Vibrational Excitation Energy Research Articles

Theoretical Insights into the Vibrational Structure of Carbon Dioxide Rare-Gas Complexes.

Two new flexible-monomer two-body ab initio potential energy surfaces (PESs) for the neon and krypton van der Waals complexes with carbon dioxide were developed, extending our previous work on the Ar-CO2 molecule. The accuracy of the PESs was validated by their agreement with the vibrational spectrum of the rare-gas complexes. The intermolecular and intramolecular vibrational excitation energies were computed at the vibrational self-consistent field and vibrational configuration interaction levels of theory. Overall, the agreement between theory and experiment is excellent throughout the vibrational spectra. The observed slight splitting of the bending modes, resulting from their nondegeneracy in the complexes, is confirmed by our computations, and the results qualitatively agree with the experiment. The splitting increases with increasing polarizability of the rare-gas atom. Additionally, we explain a discrepancy in the mode assignment in the intermolecular region of the neon complex with our VCI character assignment.

Electronic structure, spectroscopy and photophysics of rubidium mono-sulphide

We investigated the nineteen first electronic states of the RbS diatomic using post Hartree-Fock configuration interaction methods at the internally contracted multi-reference configuration interaction (MRCI+(Q)) level. We thus mapped their respective potential energy curves with and without considering spin-orbit effects. After nuclear motion treatments, we derived their equilibrium distances, rotational and vibrational constants, and dissociation and electronic excitation energies. Moreover, an evaluation of the dipole moments of RbS was conducted, which in turn were used to evaluate the radiative lifetimes of the vibrational levels of RbS (X2П and A2Σ+) states. Computations show that spin-orbit interactions are important and cannot be omitted. Afterwards, and utilizing the sum rule approximation and the Franck–Condon factors, we computed both the bound-bound contributions and the bound-free terms. Our findings suggest that RbS exhibits intriguing characteristics suitable for laser cooling experiments. In sum, this work contributes to the understanding in-depth of the spectroscopy of RbS and predicts its use as a promising molecular system for laser cooling applications.

Vibrational mode-specificity in the dynamics of the OH- + CH3I multi-channel reaction.

We report a comprehensive characterization of the vibrational mode-specific dynamics of the OH- + CH3I reaction. Quasi-classical trajectory simulations are performed at four different collision energies on our previously-developed full-dimensional high-level abinitio potential energy surface in order to examine the impact of four different normal-mode excitations in the reactants. Considering the 11 possible pathways of OH- + CH3I, pronounced mode-specificity is observed in reactivity: In general, the excitations of the OH- stretching and CH stretching exert the greatest influence on the channels. For the SN2 and proton-abstraction products, the reactant initial attack angle and the product scattering angle distributions do not show major mode-specific features, except for SN2 at higher collision energies, where forward scattering is promoted by the CI stretching and CH stretching excitations. The post-reaction energy flow is also examined for SN2 and proton abstraction, and it is unveiled that the excess vibrational excitation energies rather transfer into the product vibrational energy because the translational and rotational energy distributions of the products do not represent significant mode-specificity. Moreover, in the course of proton abstraction, the surplus vibrational energy in the OH- reactant mostly remains in the H2O product owing to the prevailing dominance of the direct stripping mechanism.

Influence of the ambipolar field on the formation of electron phase flows in the positive column of a glow discharge in a nitrogen-like gas

The formation of the electron energy distribution function (EEDF) and phase flows of electrons in the plasma of a positive column of a glow discharge in a model gas with strong vibrational excitation, similar to molecular nitrogen, is analyzed in a wide pressure range. It is found that the traditional local approximation for calculating the EEDF can only be used at medium gas pressures, when the characteristic size of the plasma volume exceeds electron energy relaxation length in the entire range of electron energies. With a decrease in gas pressure, a new phenomenon is discovered—merging the phase flow streamlines into a single line on the coordinate-energy phase plane in the energy region of the of vibrational excitation threshold. It is shown that the combination of a strong electron sink at the threshold of vibrational excitation and the deceleration of electrons in an ambipolar field lead to a practical ‘vanishing’ of the component of the phase electron flux upward in energy. As a result, the streamlines of electron phase flow approach to some approximately straight line of constant kinetic energy close to the threshold energy of vibrational excitation. The formation of this feature on the phase plane correlates with the predominant escape to the walls of electrons with kinetic energy equal to the threshold of vibrational excitation.

