Natural orbital analysis of nonadiabatic H2+ wave functions

Previously determined nonadiabatic wave functions for H₂⁺ (containing several hundred terms) are analyzed by using natural orbitals. This is the first time that the natural orbital concept has been applied to other than purely electronic wave functions. We find that the natural orbital expansion converges rapidly and that five or six terms are sufficient to reproduce the exact expectation values. Several plots are given of the orbitals so found and these allow a visualization of the somewhat abstract nonadiabatic wave function in a format more reminiscent of everyday quantum-mechanical pictures.     

Vibrational energies of H2+ using fully nonadiabatic wavefunctions

Using variational Monte Carlo methods, we examine a number of fully nonadiabatic trial wavefunctions to determine which features best describe the lowest several vibrational states of H₂⁺. Our final energies are in excellent agreement with previous calculations. © 2012 Wiley Periodicals, Inc.     

A nonadiabatic lower bound calculation of H 2 + and D 2 +

Accurate nonadiabatic lower and upper bounds for groundstate energies of H ₂ ⁺ and D ₂ ⁺ are calculated with the linearized method of variance minimization. The results in a.u. are –0.59713906₃<E ₀(H ₂ ⁺ )<–0.59713899₄ –0.59878877₅<E ₀(D ₂ ⁺ )<–0.59877873₈ i.e. the values are determined with an absolute error smaller than 0.02 cm^–1 for H ₂ ⁺ and 0.01 cm^–1 for D ₂ ⁺ .     

Effctive nonadiabatic calculations on the ground state of the HD+ molecule

The nonadiabatic methodology, which is based on an effective elimination of the center-of-mass motion rather than explicit separation achieved by a coordinate transformation, is applied to the ground state of the HD⁺ molecule. The many-body nonadiabatic wave function is generated in terms of explicitly correlated Gaussian functions. The analytical first and second derivatives of the variational functional with respect to the Gaussian exponents are applied in conjunction with the Newton–Raphson optimization method to find the nonadiabatic energy and the ground–wave function. The numerical results are compared with conventional nonadiabatic calculations. © 1995 John Wiley & Sons, Inc.     

Mechanism of the oxidation reaction of Cu with N2O via nonadiabatic electron transfer

We treat the present work as an attempt to elucidate the mechanism of the oxidation reaction of the Cu atom by nitrous oxide based on our recent work (Kryachko, E. S.; Vinckier, C.; Nguyen, M. T. J Chem Phys 2001, 114, 7911) on the electron attachment to this molecule. We suggest that the title reaction in its Arrhenius regime occurs via the nonadiabatic electron transfer from Cu to the oxygen atom at the crossing of the potential energy surfaces Cu(4s ²S_1/2) + N₂O(X ¹Σ⁺) and Cu⁺ + N₂O^?, where the latter is linked to the complex N₂O^? originated from the higher‐energy T‐shape N₂O molecule and discovered in the aforementioned work. The calculations performed in the present work using a variety of quantum chemical methods support the proposed model. We also show the existence of other reaction pathways of the title reaction that, we believe, contribute to its non‐Arrhenius behavior observed experimentally at T > 1190 K. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Electronic nonadiabatic transitions in the reactive (Ar+ + H2, Ar + H+2, ArH+ + H) system. Numerical results for the collinear configuration

In this communication are presented exact quantum mechanical nonadiabatic electronic transition probabilities for the collinear reaction Ar⁺ + H₂(v_i = 0) → ArH⁺(v_f) + H. The calculations were performed using a potential surface calculated by the DIM method. It is established that large probabilities (≈ 1.0) can be obtained only if there is enough translational energy to overcome a potential barrier formed due to the crossing between v_i = 0 of the Ar⁺ + H₂ system and v_i = 2 of the Ar + H⁺₂ system. The threshold for the reaction is found to be 0.06 eV.     

