Adiabatic Potential Energy Surfaces Research Articles

Accurate Calculation of Rate Constant and Isotope Effect for the F + H2 Reaction by the Coupled 3D Time-Dependent Wave Packet Method on the Newly Constructed Ab Initio Ground Potential Energy Surface.

We employ coupled three-dimensional (3D) time dependent wave packet formalism in hyperspherical coordinates for reactive scattering problem on the newly constructed ab initio calculated ground adiabatic potential energy surface for the F + H2/D2 reaction. The convergence profiles for various reactive channels are depicted at low collision energy regimes with respect to the total angular momentum (J) quantum numbers. For two different reactant diatomic molecules (H2 and D2) initially at their respective ground roto-vibrational state (v = 0, j = 0), calculated state-to-state as well as total integral cross sections as a function of collision energy, temperature dependent rate constants, and the kinetic isotope effect for various reactivity profiles of F + H2 and F + D2 reactions are presented along with previous theoretical and experimental results.

Classical approach based on full-size adiabatic potential energy surfaces to the thermal expansion of the Jahn-Teller molecules. Example of niobium tetrahalides NbX4 (X = Br, I)

The methods of CASSCF, the perturbation theory and taking into account relativistic effects were applied to study the structure of NbX4 (X = Br, I) molecules in the ground and excited electronic states. Due to Jahn-Teller distortion of the Td structure, the compressed D2d structure corresponds to minimum on the lower sheet of PES. For 2E ⊗ e Jahn-Teller problem the vibronic Schrödinger equation has been solved in the diabatic basis. The original method was used for the simulation of available gas-phase electron diffraction data. A good agreement between experimental and theoretical results supports the reliability of the theoretical data.

Energy dependent ratios of level-density parameters in superheavy nuclei

The nuclear level densities and level-density parameters in fissioning nuclei at their saddle points of fission barriers, ${a}_{f}$, as well as those for neutron, ${a}_{n}$, proton, ${a}_{p}$, and $\ensuremath{\alpha}$-particle, ${a}_{\ensuremath{\alpha}}$, emission residues at the ground states are calculated for isotopic chains of superheavy nuclei with $Z$ = 112--120. The calculations are performed with the superfluid formalism using the single-particle energies obtained from the diagonalization of the deformed Woods-Saxon potential. Spectra were generated at global minima of the adiabatic potential energy surfaces, found by the multidimensional minimization method, and at the proper saddle points, found by the ``immersion water flow'' technique on multidimensional energy grids, with allowed reflection and axial symmetry breaking. The influence of shell effects on the energy dependence of the ratios of level-density parameters corresponding to residues of the considered decay modes to those of neutron emission is studied. As shown, in contrast to the ${a}_{f}/{a}_{n}$ ratio, the ${a}_{p}/{a}_{n}$ and ${a}_{\ensuremath{\alpha}}/{a}_{n}$ ratios do not show characteristic maxima depending on the excitation energy of the compound nucleus being formed. In the case of $\ensuremath{\alpha}$ decay, we identified the collective enhancement caused by cluster degrees of freedom as playing quite an important role. The energetic course of the variability of the level-density parameters before reaching the asymptotic value, not taken into account so far, is of great importance for the estimation of the probabilities of de-excitation cascades via light particles emission in competition with fission and, thus, for the determination of the survival probabilities and finally for the total production cross sections of superheavy nuclei.

The Reaction Mechanism Study for the F3 System.

In order to study the F3 system, an accurate global adiabatic potential energy surface is reduced in the present work. The high-level ab initio (MCSCF/MRCI level) methods with big basis set aVQZ are used to calculate 27690 potential energy points in the MOLPRO quantum chemistry package using the Jacobi coordinate. Meanwhile, the B-spline fit method is used to reduce the global potential energy surface in this present work. The shallow well complexes are found in the present work when the angles θ = 30°, 60°, and 90°. Analysing the global potential energy surfaces can get the conclusion that reactants should overcome at least 0.894 eV energy to cross the transition state and reach products. This study will be helpful for the analysis in histopathology and for the study of biological and medical mechanisms.

Stereodynamics-Controlled Product Branching in the Nonadiabatic H + NaD → Na(3s, 3p) + HD Reaction at Low Temperatures.