Vibrational Mode-Specific Dynamics of the OH + C2H6 Reaction.

We investigate the effects of the initial vibrational excitations on the dynamics of the OH + C2H6 → H2O + C2H5 reaction using the quasi-classical trajectory method and a full-dimensional analytical ab initio potential energy surface. Excitation of the initial CH, CC, and OH stretching modes enhances, slightly inhibits, and does not affect the reactivity, respectively. Translational energy activates the early-barrier title reaction more efficiently than OH and CC stretching excitations, in accord with the Polanyi rules whereas CH stretching modes have similar or higher efficacy than translation, showing that these rules are not always valid in polyatomic processes. Scattering angle, initial attack angle, and product translational energy distributions show the dominance of direct stripping with increasing collision energy, side-on OH and isotropic C2H6 attack preferences, and substantial reactant-product translational energy transfer without any significant mode specificity. The reactant vibrational excitation energy of OH and C2H6 flows into the H2O and C2H5 product vibrations, respectively, whereas product rotations are not affected. The computed mode-specific H2O vibrational distributions show that initial OH excitation appears in the asymmetric stretching vibration of the H2O product and allow comparison with experiments.

Time-dependent nuclear-electronic orbital Hartree-Fock theory in a strong uniform magnetic field.

In an ultrastrong magnetic field, with field strength B ≈ B0 = 2.35 × 105 T, molecular structure and dynamics differ strongly from that observed on the Earth. Within the Born-Oppenheimer (BO) approximation, for example, frequent (near) crossings of electronic energy surfaces are induced by the field, suggesting that nonadiabatic phenomena and processes may play a more important role in this mixed-field regime than in the weak-field regime on Earth. To understand the chemistry in the mixed regime, it therefore becomes important to explore non-BO methods. In this work, the nuclear-electronic orbital (NEO) method is employed to study protonic vibrational excitation energies in the presence of a strong magnetic field. The NEO generalized Hartree-Fock theory and time-dependent Hartree-Fock (TDHF) theory are derived and implemented, accounting for all terms that result as a consequence of the nonperturbative treatment of molecular systems in a magnetic field. The NEO results for HCN and FHF- with clamped heavy nuclei are compared against the quadratic eigenvalue problem. Each molecule has three semi-classical modes owing to the hydrogen-two precession modes that are degenerate in the absence of a field and one stretching mode. The NEO-TDHF model is found to perform well; in particular, it automatically captures the screening effects of the electrons on the nuclei, which are quantified through the difference in energy of the precession modes.

Dissociation energy and the lowest vibrational transition in LiH without assuming the non-Born–Oppenheimer approximation

ABSTRACT The fundamental vibrational excitation energy and the dissociation energy of the main isotopologue of lithium hydride (LiH) are studied by the variational method using all-particle explicitly correlated Gaussian (ECG) basis sets. In this approach, electrons and nuclei are treated on equal footing, i.e. the Born–Oppenheimer approximation is not assumed. The leading relativistic () and the dominating part of the quantum electrodynamics () corrections to the energy levels are accounted for in the framework of the perturbation theory. The fundamental vibrational excitation energy and the dissociation energies obtained in the calculations are well within the error bars of the available experimental data.

Intermolecular vibrational states of HF trimer from rigorous nine-dimensional quantum calculations: Strong coupling between intermolecular bending and stretching vibrations and the importance of the three-body interactions.

