Vibrational Wave Functions Research Articles

Vibrational excitation in the e + CO2 system: Analysis of the two-dimensional energy-loss spectrum

We present a detailed analysis of the two-dimensional electron energy-loss spectrum of ${\mathrm{CO}}_{2}$, which extends our recent Letter [Phys. Rev. Lett. 129, 013401 (2022)]. We show that our vibronic coupling model [Phys. Rev. A 105, 062821 (2022)] captures primary features of the multidimensional dynamics of the temporary molecular anion, and the calculations qualitatively reproduce the spectrum. The shape of the spectrum is given by two overlapping contributions that originate in excitation of vibrational states within ${\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ and ${\mathrm{\ensuremath{\Pi}}}_{u}$ Fermi polyads. Propensity rules in terms of scattered and vibrational wave functions are also discussed to clarify the selectivity of states from the vibrational pseudocontinuum that is responsible for the observed fine structure.

Photodetachment of Deprotonated R-Mandelic Acid: The Role of Proton Delocalization on the Radical Stability.

The photodetachment and stability of R-Mandelate, the deprotonated form of the R-Mandelic acid, was investigated by observing the neutral species issued from either simple photodetachment or dissociative photodetachment in a cold anions set-up. R-Mandalate has the possibility to form an intramolecular ionic hydrogen-bond between adjacent hydroxyl and carboxylate groups. The potential energy surface along the proton transfer (PT) coordinate between both groups (O- …H+ …- OCO) features a single local minima, with the proton localized on the O- group (OH…- OCO). However, the structure with the proton localized on the - OCO group (O- …HOCO) is also observed because it falls within the extremity of the vibrational wavefunction of the OH…- OCO isomer along the PT coordinate. The stability of the corresponding radicals, produced upon photodetachment, is strongly dependent on the position of the proton in the anion: the radicals produced from the OH…- OCO isomer decarboxylate without barrier, while the radicals produced from the O- …HOCO isomer are stable.

Single and double Auger decays from highly-excited vibrational sublevels in core-ionized N2 molecules

Single and double Auger decays from vibrationally excited core-ionized N2 molecules are studied using multielectron coincidence spectroscopy. The high vibrational sublevels (ν ≥ 5) of the core-hole state are populated via autoionization following core-valence double excitation. The features of the Auger spectra vary significantly as the initial vibrational excitation increases, which reflects the vibrational wave functions in the core-hole state and the repulsive potential energy curves for Auger final states.

Evaluation of vibrational energies and wave functions of CO2 on a quantum computer

In order to develop a method for evaluating vibrational energies and wave functions of a polyatomic molecule by quantum computing, we introduce the reduced multistate contracted variational quantum eigensolver (RMC-VQE) method, which is a variant of the multistate contracted VQE method [Parrish et al., Phys. Rev. Lett. 122, 230401 (2019)], and apply the RMC-VQE method to a two-mode model of CO2. In the RMC-VQE method, much fewer matrix elements of the Hamiltonian are evaluated on the quantum computer than in the MC-VQE method. By measuring the matrix elements of the Hamiltonian using the quantum computer ibm_kawasaki and diagonalizing the Hamiltonian matrix on a classical computer, we obtain the vibrational energies of the Fermi doublet, which differ from the exact energies obtained using a classical computer by less than 0.1 cm−1. We also obtain accurate vibrational wave functions of the Fermi doublet states.

Unique non‐resonance hyper‐Raman bands of glucose in phosphate‐buffered saline

AbstractWe report the 532 nm‐excited hyper‐Raman (HR) spectrum of D‐glucose in phosphate‐buffered saline (PBS) at pH 7.4. Large and unique HR bands were observed from 1500 to 1650 cm−1. The HR spectral pattern was completely different from those of infrared absorption and Raman spectra. The HR bands were affected by isotope labeling on glucose but not phosphate. The HR bands were attributed to the combination or overtone modes of glucose. These bands were also observed in buffers containing phosphate, carbonate, and Tris but not in H2O. We tentatively attributed the origin of the HR bands to the charges of the buffer molecule(s) and the resultant electric field effect on the electronic and/or vibrational wavefunctions.

Quantum simulation of the photodissociation cross section of the NaH molecule

The photodissociation cross section of the NaH molecule from the ground state X1Σ+ to the excited state B1Π is calculated by solving the time-dependent Schrödinger equation with the consideration of two sets of potential energy curves (PECs). It is found that by using PECs, the maximum photodissociation cross section, the corresponding photon energy, and the effective range of photon energy which can result in the cross section greater than 0.1 Å2 all vary significantly. These differences are ascribed to the variations of the PECs, the vertical excitation energy, the vibrational wavefunction of the X1Σ+ state, and the Franck–Condon factors, etc. These findings provide a deep insight into the spectrum of the NaH molecule and are expected to inspire further relevant investigations in experiment and theory.

