lies in collinear geometries, and the barrier height is 32.84 kJ/mol; for the H + ClH exchange reaction, the barrier of BW3 is also linear, with a height of 77.40 kJ/mol.     

The quantum dynamics of the reactions N+H2(HD,D2) and their vibrational excitation effect

The N(⁴S)+H₂ reaction and its isotopic variants have been investigated by means of time‐dependent quantum wave packet with split operator method on the ground state potential energy surface (Zhai and Han, J. Chem. Phys. 2011, 135, 104314). The reaction probabilities, integral cross sections, branching ratio of the integral cross sections, and effect of vibrational excitation of H₂, HD, and D₂ diatomic molecules are presented and discussed. The results reveal that the intramolecular isotopic effect is greater than the intermolecular one, and that the vibrational excitation of the diatomic molecules can promote the progress of this reaction. In addition, a limited number of rigorous Coriolis coupling calculations of the integral cross sections of the N(⁴S)+H₂ reaction have been carried out. Also shown is that since the Coriolis coupling plays a small part in this accurate quantum calculation, the cheaper centrifugal sudden calculations here reported are effective for this reactive system. © 2014 Wiley Periodicals, Inc.     

Estimation of the R-H bond energy from the activation energy for the reaction RH + O2 → R· + HO2·

Since the activation energy for the reaction RH + O₂ → R· + HO₂. is very close to its endothermicity, the R-H bond energy can be calculated from the activation energy for free radical formation by the reaction RH + O₂. The relation between E_i and Q_R–H was found empirically after measuring E_i by the method of inhibitors for the oxidation of cyclohexane, n? heptane, and toluene: The values of Q_R–H are calculated from these and earlier experimental data for five hydrocarbons, five phenols, and four aromatic amines.     

Reaction mechanism of the preferential oxidation of the CO reaction in an H<Subscript>2</Subscript> stream over Cu–Ni bimetallic catalysts: A computational study

The preferential oxidation (PROX, CO + H₂ + O₂ → CO₂ + H₂O) of the CO reaction in an H₂ stream is the simplest and most cost-effective method to remove CO gas to less than 10 ppm in reformed fuel gas. We study the mechanism of PROX of the CO reaction in the H₂ stream catalyzed by Cu _n Ni (n = 3-12) clusters using a density functional theory (DFT) calculation to investigate bimetallic effects on the catalytic activation. Our results indicate that the Cu₁₂Ni cluster is the most efficient catalyst for H₂ dissociation and the Cu₆Ni cluster is the most efficient catalyst for CO-PROX in excess hydrogen among Cu _n Ni (n = 3-12) clusters. To gain insight into the adsorption and dissociation of the H₂ molecule effect in the catalytic activity over the Cu₁₂Ni cluster and the potential energy surfaces about PROX of CO oxidation on the Cu₆Ni cluster, the nature of the interaction between the adsorbate and substrate is analyzed by detailed electron local densities of states (LDOS) as well as molecular structures.     

Potential energy surface for the Pd-H2 system: Comparison with matrix isolation experiments

Summary We present here those aspects of the Pd-H₂ potential energy surface that are most directly related to the questions raised by matrix isolation experiments for the formation of Pd(¹-H₂) and Pd(²-H₂) complexes. 125 points of this potential energy surface were obtained at a CI level using the CIPSI Scheme and including the order of 10⁵ configurations. Relativistic effects are included and shown not to be crucial in understanding the main features of the surfaces. The theoretical results serve to explain many features of the low-temperature experiments on the Pd-H₂ reaction, especially those concerning the spectroscopic changes observed when different noble gas supports, Kr or Xe, are utilized.On Sabbatical leave from Instituto de Física, UNAM     

单分子水对H_2O_2+Cl气相反应影响的理论研究

在aug-cc-pVTZ基组下采用CCSD(T)和B3LYP方法,研究了H2O2+Cl反应,并考虑在大气中单个水分子对该反应的影响.结果表明,H2O2+Cl反应只存在一条生成产物为HO2+HCl的通道,其表观活化能为10.21kJ·mol-1.加入一分子水后,H2O2+Cl反应的产物并没有发生改变,但是所得势能面却比裸反应复杂得多,经历了RW1、RW2和RW3三条通道.水分子在通道RW1和RW2中对产物生成能垒的降低起显著的负催化作用,而在通道RW3中则起明显的正催化作用.利用经典过渡态理论(TST)并结合Wigner矫正模型计算了216.7-298.2 K温度范围内标题反应的速率常数.结果显示,298.2 K时通道R1的速率常数为1.60×10-13cm3·molecule-1·s-1,与所测实验值非常接近.此外,尽管通道RW3的速率常数kRW3比对应裸反应的速率常数kR1大了46.6-131倍,但该通道的有效速率常数k'RW3却比kR1小了10-14个数量级,表明在实际大气环境中水分子对H2O2+Cl反应几乎没有影响.     

