arXiv subjects

Andrey Yachmenev

Publications and source records attributed to Andrey Yachmenev.

At least 19 recordsLinked to original sources

arXiv2025

Transferability and interpretability of vibrational normalizing-flow coordinates

The choice of vibrational coordinates is crucial for the accuracy, efficiency, and interpretability of molecular vibrational dynamics and spectra calculations. We explore the recently proposed normalizing-flow vibrational coordinates, which are learned molecule-specific coordinate transformations optimized for a given basis set. Much like how spherical coordinates naturally simplify the hydrogen atom by embedding physical insight into the coordinate system, normalizing-flow coordinates offload complexity from the basis functions into the coordinate transformation itself. This shift not only improves basis-set convergence, but also enhances interpretability of vibrational motions. We provide an analysis of the utility, interpretation and associated constraints of normalizing-flow vibrational coordinates. Moreover, we demonstrate that these coordinates can be generalized across different isotopologues, and even structurally related molecules, achieved with minimal fine-tuning of selected output parameters.

physics.chem-ph↗

arXiv2025

Taylor-mode automatic differentiation for constructing molecular rovibrational Hamiltonian operators

We present an automated framework for constructing Taylor series expansions of rovibrational kinetic and potential energy operators for arbitrary molecules, internal coordinate systems, and molecular frame embedding conditions. Expressing operators in a sum-of-products form allows for computationally efficient evaluations of matrix elements in product basis sets. Our approach uses automatic differentiation tools from the Python machine learning ecosystem, particularly the JAX library, to efficiently and accurately generate high-order Taylor expansions of rovibrational operators. The implementation is available at https://github.com/robochimps/vibrojet.

physics.atm-clus↗

arXiv2025

Controlling rovibrational state populations of polar molecules in inhomogeneous electric fields of the Stark deceleration: molecular dynamics and quantum chemistry simulations

We propose a modified Stark-chirped rapid adiabatic passage technique for a robust rovibrational population transfer in the gas phase molecules in the presence of certain inhomogeneous electric fields. As an example application, the new state switching scheme is shown to greatly enhance the process of slowing polar ammonia molecules in the Stark decelerator. High-level quantum mechanical simulations show that a virtually complete population inversion between a selected pair of weak-field and strong-field seeking states of NH$_3$ can be achieved. Strong dc electric fields within the Stark decelerator are used as part of the rovibrational population transfer protocol. Classical-dynamics simulations for ammonia demonstrate notable improvements in the longitudinal phase space acceptance of the Stark decelerator upgraded with the state switching and an increased deceleration efficiency with respect to the standard Stark deceleration technique.

physics.atom-ph↗

arXiv2025

Computing excited states of molecules using normalizing flows

Calculations of highly excited and delocalized molecular vibrational states are computationally challenging tasks, which strongly depends on the choice of coordinates for describing vibrational motions. We introduce a new method that leverages normalizing flows -- parametrized invertible functions -- to learn optimal vibrational coordinates that satisfy the variational principle. This approach produces coordinates tailored to the vibrational problem at hand, significantly increasing the accuracy and enhancing basis-set convergence of the calculated energy spectrum. The efficiency of the method is demonstrated in calculations of the 100 lowest excited vibrational states of H$_2$S, H$_2$CO, and HCN/HNC. The method effectively captures the essential vibrational behavior of molecules by enhancing the separability of the Hamiltonian and hence allows for an effective assignment of approximate quantum numbers. We demonstrate that the optimized coordinates are transferable across different levels of basis-set truncation, enabling a cost-efficient protocol for computing vibrational spectra of high-dimensional systems.

physics.chem-ph↗

arXiv2025

Nuclear spin symmetry-breaking and spin polarization in rotational energy level clusters

We present the first quantum mechanical study of hyperfine effects in the rotational cluster states of a symmetric triatomic molecule H$_2$S. Rotational clusters arise from spontaneous symmetry breaking induced by high-angular-momentum rotational motions in certain rigid molecules, resulting in dynamic enantiomorphism driven by kinetic distortion effects. Hyperfine interactions in the cluster states lead to collision-free breaking of nuclear spin symmetry, with the magnitude of nuclear spin ortho-para mixing significantly exceeding that in other states with same or lower angular momentum. The ortho-para mixing induces nuclear spin polarization in the laboratory frame and gives rise to two sets of enantiomers, that have different energies and oppositely oriented nuclear spin projections. Although hyperfine interactions preserve parity, they lift the degeneracy of opposite-parity cluster states. This phenomenon, previously observed experimentally, is explained as a result of tunneling between rotating enantiomers, facilitated by the Pauli exclusion principle.