Nonadiabatic processes play an important role at energies near or higher than conical intersection of adiabatic potential energy surfaces in chemical reactions. In this work, dynamics of the nonadiabatic H + NaD reaction at low temperatures are studied by using the quantum wave packet method based on an improved L-shaped grid. The nonadiabatic H + NaD reaction has two exothermic reaction channels: Na(3s) + HD and Na(3p) + HD; the latter can only occur via nonadiabatic transition. The dynamics results show that the product branching of the H + NaD reaction at collision energies ranging from 20 to 80 cm-1 is controlled by stereodynamics. The Na(3s) and Na(3p) reaction channels occur through collinear collision and side-on collision, respectively. When the collision energy is lower than 20 cm-1, the resonance-mediated reaction mechanism is dominant in both the Na(3s) and Na(3p) reaction channels.

Manifestation of the Jahn–Teller effect subject to quadratic problem in ultrasonic attenuation. Case study of CaF2:Cr crystal with isovalent and aliovalent substitution

A new approach is introduced to obtain information about the adiabatic potential energy surface of the Jahn–Teller (JT) complexes subject to the problem in doped crystals. It employs simulation of the contribution of the JT sub-system to ultrasonic attenuation with account of three mechanisms of relaxation and subsequent comparison with the experimental data on temperature dependence of the attenuation obtained with the use of doped crystal and nominally pure one. The approach has been applied to the CaF2 crystal doped with chromium. The experiment has been carried out at the frequencies of (13–158) × 106 Hz at low temperatures (4–170 K). Peak for all the ultrasonic normal modes propagating along the [110] axis has been observed at about 8 K. It has been considered as the JT effect manifestation by the sub-system of Cr2+ complexes. Symmetry properties of the global minima and saddle points have been identified, the JT stabilization energies and coordinates of the extrema points in the five-dimensional space of symmetrized displacements have been evaluated. Besides, a broad shoulder has been found at 15–40 K and attributed to contribution of the Cr3+ sub-system.

Non-adiabatic quantum wavepacket dynamics simulation based on electronic structure calculations using the variational quantum eigensolver

A non-adiabatic nuclear wavepacket dynamics simulation of the H$_2$O$^+$ de-excitation process is performed based on electronic structure calculations using the variational quantum eigensolver. The adiabatic potential energy surfaces and non-adiabatic coupling vectors are computed with algorithms for noisy intermediate-scale quantum devices, and time propagation is simulated with conventional methods for classical computers. The results of non-adiabatic transition dynamics from the $\tilde{B}$ state to $\tilde{A}$ state reproduce the trend reported in previous studies, which suggests that this quantum-classical hybrid scheme may be a useful application for noisy intermediate-scale quantum devices.

Revising the performance of the Landau–Zener surface hopping on some typical one-dimensional nonadiabatic models

We implement the Landau–Zener surface hopping (LZSH) method to study the nonadiabatic dynamics of some typical one-dimensional (1D) models, including well-tested Tully's models. For models like the original linear avoided crossing model used to derive the LZ formula, the LZSH method can provide very accurate results compared with full quantum calculations and fewest-switches surface hopping (FSSH) simulations. For the Tully's single avoided crossing model, the LZSH method can only present us semi-quantitative results. And for Tully's dual avoided crossing model, the LZSH fails to capture the quantum interference effect. Furthermore, the LZSH shows a better performance for a three-state model compared with FSSH due to no coherence when the nuclear momentum is small. The simulation results show us the performance of LZSH method depends on the shape of adiabatic potential energy surface, which deepens our understanding of nonadiabatic dynamics for some typical 1D models and provides solid basics for further developing new methods based on the LZ formula.

Common defects in diamond lattices as instances of the general T ⊗ (e+t2) Jahn-Teller effect

Finding the ground-state configuration of point defects in semiconductors is in general a high-dimensional optimization problem. However, their adiabatic potential energy surfaces (APES) can be described with few effective coordinates by exploiting symmetry arguments within the Jahn-Teller (JT) theoretical framework. In this paper, we propose a general framework, that combines group theory and ab initio calculations, to build a full picture of common defects in diamond lattices (vacancies and substitutional impurities) as instances of the general T $\ensuremath{\bigotimes}\phantom{\rule{4pt}{0ex}}(e+{t}_{2})$ APES. Starting from the original tetrahedral symmetry, we consider all possible JT symmetries and we numerically investigate the shape of the APES by targeting the minimum energy path between equivalent JT distortions taking as examples the vacancy (V) and the metallic impurities Pd, Pt, and Au in crystalline silicon.