Quantum nonadiabatic dynamics of hydrogen exchange reactions

In continuation of our earlier effort to understand the nonadiabatic coupling effects in the prototypical H + H₂ exchange reaction [Jayachander Rao et al. Chem. Phys. 333 (2007) 135], we present here further quantum dynamical investigations on its isotopic variants. The present work also corrects a technical scaling error occurred in our previous studies on the H + HD reaction. Initial state-selected total reaction cross sections and Boltzmann averaged thermal rate constants are calculated with the aid of a time-dependent wave packet approach employing the double many body expansion potential energy surfaces of the system. The theoretical results are compared with the experimental and other theoretical data whenever available. The results re-establish our earlier conclusion, on a more general perspective, that the electronic nonadiabatic effects are negligible on the important quantum dynamical observables of these reactive systems reported here.     

Strong nonadiabatic effects in reactions of photoisomerization

Reactions of photoisomerization proceeding through a “funnel” are discussed (Fig. 1a, θ ? θ*, where θ is the angle of isomerization). Strong nonadiabatic interactions in the region of conical intersection of the multidimensional adiabatic potentials U_s and U_s0 are supposed to be responsible for the ultrafast nonradiative transition S → K₂ S₀ (K₂ ? 10¹⁰-10¹² s^?1). The K₂ dependence on the solvent viscosity (isomerization of t-stilbene in series ethanol--octanol) and polarity (isomerization of cyanine dyes in polar solvents) was determined to be in a good agreement with experiments.     

Nonadiabatic collision model calculations of ion-pair formation cross sections of Cs+O2→Cs++O

This paper has improved Hickman's nonadiabatic collision model by substituting Hickman's constant velocity classical straight line trajectory approximation with the solution of motion equation mR=?dV(R)/dR, and has calculated the cross sections of ion-pair formation Cs+O₂→Cs⁺+O^?₂ with the improved nonadiabatic collision model (INCM). A comparison of our results with other theoretical and experimental results has been made.     

The dynamics of nonadiabatic transitions in collisions between the I<Subscript>2</Subscript>(<Emphasis Type="Italic">E</Emphasis>) and I<Subscript>2</Subscript>(<Emphasis Type="Italic">X</Emphasis>) molecules

The paper presents the results of a theoretical study of the dynamics of nonadiabatic transitions between the ion-pair states E0 _g ⁺ and D0 _u ⁺ of the I₂ molecule induced by collisions with the I₂ molecule in the ground electronic state X0 _g ⁺ . The potential energy surfaces and diabatic coupling matrix elements of electronic states were obtained using a model based on the diatomics-in-molecule approximation. Special perturbation theory for intermolecular interaction was used to show that the large transition dipole moment between the E0 _g ⁺ and D0 _u ⁺ states caused the appearance of additional long-range corrections, an electrostatic dipole-quadrupole correction to the diabatic coupling matrix elements and induction dipole-dipole correction to the potential energy surface. The influence of these corrections on nonadiabatic dynamics was studied at the level of the semiclassical approximation. The electrostatic correction was found to sharply increase the contribution of resonance (accompanied by minimum kinetic energy changes) vibronic transitions at large distances between the colliding molecules. The induction correction had the opposite effect because of the high transition probability at short distances. The results obtained were in qualitative agreement with experimental data. The conclusion was drawn that obtaining quantitative agreement required a more balanced inclusion of interactions at short and long distances.     

Photodissociation Spectroscopy and Dynamics of Weakly Bonded Metal Ion—Ethylene Complexes

The photodissociation spectroscopy of weakly bonded bimolecular complexes can give important insight into fundamental molecular interactions and dynamics. We have applied these techniques to a study of metal ion‐ethylene interactions in the Mg⁺(3s)‐C₂H₄ and Al⁺(3s²)‐C₂H₄ π‐bonded complexes. Experimental work is supported by ab‐initio electronic structure calculations. These experiments allow us to explore and compare the chemical binding, electronic structure, and nonadiabatic dissociation dynamics of these complexes.     

Nonadiabatic Corrections To The Vibrational Energies Of The Hydrogen Molecule

The nonadiabatic corrections to the vibrational levels of H₂ and D₂ are evaluated for the X¹∑⁺_g state by taking into account the coupling with the E, F¹∑⁺_g electronic state. The computed corrections diminish the existing discrepancy between the experimental and theoretical vibrational quanta by about 20%.     