Efficient and automated quantum chemical calculation of rovibrational nonresonant Raman spectra.

An outline of a newly developed program for the simulation of rovibrational nonresonant Raman spectra is presented. This program is an extension of our recently developed code for rovibrational infrared spectra [Erfort et al., J. Chem Phys. 152, 244104 (2020)] and relies on vibrational wavefunctions from variational configuration interaction theory to allow for an almost fully automated calculation of such spectra in a pure ab initio fashion. Due to efficient contraction schemes, this program requires modest computational resources, and it can be controlled by only a few lines of input. As the required polarizability surfaces are also computed in an automated fashion, this implementation enables the routine application to small molecules. For demonstrating its capabilities, benchmark calculations for water H2 16O are compared to reference data, and spectra for the beryllium dihydride dimer, Be2H4 (D2h), are predicted. The inversion symmetry of the D2h systems lead to complementary infrared and Raman spectra, which are both needed for a comprehensive investigation of this system.

Program Synthesis of Sparse Algorithms for Wave Function and Energy Prediction in Grid-Based Quantum Simulations.

We have recently shown how program synthesis (PS), or the concept of “self-writing code”, can generate novel algorithms that solve the vibrational Schrödinger equation, providing approximations to the allowed wave functions for bound, one-dimensional (1-D) potential energy surfaces (PESs). The resulting algorithms use a grid-based representation of the underlying wave function ψ(x) and PES V(x), providing codes which represent approximations to standard discrete variable representation (DVR) methods. In this Article, we show how this inductive PS strategy can be improved and modified to enable prediction of both vibrational wave functions and energy eigenvalues of representative model PESs (both 1-D and multidimensional). We show that PS can generate algorithms that offer some improvements in energy eigenvalue accuracy over standard DVR schemes; however, we also demonstrate that PS can identify accurate numerical methods that exhibit desirable computational features, such as employing very sparse (tridiagonal) matrices. The resulting PS-generated algorithms are initially developed and tested for 1-D vibrational eigenproblems, before solution of multidimensional problems is demonstrated; we find that our new PS-generated algorithms can reduce calculation times for grid-based eigenvector computation by an order of magnitude or more. More generally, with further development and optimization, we anticipate that PS-generated algorithms based on effective Hamiltonian approximations, such as those proposed here, could be useful in direct simulations of quantum dynamics via wave function propagation and evaluation of molecular electronic structure.

Quantum vibration perturbation approach with polyatomic probe in simulating infrared spectra.

The quantitative prediction of vibrational spectra of chromophore molecules in solution is challenging and numerous methods have been developed. In this work, we present a quantum vibration perturbation (QVP) approach, which is a procedure that combines molecular quantum vibration and molecular dynamics with perturbation theory. In this framework, an initial Newtonian molecular dynamics simulation is performed, followed by a substitution process to embed molecular quantum vibrational wave functions into the trajectory. The instantaneous vibrational frequency shift at each time step is calculated using the Rayleigh-Schrödinger perturbation theory, where the perturbation operator is the difference in the vibrational potential between the reference chromophore and the perturbed chromophore in the environment. Semi-classical statistical mechanics is employed to obtain the spectral lineshape function. We validated our method using HCOOH·nH2O (n = 1-2) clusters and HCOOH aqueous solution as examples. The QVP method can be employed for rapid prediction of the vibrational spectrum of a specific mode in solution.

Electron transport properties of molecular junctions with anharmonic double-well potentials

In the present paper, we investigated the electron transport properties of molecular junctions with anharmonic vibrations described by double-well potentials in the sequential tunneling regime. It was found that the suppression of the low-bias current caused by strong electron-vibration couplings under harmonic approximation, i.e., the Franck-Condon blockade effect, could be lifted in the case of symmetric double-well potentials. The removal of the Franck-Condon blockade effect is a result of the distribution of the ground vibrational wave function in the two wells. Such a feature also enables the Franck-Condon blockade effect to be restored by breaking the symmetry of the double-well potential. We further demonstrated that the special vibrational transition properties of asymmetric double-well potentials could enable the effective modulation of the charge transport properties of such molecular junctions in the Franck-Condon blockade region by inducing population in excited vibrational levels with external fields such as infrared excitation.