We present the computational methodology that allows rigorous and efficient nine-dimensional (9D) quantum calculations of the intermolecular vibrational states of noncovalently bound trimers of diatomic molecules, with the monomers treated as rigid. The full 9D vibrational Hamiltonian of the trimer is partitioned into a 3D "frame" (or stretching) Hamiltonian and a 6D "bend" Hamiltonian. These two Hamiltonians are diagonalized separately, and a certain number of their lowest-energy eigenstates is included in the final 9D product contracted basis in which the full 9D intermolecular vibrational Hamiltonian is diagonalized. This methodology is applied to the 9D calculations of the intermolecular vibrational levels of (HF)3, a prototypical hydrogen-bonded trimer, on the rigid-monomer version of an ab initio calculated potential energy surface (PES). They are the first to include fully the stretch-bend coupling present in the trimer. The frequencies of all bending fundamentals considered from the present 9D calculations are about 10% lower than those from the earlier quantum 6D calculations that considered only the bending modes of the HF trimer. This means that the stretch-bend coupling is strong, and it is imperative to include it in any accurate treatment of the (HF)3 vibrations aiming to assess the accuracy of the PES employed. Moreover, the 9D results are in better agreement with the limited available spectroscopic data that those from the 6D calculations. In addition, the 9D results show sensitivity to the value of the HF bond length, equilibrium or vibrationally averaged, used in the calculations. The implication is that full-dimensional 12D quantum calculations will be required to obtain definitive vibrational excitation energies for a given PES. Our study also demonstrates that the nonadditive three-body interactions are very significant in (HF)3 and have to be included in order to obtain accurate intermolecular vibrational energy levels of the trimer.

Influence of high temperature non-equilibrium effects on Mach 12 scramjet inlet

To better understand the high temperature non-equilibrium effects of a high Mach number (above Mach 8) scramjet inlet, the thermal and chemical non-equilibrium flow of Mach 12 two-dimensional inlet is numerically analyzed by using the thermochemical non-equilibrium gas model including a two-temperature model and air chemical reactions. The thermal equilibrium flow is simulated by using the models of thermally perfect gas and chemical non-equilibrium gas. It is found that the thermal non-equilibrium effects are relatively strong near the cowl shock and in the outer layer of the boundary layer, and gradually weaken in the downstream zone of the cowl shock. The chemical non-equilibrium effects and thermal equilibrium flows mainly exist in the high-temperature region of the boundary layer. Compared with the chemical non-equilibrium gas, the oxygen dissociation reaction near the lower wall for the thermochemical non-equilibrium gas is weaker in the external compression section; It is stronger due to fully excited vibration energy, in the internal compression section. Compared with the other models, the inlet compression ability for the thermochemical non-equilibrium gas is higher, the coefficient of mass flow and total pressure recovery for it are lower. Hence, the high temperature non-equilibrium effects can not be ignored in the design of the high Mach number scramjet inlet.

Torsionally broken symmetry assists infrared excitation of biomimetic charge-coupled nuclear motions in the electronic ground state.

The concerted interplay between reactive nuclear and electronic motions in molecules actuates chemistry. Here, we demonstrate that out-of-plane torsional deformation and vibrational excitation of stretching motions in the electronic ground state modulate the charge-density distribution in a donor-bridge-acceptor molecule in solution. The vibrationally-induced change, visualised by transient absorption spectroscopy with a mid-infrared pump and a visible probe, is mechanistically resolved by ab initio molecular dynamics simulations. Mapping the potential energy landscape attributes the observed charge-coupled coherent nuclear motions to the population of the initial segment of a double-bond isomerization channel, also seen in biological molecules. Our results illustrate the pivotal role of pre-twisted molecular geometries in enhancing the transfer of vibrational energy to specific molecular modes, prior to thermal redistribution. This motivates the search for synthetic strategies towards achieving potentially new infrared-mediated chemistry.

Excited-State DMRG Made Simple with FEAST

We introduce DMRG[FEAST], a new method for optimizing excited-state many-body wave functions with the density matrix renormalization group (DMRG) algorithm. Our approach applies the FEAST algorithm, originally designed for large-scale diagonalization problems, to matrix product state wave functions. We show that DMRG[FEAST] enables the stable optimization of both low- and high-energy eigenstates, therefore overcoming the limitations of state-of-the-art excited-state DMRG algorithms. We demonstrate the reliability of DMRG[FEAST] by calculating anharmonic vibrational excitation energies of molecules with up to 30 fully coupled degrees of freedom.

Direct Dynamics with Nuclear-Electronic Orbital Density Functional Theory.