Rationalizing the structural changes and spectra of manganese and their temperature dependence in a series of garnets with first-principles calculations

Detailed first-principles calculations have been carried out to study the stabilization, excitation and luminescence mechanisms of the ion ${\mathrm{Mn}}^{3+}$ in a series of ${A}_{3}{B}_{2}{B}_{3}^{\ensuremath{'}}{\mathrm{O}}_{12}$ garnet hosts. The formation energy shows that ${\mathrm{Mn}}^{3+}$ is dominant and is situated at the octahedral $B$ site. The excited states, excitation, and emission energies of ${\mathrm{Mn}}^{3+}$ have then been calculated. The calculated energy levels of ${\mathrm{Mn}}^{3+}$ confirm that the red emission is due to the ${}^{5}{\mathrm{T}}_{2}\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}{\phantom{\rule{4pt}{0ex}}}^{5}{\mathrm{E}}^{\ensuremath{'}}$ transition and the near-infrared (NIR) emission arises from the ${}^{1}{\mathrm{T}}_{2}\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}{\phantom{\rule{4pt}{0ex}}}^{3}{\mathrm{T}}_{1}$ transition. The populations of the ${}^{5}{\mathrm{T}}_{2}$ and ${}^{1}{\mathrm{T}}_{2}$ excited states and the corresponding radiative rates lead to the temperature dependence of the red to NIR emission. Furthermore, the adiabatic potential energy surfaces along the ${A}_{1g}$ and ${E}_{g}$ moeity modes of [${\mathrm{MnO}}_{6}$] have been calculated and fitted well in the harmonic approximation. The high activation energy for ${\mathrm{Mn}}^{3+}$ indicates a low nonradiative multiphonon relaxation rate of ${}^{5}{\mathrm{T}}_{2}$ to ${}^{3}{\mathrm{T}}_{1}$. Hence, the ionization process was considered, and we show that it is responsible for the luminescence quenching of ${\mathrm{Mn}}^{3+}$, so that the luminescence has rarely been reported experimentally. This work illustrates a well-designed approach based on the density-functional theory framework to predict the optical transition properties of the transition metal ion ${\mathrm{Mn}}^{3+}$ by calculating the structural distortions due to the Jahn-Teller effect, the optical transitions, quenching processes and the influence of pressure.

Jahn-Teller Effect in Orthorhombic Manganites: Ab Initio Hamiltonian and Roto-vibrational Spectrum.

For the first time, using three different electronic structure methodologies, namely, CASSCF, RS2c, and MRCI(SD), we construct ab initio adiabatic potential energy surfaces (APESs) and nonadiabatic coupling term (NACT) of two electronic states (5Eg) of MnO69- unit, where eight such units share one La atom in LaMnO3 crystal. While fitting those APESs with analytic functions of normal modes (Qx, Qy), an empirical scaling factor is introduced considering the mass ratio of eight MnO69- units with and without one La atom to explore the environmental (mass) effect on MnO69- unit. When the roto-vibrational levels of MnO69- Hamiltonian are calculated, peak positions computed from ab initio constructed excited APESs are found to be enough close with the experimental satellite transitions [ J. Exp. Theor. Phys. 2016, 122, 890-901] endorsing our earlier model results [ J. Chem. Phys. 2019, 150, 064703]. In order to explore the electron-nuclear coupling in an alternate way, theoretically "exact" and numerically "accurate" beyond Born-Oppenheimer (BBO) theory based diabatic potential energy surfaces (PESs) of MnO69- are constructed to generate the photoelectron (PE) spectra. The PE spectral band also exhibits good peak by peak correspondence with the higher satellite transitions in the dielectric function spectra of the LaMnO3 complex.

Adiabatic potential energy surfaces and photodissociation mechanisms for highly excited states of H2O

Full-dimensional adiabatic potential energy surfaces of the electronic ground state X̃ and nine excited states Ã, Ĩ, B̃, C̃, D̃, D̃′, D̃″, Ẽ′ and F̃ of H2O molecule are developed at the level of internally contracted multireference configuration interaction with the Davidson correction. The potential energy surfaces are fitted by using Gaussian process regression combining permutation invariant polynomials. With a large selected active space and extra diffuse basis set to describe these Rydberg states, the calculated vertical excited energies and equilibrium geometries are in good agreement with the previous theoretical and experimental values. Compared with the well-investigated photodissociation of the first three low-lying states, both theoretical and experimental studies on higher states are still limited. In this work, we focus on all the three channels of the highly excited state, which are directly involved in the vacuum ultraviolet photodissociation of water. In particular, some conical intersections of D̃–Ẽ′, Ẽ′-F̃, ÖĨ and Ĩ–C̃ states are clearly illustrated for the first time based on the newly developed potential energy surfaces (PESs). The nonadiabatic dissociation pathways for these excited states are discussed in detail, which may shed light on the photodissociation mechanisms for these highly excited states.