Over-barrier crossing in multidimensional tunneling

Studies of the dissociative chemisorption of N2 using two-dimensional empirical potential energy surfaces that differ by the position of the saddle point, all show high tunneling probabilities at energies well below the saddle-point energy of the reaction. This is highly unusual for a heavy-atom system and contradicted by one-dimensional analysis along the minimum-energy path. A mechanism of over-barrier crossing, related to the high-momentum tail of the vibrational wave function of N2, is demonstrated. We analyze the two-dimensional wave-packet propagation and compares to the probability of having vibrational momenta that exceeds the value required to overcome the relevant barrier.

Development of anharmonic vibrational structure theory using backflow transformation

A backflow (BF) transformation was applied to a vibrational self-consistent field wavefunction, which is the mean-field approximation in an anharmonic vibrational structure theory. We tested its effectiveness on the H2O molecule using quantum Monte Carlo method. Each normal mode coordinate was transformed into collective coordinates using the correlation function depending on whole coordinates. The vibrational frequencies with the BF transformation reasonably agree with the vibrational configuration interaction (VCI) results. The vibrational probability density to which the BF transformation was applied was also consistent with the VCI results and showed that the BF transformation appropriately take into account the inter-mode couplings.

Advances in vibrational configuration interaction theory - part 2: Fast screening of the correlation space.

For larger molecules, the computational demands of configuration selective vibrational configuration interaction theory (cs-VCI) are usually dominated by the configuration selection process, which commonly is based on second order vibrational Møller-Plesset perturbation (VMP2) theory. Here we present two techniques, which lead to substantial accelerations of such calculations while retaining the desired high accuracy of the final results. The first one introduces the concept of configuration classes, which allows for a highly efficient exploitation of the analogs of the Slater-Condon rules in vibrational structure calculations with large correlation spaces. The second approach uses a VMP2 like vector for augmenting the targeted vibrational wavefunction within the selection of configurations and thus avoids any intermediate diagonalization steps. The underlying theory is outlined and benchmark calculations are provided for highly correlated vibrational states of several molecules.

Enhancing oxygen reduction electrocatalysis by tuning interfacial hydrogen bonds

Proton activity at the electrified interface is central to the kinetics of proton-coupled electron transfer (PCET) reactions for making chemicals and fuels. Here we employ a library of protic ionic liquids in an interfacial layer on platinum and gold to alter local proton activity, where the intrinsic oxygen-reduction reaction (ORR) activity is enhanced up to fivefold, exhibiting a volcano-shaped dependence on the pKa of the ionic liquid. The enhanced ORR activity is attributed to strengthened hydrogen bonds between ORR products and ionic liquids with comparable pKas, resulting in favourable PCET kinetics. This proposed mechanism is supported by in situ surface-enhanced Fourier-transform infrared spectroscopy and our simulation of PCET kinetics based on computed proton vibrational wavefunctions at the hydrogen-bonding interface. These findings highlight opportunities for using non-covalent interactions between hydrogen-bonded structures and solvation environments at the electrified interface to tune the kinetics of ORR and beyond. Understanding the role of hydrogen bonds at the electrode interface is important for controlling the kinetics of the oxygen-reduction reaction. Here the authors modify gold and platinum surfaces with a series of protic ionic liquids to show that pKa can be used to optimize proton-coupled electron transfer through hydrogen bonding.

Deep learning methods for the computation of vibrational wavefunctions

In this paper, we design and use two Deep Learning models to generate the ground and excited wavefunctions of different Hamiltonians suitable for the study of the vibrations of molecular systems. The generated neural networks are trained with Hamiltonians that have analytical solutions and ask the network to generalize these solutions to more complex Hamiltonian functions. Since the Hamiltonians solutions used to train the neural networks are computationally cheap, the training process is fast and efficient. This approach allows to reproduce the excited vibrational wavefunctions of different molecular potentials. All methodologies used here are data-driven, therefore they do not assume any information about the underlying physical model of the system. This makes this approach versatile and can be used in the study of multiple systems in quantum chemistry.

Calculation of vibrational eigenenergies on a quantum computer: Application to the Fermi resonance in CO2

We apply a modified version of the multistate contracted variational quantum eigensolver method to calculate vibrational eigenstates of ${\mathrm{CO}}_{2}$ on a quantum computer. A two-mode model of ${\mathrm{CO}}_{2}$ is employed, and the vibrational wave function is expanded using three harmonic-oscillator basis functions for each mode. The wave functions are mapped to four qubits by a compact mapping method. The Hamiltonian matrix elements are evaluated on a simulator including noise and on a quantum computer available at IBM Quantum, while the Hamiltonian matrix is diagonalized on a classical computer. We propose an error mitigation method by which the shift of the numerical values of the matrix elements originating from the noise can be corrected, and examine the dependence of the statistical uncertainties on the number of executions of each quantum circuit. We find that, at about $8\ifmmode\times\else\texttimes\fi{}{10}^{6}$ executions, the energy eigenvalues of the Fermi resonance states in ${\mathrm{CO}}_{2}$ can be obtained with an uncertainty within 1 ${\mathrm{cm}}^{\ensuremath{-}1}$.