Direct dynamics simulations of chemical reactions typically require the selection of a method for generating the potential energy surfaces and a method for the dynamical propagation of the nuclei on these surfaces. The nuclear-electronic orbital (NEO) framework avoids this Born-Oppenheimer separation by treating specified nuclei on the same level as the electrons with wave function methods or density functional theory (DFT). The NEO approach is particularly applicable to proton, hydride, and proton-coupled electron transfer reactions, where the transferring proton(s) and all electrons are treated quantum mechanically. In this manner, the zero-point energy, density delocalization, and anharmonicity of the transferring protons are inherently and efficiently included in the energies, optimized geometries, and dynamics.This Account describes how various NEO methods can be used for direct dynamics simulations on electron-proton vibronic surfaces. The strengths and limitations of these approaches are discussed, and illustrative examples are presented. The NEO-DFT method can be used to simulate chemical reactions on the ground state vibronic surface, as illustrated by the application to hydride transfer in C4H9+. The NEO multistate DFT (NEO-MSDFT) method is useful for simulating ground state reactions in which the proton density becomes bilobal during the dynamics, a characteristic of hydrogen tunneling, as illustrated by proton transfer in malonaldehyde. The NEO time-dependent DFT (NEO-TDDFT) method produces excited electronic, vibrational, and vibronic surfaces. The application of linear-response NEO-TDDFT to H2 and H3+, as well as the partially and fully deuterated counterparts, shows that this approach produces accurate fundamental vibrational excitation energies when all nuclei and all electrons are treated quantum mechanically. Moreover, when only specified nuclei are treated quantum mechanically, this approach can be used to optimize geometries on excited state vibronic surfaces, as illustrated by photoinduced single and double proton transfer systems, and to conduct adiabatic dynamics on these surfaces. The real-time NEO-TDDFT method provides an alternative approach for simulating nonequilibrium nuclear-electronic dynamics of such systems. These various NEO methods can be combined with nonadiabatic dynamics methods such as Ehrenfest and surface hopping dynamics to include the nonadiabatic effects between the quantum and classical subsystems. The real-time NEO-TDDFT Ehrenfest dynamics simulation of excited state intramolecular proton transfer in o-hydroxybenzaldehyde illustrates the power of this type of combined approach. The field of multicomponent quantum chemistry is in the early stages, and the methods discussed herein provide the foundation for a wide range of promising future directions to be explored. An appealing future direction is the expansion of the real-time NEO-TDDFT method to describe the dynamics of all nuclei and electrons on the same level. Direct dynamics simulations using NEO wave function methods such as equation-of-motion coupled cluster or multiconfigurational approaches are also attractive but computationally expensive options. The further development of NEO direct dynamics methods will enable the simulation of the nuclear-electronic dynamics for a vast array of chemical and biological processes that extend beyond the Born-Oppenheimer approximation.

Electronic Structure of RhO2+, Its Ammoniated Complexes (NH3)1-5RhO2+, and Mechanistic Exploration of CH4 Activation by Them.

High-level electronic structure calculations are initially performed to investigate the electronic structure of RhO2+. The construction of potential energy curves for the ground and low-lying excited states allowed the calculation of spectroscopic constants, including harmonic and anharmonic vibrational frequencies, bond lengths, spin-orbit constants, and excitation energies. The equilibrium electronic configurations were used for the interpretation of the chemical bonding. We further monitored how the Rh-O bonding scheme changes with the gradual addition of ammonia ligands. The nature of this bond remains unaffected up to four ammonia ligands but adopts a different electronic configuration in the pseudo-octahedral geometry of (NH3)5RhO2+. This has consequences in the activation mechanism of the C-H bond of methane by these complexes, especially (NH3)4RhO2+. We show that the [2 + 2] mechanism in the (NH3)4RhO2+ case has a very low energy barrier comparable to that of a radical mechanism. We also demonstrate that methane can coordinate to the metal in a similar fashion to ammonia and that knowledge of the electronic structure of the pure ammonia complexes provides qualitative insights into the optimal reaction mechanism.