The Jahn–Teller and Pseudo-Jahn–Teller Effects: A Unique and Only Source of Spontaneous Symmetry Breaking in Atomic Matter

In a mostly review paper, we show that the important problem of symmetry, broken symmetry, and spontaneous broken symmetry of polyatomic systems is directly related to the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) effects, including the hidden-JT and hidden-PJT effects, and these JT effects (JTEs) are the only source of spontaneous symmetry breaking in matter. They are directly related to the violation of the adiabatic approximation by the vibronic and other nonadiabatic couplings (jointly termed nonadiabaticity) in the interaction between the electrons and nuclei, which becomes significant in the presence of two or more degenerate or pseudodegenerate electronic states. In a generalization of this understanding of symmetry, we suggest an improved (quantum) definition of stereo-chemical polyatomic space configuration, in which, starting with their high-symmetry configuration, we separate all atomic systems into three distinguishable groups: (1) weak nonadiabaticity, stable high-symmetry configurations; (2) moderate-to-strong nonadiabaticity, unstable high-symmetry configurations, JTEs, spontaneous symmetry breaking (SSB); (3) very strong nonadiabaticity, stable distorted configurations. The JTEs, inherent to the second group of systems, produce a rich variety of novel properties, based on their multiminimum adiabatic potential energy surface (APES), leading to a short lifetime in the distorted configuration. We show the role of the Curie principle in the possibilities to observe the SSB in atomic matter, and mention briefly the revealed recently gamma of novel properties of matter in its interaction with external perturbation that occur due to the SSB, including ferroelectricity and orientational polarization, leading to enhanced permittivity and flexoelectricity.

Combined Surface-Hopping, Dyson Orbital, and B-Spline Approach for the Computation of Time-Resolved Photoelectron Spectroscopy Signals: The Internal Conversion in Pyrazine.

A computational protocol for simulating time-resolved photoelectron signals of medium-sized molecules is presented. The procedure is based on a trajectory surface-hopping description of the excited-state dynamics and a combined Dyson orbital and multicenter B-spline approach for the computation of cross sections and asymmetry parameters. The accuracy of the procedure has been illustrated for the case of ultrafast internal conversion of gas-phase pyrazine excited to the 1B2u(ππ*) state. The simulated spectra and the asymmetry map are compared to the experimental data, and a very good agreement was obtained without applying any energy-dependent rescaling or broadening. An interesting side result of this work is the finding that the signature of the 1Au(nπ*) state is indistinguishable from that of the 1B3u(nπ*) state in the time-resolved photoelectron spectrum. By locating four symmetrically equivalent minima on the lowest-excited (S1) adiabatic potential energy surface of pyrazine, we revealed the strong vibronic coupling of the 1Au(nπ*) and 1B3u(nπ*) states near the S1 ← S0 band origin.

Pseudo Jahn-Teller Origin of the Proton-transfer Energy Barrier in the Hydrogen-bonded [FHF]-System

The results of ab initio calculations of the adiabatic potential energy surfaces for the proton-bound [FHF]- system at different F-F distances have been rationalized in the framework of the vibronic theory. It is shown that the instability of the symmetric D∞h structure at increased F∙∙∙F distances and the proton displacement to one of the fluorine atoms is due to the pseudo Jahn–Teller mixing of the ground 1Σg electronic state with the lowest excited state of 1Σu symmetry through the asymmetric σu vibrational mode.

Additive CHARMM36 Force Field for Nonstandard Amino Acids.

Nonstandard amino acids are both abundant in nature, where they play a key role in various cellular processes, and can be synthesized in laboratories, for example, for the manufacture of a range of pharmaceutical agents. In this work, we have extended the additive all-atom CHARMM36 and CHARMM General force field (CGenFF) to a large set of 333 nonstandard amino acids. These include both amino acids with nonstandard side chains, such as post-translationally modified and artificial amino acids, as well as amino acids with modified backbone groups, such as chromophores composed of several amino acids. Model compounds representative of the nonstandard amino acids were parametrized for protonation states that are likely at the physiological pH of 7 and, for some more common residues, in both d- and l-stereoisomers. Considering all protonation, tautomeric, and stereoisomeric forms, a total of 406 nonstandard amino acids were parametrized. Emphasis was placed on the quality of both intra- and intermolecular parameters. Partial charges were derived using quantum mechanical (QM) data on model compound dipole moments, electrostatic potentials, and interactions with water. Optimization of all intramolecular parameters, including torsion angle parameters, was performed against information from QM adiabatic potential energy surface (PES) scans. Special emphasis was put on the quality of terms corresponding to PES around rotatable dihedral angles. Validation of the force field was based on molecular dynamics simulations of 20 protein complexes containing different nonstandard amino acids. Overall, the presented parameters will allow for computational studies of a wide range of proteins containing nonstandard amino acids, including natural and artificial residues.