Solving the Kratzer oscillator in diatomic molecules: an algebraic approach based on the so(2,1) Lie algebra

In this article, we solve the rovibrational Schrödinger equation for diatomic molecules using the Kratzer oscillator by means of the Lie algebra. The main contribution of our algebraic approach is that this allows us to reduce the degree of the Schrödinger equation giving thus a first-order differential equation, by which the vibrational ground state wave function is obtained, clearly and in few steps. The energies are obtained by scaling of the observables r and p r which preserves the canonical commutation relation, and a recurrence relation for the bound states written in terms of the raising operator is also given. Also we calculate the rovibrational spectrum of H 2 and CO molecules, showing that the energies of the Kratzer oscillator not only depends on vibrational and rotational quantum numbers, but also in the difference between the vibrational quantum number with its minimum value, for a fixed l. The article ends giving a physical insight of the symmetry transformation of the SO(2, 1) Lie group in order to show the relationship between this group and its associated Lie algebra. Finally, as an illustrative example, we calculated the selection rules for the vibrational quantum number, from a purely algebraic approach.

Understanding the structure of complex multidimensional wave functions. A case study of excited vibrational states of ammonia

Generalization of an earlier reduced-density-matrix-based vibrational assignment algorithm is given, applicable for systems exhibiting both large-amplitude motions, including tunneling, and degenerate vibrational modes. The algorithm developed is used to study the structure of the excited vibrational wave functions of the ammonia molecule, 14NH3. Characterization of the complex dynamics of systems with several degenerate vibrations requires reconsidering the traditional degenerate-mode description given by vibrational angular momentum quantum numbers and switching to a symmetry-based approach that directly predicts state degeneracy and uncovers relations between degenerate modes. Out of the 600 distinct vibrational eigenstates of ammonia obtained by a full-dimensional variational computation, the developed methodology allows for the assignment of about 500 with meaningful labels. This study confirms that vibrationally excited states truly have modal character recognizable up to very high energies even for the non-trivial case of ammonia, a molecule which exhibits a tunneling motion and has two two-dimensional normal modes. The modal characteristics of the excited states and the interplay of the vibrational modes can be easily visualized by the reduced-density matrices, giving an insight into the complex modal behavior directed by symmetry.

Vibrational spectra and Wavefunction investigation for antidepressant drug of Amoxapine based on quantum computational studies

Abstract The title compound, Amoxapine was examined by the computational calculation using the density functional theory (DFT) with B3LYP method and 6–311++G(d,p) as the basis set. The optimized molecular structure of AMX were analyzed and its geometric parameters were calculated. The Frontier molecular orbital energy conclusion shows that there is a good charge exchange developed within the molecule. Donor-acceptor interactions were determined using NBO analysis method. The Fukui function and Molecular Electrostatic Potential (MEP) and Hirshfeld studies were carried out to analyze the surface of the molecule. The hyperpolarizability computation shows that AMX has desirable NLO property. ELF and LOL computation were carried to calculate the probability of electron density at bonding and antibonding sites. Thermodynamic properties of the title compound were closely examined at different temperatures. The paper further explains that the Drug likeness and molecular docking studies.

Artificial Neural Networks as Mappings between Proton Potentials, Wave Functions, Densities, and Energy Levels.

Artificial neural networks (ANNs) have become important in quantum chemistry. Herein, applications to nuclear quantum effects, such as zero-point energy, vibrationally excited states, and hydrogen tunneling, are explored. ANNs are used to solve the time-independent Schrödinger equation for single- and double-well potentials representing hydrogen-bonded molecular systems capable of proton transfer. ANN mappings are trained to predict the lowest five proton vibrational energies, wave functions, and densities from the proton potentials and to predict the excited state proton vibrational energies and densities from the proton ground state density. For the inverse problem, ANN mappings are trained to predict the proton potential from the proton vibrational energy levels or the proton ground state density. This latter mapping is theoretically justified by the first Hohenberg-Kohn theorem establishing a one-to-one correspondence between the external potential and the ground state density. ANNs for two- and three-dimensional systems are also presented to illustrate the straightforward extension to higher dimensions.