Pseudospectral implementations of long-range corrected density functional theory.

We have implemented pseudospectral density-functional theory (DFT) with long-range corrected DFT functionals (PS-LRC) in quantum mechanics package Jaguar, and applied it in the calculations of geometry optimizations, dimmer interaction energies, polarizabilities and first-order hyperpolarizabilities, harmonic vibrational frequencies, S1 and T1 excitation energies, singlet-triplet gaps, charge transfer numbers, oscillator strengths, reaction barrier heights, electron-transfer couplings, and charge-transfer excitation energies. From our accuracy benchmark analysis, PS grids, PS dealiasing functions, PS atomic corrections, PS multigrid strategy, PS length scales, and PS cutoff scheme perform well in PS DFT with LRC density functionals with very small and ignorable deviations when compared to the conventional spectral (CS) method. The timing benchmark study of S1 excitation energy calculations of fullerenes (Cn , n up to 540) demonstrates that PS-LRC achieves 1.4-8.4-fold speedups in SCF, 22-32-fold speedups in Tamm-Dancoff approximation, and 6-15-fold speedups in total wall clock time with an average error 0.004 eV of excitation energies compared to the CS method.

Calculating vibrational excitation energies using tensor-decomposed vibrational coupled-cluster response theory.

The first implementation of tensor-decomposed vibrational coupled cluster (CP-VCC) response theory for calculating vibrational excitation energies is presented. The CP-VCC algorithm, which has previously been applied to solving the vibrational coupled cluster (VCC) ground-state equations without explicitly constructing any tensors of order three or higher, has been generalized to allow transformations with the Jacobian matrix necessary for computation of response excitation energies by iterative algorithms. A new eigenvalue solver for computing CP-VCC excitation energies is introduced, and the different numerical thresholds used for controlling the accuracy of the obtained eigenvalues are discussed. Numerical results are presented for calculations of the 20 lowest eigenvalues on a set of 10 four-atomic molecules, as well as for a number of polycyclic aromatic hydrocarbons (PAHs) of increasing size, up to PAH8 with 120 modes. It is shown that the errors introduced by the tensor decomposition can be controlled by the choice of numerical thresholds. Furthermore, all thresholds can be defined relative to the requested convergence threshold of the equation solver, which allows black-box calculations with minimal user input to be performed. Eigenstates of PAHs were efficiently computed without any explicitly constructed tensors, showing improvements in both memory and central processing unit time compared to the existing full-tensor versions.

Quantum Tunneling of a He Atom Above and Below a Benzene Ring.

Van der Waals (vdW) complexes with helium atoms have deserved much attention for their intriguing quantum nature relevant to microscopic superfluidity. However, tunneling splitting, the clear signature of quantum delocalization of He atoms, has rarely been identified in any of the He-containing complexes. Here, UV excitation spectra of benzene-He were extensively examined with almost full rotational resolution to identify two weak vibronic bands with vibrational excitation energies of only ∼13 and ∼16 cm-1. Each of rotational transitions appears to be split into doublets in the higher-frequency band. This splitting is attributed to quantum tunneling due to the delocalization of He spread over two minimum locations below and above the benzene ring. The magnitude of the tunneling splitting as well as the vibrational frequencies of the two vdW modes are compared with the reported theoretical prediction to quantitatively assess the intermolecular potential energy surfaces so far derived.

On derivation and verification of a kinetic model for quantum vibrational energy of polyatomic gases in the gas-kinetic unified algorithm

In this paper, a kinetic Boltzmann model equation involving internal degrees of freedom is constructed for thermodynamic non-equilibrium polyatomic gases, in which the continuous distribution mode of rotational energy and discrete quantum effect of the vibrational energy are both considered, respectively. By theoretically analyzing the “recurrence feature” of this model, it is found that the root of the quantum effect comes from the translational-rotational-vibrational relaxation term (G3t,r,v), because of the additional term relative to the continuous distribution mode of vibrational energy. Besides, some important properties of this model are also analyzed and proved, including the conservative property and entropy inequality. Then, the balance equations on each vibrational energy level and balance equations about macroscopic variables are derived by the moment method. The corresponding thermodynamic relationship in the hydrodynamic limit is also analyzed by the simplified version of Chapman-Enskog method, and the correct Prandtl number is obtained. Numerical methods and wall surface boundary condition to solve this model equation are presented here. Finally, planar flows past a cylinder with different Mach numbers are numerically simulated to test and verify the reliability of this model, and to analyze the influence rules of the excited quantum vibrational energy for polyatomic gas flows.