Mechanism of the O2(1Δg) generation from the Cl2/H2O2 basic aqueous solution explored by the combined ab initio calculation and nonadiabatic dynamics simulation

In the present work, mechanism of the O₂(¹Δ_g) generation from the reaction of the dissolved Cl₂ with H₂O₂ in basic aqueous solution has been explored by the combined ab initio calculation and nonadiabatic dynamics simulation, together with different solvent models. Three possible pathways have been determined for the O₂(¹Δ_g) generation, but two of them are sequentially downhill processes until formation of the OOCl⁻ complex with water, which are of high exothermic character. Once the complex is formed, singlet molecular oxygen is easily generated by its decomposition along the singlet-state pathway. However, triplet molecular oxygen of O₂() can be produced with considerable probability through nonadiabatic intersystem crossing in the ¹Δ_g/ intersection region. It has been found that the coupled solvent, heavy-atom, and nonadiabatic effects have an important influence on the quantum yield of the O₂(¹Δ_g) generation. © 2018 Wiley Periodicals, Inc.     

MRD-CI ground state geometry and vertical spectrum of N3

CI calculations have been carried out for the prediction of the ground state geometry and of the vertical spectrum of N₃. The first three states are ²Π_g, ⁴Π_u and ²Σ⁺_u. The C_∞v correlation diagram for the first dissociation limits is discussed by taking into account possible nonadiabatic pathways.     

The investigation of nonadiabatic effects for the N + ND → N2 + D reaction

Nonadiabatic quantum dynamical calculations have been carried out on the two coupled potential energy surfaces (1²A′ and 2²A′) (Mota et al., J Theor Comput Chem 2009, 8, 849) for the title reaction. Initial state‐resolved reaction probabilities and cross sections for ground and excited states for collision energies of 0.005–1.0 eV are determined, respectively. Nonadiabatic transition is enhanced about four times by isotopic substitution of N + NH by N + ND reaction. It turns out that the nonadiabatic effects exert no significant contribution in the N + ND → N₂ + D reaction. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Model study of the nonadiabatic effects in the interaction of atomic hydrogen with lithium metal clusters

Study is made of the effects of adsorption site position on mutual arrangement and nonadiabatic coupling between the lowest two singlet potential energy surfaces of the Li₉(4, 1, 4)-H chemisorption system. Special attention is paid to a normal approach of H atom to Li₉ cluster. The necessary energy and coupling data are obtained by use of the method of the diatomics-in-molecules. The changes with the alteration of the adsorption site position of the degree of nonadiabatic behaviour of system is shown to be quite significant.     

Curl equations as substratum for the derivation of the electronic nonadiabatic coupling terms

The idea to derive the nonadiabatic coupling terms by solving the Curl equations (Avery, J.; Baer, M.; Billing, G. D. Mol Phys 2002, 100, 1011) is extended to a three‐state system where the first and second states form one conical intersection, i.e., τ₁₂ and the second and the third states form another conical intersection, i.e., τ₂₃. Whereas the two‐state Curl equations form a set of linear differential equations, the extension to a three‐state system not only increases the number of equations but also leads to nonlinear terms. In the present study, we developed a perturbative scheme, which guarantees convergence if the overlap between the two interacting conical intersections is not too strong. Among other things, we also revealed that the nonadiabatic coupling term between the first and third states, i.e., τ₁₃ (such interactions do not originate from conical intersection) is formed due to the interaction between τ₁₂ and τ₂₃. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Vibronic dressed electronic states and nonadiabatic effects in polyacetylene

Conditions for low and high T_c superconductors following from the nonadiabatic electron-vibrational theory at ab initio level have been obtained. According to the presented results, the supercurrent is realized by the motion of the ground-state electronic-charge distribution of the fully occupied band. The motion of the electronic-charge distribution is conditioned by the newly arisen, nondissipative degrees of freedom of nuclear, Jahn–Teller-like, microflows. The Meissner effect is also interpreted.