Theoretical study of the H 5 + system

Ab initio calculations have been carried out for the ground state of H ₅ ⁺ in order to predict its equilibrium geometry, binding energy, enthalpy of formation, and the features of the H₂ · H ₃ ⁺ interaction at large and intermediate intermolecular distances. The extended basis set of Gaussian functions was carefully optimized to describe the various kinds of intermolecular interactions. Electron correlation was accounted for by means of CI calculations. Different from previous studies we find a D _2d equilibrium geometry with D _e = 7.4 kcal/mol and H ₃₀₀ ⁰ –8.7 kcal/mol. The potential surface turns out to be extremely shallow in the vicinity of the D _2d structure which results in a great mobility of the central nucleus at room temperature.     

Quantum scattering LCAC-SW theory studies on reaction probabilities of three-dimensional H + H2 (v, j) → H2 (v′, j′) + H reaction

Upon the Liu, Siegbahn, Truhlar, Horowitz (LSTH) potential energy surface, the reaction probabilities of the three-dimensional (3-D) state-to-state H + H₂ (v, j) →H ₂(v′, j′) + H reaction are calculated with the linear combination of arrangement channels-scattering wavefunction (LCAC-SW) method. In the calculation, the vibration function of H₂ and the radial propagating wave functions are expanded by the real Gauss functions. The calculated threshold energy and the resonating structure are consistent with the results of the accurate quantum scattering calculations, which shows the accuration, simplicity and practicability of the LCAC-SW method. Project supported by the National Natural Science Fondation of China and the Doctoral Foundation of the State Education Commission of China.     

Modulated potential electrogenerated chemiluminescence of luminol and Ru(bpy) 3 2+

Chemiluminescence emission intensity is modulated by modulating the potential of a working electrode which is used to generate a key species in the electrogenerated Chemiluminescence (ECL) reaction. The emission is monitored synchronously using a lock-in amplifier. The reactions used in the characterization are luminol with hydrogen peroxide and tris(2,2-bipyridyl)ruthenium (II) (or Ru(bpy) ₃ ²⁺ ) with oxalate. Modulation widths of ± 50 mV yield maximum signals for luminol when centered at 0.45 V (vs Ag/AgCl) and for Ru(bpy) ₃ ²⁺ when centered at 1.05 V. The resulting signal decreases with increasing modulation frequency and shows that luminol/H₂O₂ is a faster ECL system than Ru(bpy) ₃ ²⁺ /oxalate. Working curves for luminol and for oxalate have essentially the same linear range and slope with the modulated potential approach as with a DC electrode potential. This approach provides capability for differentiating the analytical signal from constant background emission or stray light.     

Basis-independent potential energy curves for the neutral diatomics of Li,Na and K evaluated by means of Hartree-Fock and different density functional potentials

Summary The solution of the Schrödinger equation for diatomic molecules when the finite element method is used gives the possibility to evaluate highly accurate basis-independent potential energy curves. In this work such types of numerically accurate potential energy curves on the HF level have been evaluated for Li₂, Na₂ and K₂ and could be used as benchmarks in the optimization of basis sets. A comparison between recent LCAO HF calculations in which extended basis sets are used and the accurate values determined in this work show that there is a difference in total energy of 4×10^–5 and 10^–3 a.u. for Li, Li₂, and Na, Na₂, respectively. Evaluated dissociation energies are, however, due to the cancellation of numerical errors in much better agreement. Further, it is found that different exchange correlation potentials for the heavier molecules such as those given by von Barth-Hedin and Vosko, Wilk and Nusair reproduce experimental properties such as dissociation energies, vibrational frequencies almost as well as those achieved with advanced CI methods. TheX potential gives accurate bond lengths for Na₂ and K₂, whereas the dissociation energies are too small.     

Reaction mechanism of platinum dimer cation with ammonia based on the relativistic density functional study

The gas‐phase reactions between Pt and NH₃ have been investigated using the relativistic density functional approach (ZORA‐PW91/TZ2P). The quartet and doublet potential energy surfaces of Pt + NH₃ have been explored. The minimum energy reaction path proceeds through the following steps: Pt(⁴Σ_u) + NH₃ → q‐1 → d‐2 → d‐3 → d‐4 → d‐Pt₂NH⁺ + H₂. In the whole reaction pathway, the step of d‐2 → d‐3 is the rate‐determining step with a energy barrier of 36.1 kcal/mol, and exoergicity of the whole reaction is 12.0 kcal/mol. When Pt₂NH⁺ reacts with NH₃ again, there are two rival reaction paths in the doublet state. One is degradation of NH and another is loss of H₂. In the case of degradation of NH, the activation energy is only 3.4 kcal/mol, and the overall reaction is exothermic by 8.9 kcal/mol. Thus, this reaction is favored both thermodynamically and kinetically. However, in the case of loss of H₂, the rate‐determining step's energy barrier is 64.3 kcal/mol and the overall reaction is endothermic by 8.5 kcal/mol, so it is difficult to take place. Predicted relative energies and barriers along the suggested reaction paths are in reasonable agreement with experimental observations. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007