Photochemistry of NH2NO2 and implications for chemistry in the atmosphere.

Recent studies have indicated that nitramide (NH2NO2) may be formed more plentifully in the atmosphere than previously thought, while also being a missing source of the greenhouse gas nitrous oxide (N2O) via catalyzed isomerization. To validate the importance of NH2NO2 in the Earth's atmosphere, the ground and first electronic excited states of NH2NO2 were characterized and its photochemistry was investigated using multireference and coupled cluster methods. NH2NO2 is non-planar and of singlet multiplicity in the ground state while exhibiting large out-of-plane rotation in the triplet first excited state. One-dimensional cuts of the adiabatic potential energy surface calculated using the MRCI+Q method show low-lying singlet electronic states with minima in their potential along the N-N and N-O bond coordinates. Due to vertical excitation energies in the 225-180nm region, photochemical processes will not compete in the troposphere, causing N2O production to be the predicted major removal process of NH2NO2. In the upper atmosphere, photodissociation to form NH2NO + O (3P) is suggested to be a major photochemical removal pathway.

Vibrational energy levels of the S 0 and S 1 states of formaldehyde using an accurate ab initio based global diabatic potential energy matrix

Low-lying vibrational energy levels of both the ground (S 0) and first excited singlet (S 1) states of formaldehyde have been determined using an exact kinetic energy operator and adiabatic potential energy surfaces derived from a recently developed full-dimensional global diabatic potential energy matrix (DPEM) based on a neural network representation of high level ab initio data. The agreement with available experimental band origins provides strong evidence in support of the accuracy of the DPEM, which can be used in the future for understanding the internal conversion of H2CO(S 1) and the subsequent roaming dynamics on its S 0 state.

Jahn-Teller effect in the cubic fullerides A3C60

Compared to isolated C$_{60}^{3-}$ ions, characterized by a threedimensional equipotential trough at the bottom of the lowest adiabatic potential energy surface (APES), the Jahn-Teller (JT) effect in cubic fullerides is additionally influenced by the interaction of JT distortions at C$_{60}$ sites with vibrational modes of the lattice. This leads to modification of JT stabilization energy and to the warping of the trough at each fullerene site, as well as to the interaction of JT distortions at different sites. Here we investigate these effects in three fcc fullerides with A=K,Rb,Cs and in Cs$_3$C$_{60}$ with bcc (A15) structure. DFT calculations of orbital vibronic coupling constants at C$_{60}$ sites and of phonon spectra have been done for fully ordered lattices (1 C$_{60}$/u.c.). Based on them the elastic response function for local JT distortions has been evaluated and the lowest APES investigated. To this end an expression for the latter in function of trough coordinates of all sites has been derived. The results show that the JT stabilization energy slightly increases compared to an isolated C$_{60}^{3-}$ and a warping of the trough of few meV occurs. The interaction of JT distortions on nearest- and next-nearest-neighbor fullerene sites is of similar order of magnitude. These effects arise first of all due to the interaction of C$_{60}$ sites with the displacements of neighbor alkali atoms and are more pronounced in fcc fullerides than in the A15 compound. The results of this study support the picture of weakly hindered independent rotations of JT deformations at C$_{60}$ sites in cubic A$_3$C$_{60}$.

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

Diabatization of the molecular Hamiltonian is a standard approach to remove the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it is impossible to eliminate the nonadiabatic couplings entirely-the resulting "quasidiabatic" states are still coupled by smaller but nonvanishing residual nonadiabatic couplings, which are typically neglected. Here, we propose a general method for assessing the validity of this potentially drastic approximation by comparing quantum dynamics simulated either with or without the residual couplings. To make the numerical errors negligible to the errors due to neglecting the residual couplings, we use the highly accurate and general eighth-order composition of the implicit midpoint method. The usefulness of the proposed method is demonstrated on nonadiabatic simulations in the cubic Jahn-Teller model of nitrogen trioxide and in the induced Renner-Teller model of hydrogen cyanide. We find that, depending on the system, initial state, and employed quasidiabatization scheme, neglecting the residual couplings can result in wrong dynamics. In contrast, simulations with the exact quasidiabatic Hamiltonian, which contains the residual couplings, always yield accurate results.