Development of nuclear basis sets for multicomponent quantum chemistry methods.

The nuclear-electronic orbital (NEO) framework provides a practical approach for directly incorporating nuclear quantum effects and non-Born-Oppenheimer effects of specified nuclei, typically protons, into quantum chemistry calculations. Multicomponent wave function based methods, such as NEO coupled cluster singles and doubles, and multicomponent density functional theory (DFT), such as NEO-DFT, require the appropriate selection of electronic and nuclear basis sets. Although a wide array of electronic basis sets are available, systematically developed nuclear basis sets that balance accuracy and efficiency have been lacking. Herein, a series of nuclear basis sets are developed and shown to be accurate and efficient for describing both ground and excited state properties of multicomponent systems in which electrons and specified protons are treated quantum mechanically. Three series of Gaussian-type nuclear basis sets, denoted PB4, PB5, and PB6, are developed with varying levels of angular momentum. A machine-learning optimization procedure relying on the Gaussian process regression method is utilized to accelerate the optimization process. The basis sets are validated in terms of predictions of ground state energies, proton densities, proton affinities, and proton vibrational excitation energies, allowing the user to select the desired balance between accuracy and efficiency for the properties of interest. These nuclear basis sets will enhance the tractability of NEO methods for applications to a wide range of chemical systems.

Vibrational Relaxation of Functional Groups in dAMP Molecules Probed with UV Resonance Raman Spectroscopy

Dynamical properties of functional groups in 2�-deoxyadenosine-5�-monophosphate (dAMP) compound, were identified by UV resonance Raman spectroscopy (UVRR), upon varying nucleotide concentration in aqueous solution (200-600 μM). The studied full-widths at half-maximum (fwhm�s) were found between 13 - 21 cm-1 and the corresponding global relaxation times were faster than 0.817 ps and slower than 0.506 ps. Also, the band around 1430 cm-1 (C4N9-δC8H) in the UV resonance Raman spectrum of dAMP molecule at 400 μM concentration in aqueous solution, was selected for vibrational band shape analysis through time correlation function (CF) concept. Current theories developed for vibrational dephasing (Kubo-Rothschild and Oxtoby) have been applied to this profile and relevant relaxation parameters have been obtained and discussed. The best fit parameters for this dissipation channel of the vibrational excitation energy were established. To our knowledge this is the first UVRR study on nucleotide vibrational band shape analysis through time correlation function concept.

Control of Impulsively Excited Vibration Energy Harvesters: Design and Viability Assessment

In energy harvesting technologies, the circuitry used to extract power can be viewed as imposing a feedback law on the harvester’s dynamics. Each circuit topology affords some degree of controllability, and consequently, a feasibility domain over which its feedback law can be optimized to maximize the harvested energy. The parasitic losses associated with a given circuit can be large enough that they are comparable to or exceed the available resource, thus precluding its viability. This article examines these issues for single-degree-of-freedom vibration energy harvesters subjected to a single-impulsive inertial loading. We introduce two different quadratic overbound techniques for parasitic loss modeling: one based on physical circuit parameters and the other based on a static efficiency model. We consider the choice between an active rectifier and active drive circuit to condition the power, and also the choice of whether to include power-factor correction circuitry. The four resultant design combinations represent different tradeoffs between the control functionality and the parasitic loss. For all cases, we illustrate a technique for determining the maximum energy that can be harvested from the impulse using the optimal control theory. We then use this analysis to determine, for each case, whether the parasitic power it must sustain to operate is justified by the performance it achieves. We also determine the critical threshold of parasitic loss, below which a given case is not a viable technology. Finally, we show that the relative favorability of each circuit depends strongly on the characteristics of the harvesting device, as well as the disturbance intensity.