physics.atm-clus↗

arXiv2024

Learning phase-space flows using time-discrete implicit Runge-Kutta PINNs

We present a computational framework for obtaining multidimensional phase-space solutions of systems of non-linear coupled differential equations, using high-order implicit Runge-Kutta Physics- Informed Neural Networks (IRK-PINNs) schemes. Building upon foundational work originally solving differential equations for fields depending on coordinates [J. Comput. Phys. 378, 686 (2019)], we adapt the scheme to a context where the coordinates are treated as functions. This modification enables us to efficiently solve equations of motion for a particle in an external field. Our scheme is particularly useful for explicitly time-independent and periodic fields. We apply this approach to successfully solve the equations of motion for a mass particle placed in a central force field and a charged particle in a periodic electric field.

cs.LG↗

arXiv2024

Molecular influence on nuclear-quadrupole-coupling effects in laser induced alignment

We studied the effect of nuclear-quadrupole interactions on the field-free impulsive alignment of different asymmetric-top molecules. Our analysis is focused on the influence of the hyperfine- and rotational-energy-level structures. These depend on the number of nuclear spins, the rotational constants, and the symmetry of the tensors involved in the nuclear spin and external field interactions. Comparing the prototypical large-nuclear-spin molecules iodobenzene, 1,2-diiodobenzene, 1,3-diiodobenzene, and 2,5-diiodobenzonitrile, we demonstrate that the magnitude of the hyperfine splittings compared to the rotational-energy splittings plays a crucial role in the spin-rotational dynamics after the laser pulse. Moreover, we point out that the impact of the quadrupole coupling on the rotational dynamics decreases when highly excited rotational states dominate the dynamics.

physics.atom-ph↗

arXiv2023

Fractional integration and differentiation

In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of functions and provides a series representation of integration. This representation will be useful for working with smooth functions and for approximation due to the potential reduction of the value of the sequential elements.

math.GM↗

arXiv2023

Self-broadening and self-shift in the $\mathbf{3ν_{2}}$ band of ammonia from mid-infrared-frequency-comb spectroscopy

We report the broadband absorption spectrum of the $3ν_{2}$ band of $^{14}$NH$_{3}$ near 4 $μm$. The data were recorded using a mid-infrared frequency comb coupled to a homebuilt Fourier-transform spectrometer with a resolution of 0.00501 $cm^{-1}$. Line positions, line intensities, self-broadening, and self-shift parameters for six rovibrational lines were determined at room temperature ($T=296$ K). Comparison with HITRAN 2016 shows good agreement at improved precision. The high precision and the rapid tunability of our experiment enables advanced fast spectroscopy of molecular gases.

physics.chem-ph↗

arXiv2022

Augmenting Basis Sets by Normalizing Flows

Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by provable approximation orders. On the down side, however, these methods often suffer from the curse of dimensionality, which limits their approximation behavior, especially in situations of highly oscillatory target functions. Nonlinear approximation methods, such as neural networks, were shown to be very efficient in approximating high-dimensional functions. We investigate nonlinear approximation methods that are constructed by composing standard basis sets with normalizing flows. Such models yield richer approximation spaces while maintaining the density properties of the initial basis set, as we show. Simulations to approximate eigenfunctions of a perturbed quantum harmonic oscillator indicate convergence with respect to the size of the basis set.

math.NA↗

arXiv2022

The nuclear-spin-forbidden rovibrational transitions of water from first principles

The water molecule occurs in two nuclear-spin isomers that differ by the value of the total nuclear spin of the hydrogen atoms, i.e., $I=0$ for para-H$_2$O and $I=1$ for ortho-H$_2$O. Spectroscopic transitions between rovibrational states of ortho and para water are extremely weak due to the tiny hyperfine nuclear-spin-rotation interaction of only $\sim30$ kHz and so far were not observed. We report the first comprehensive theoretical investigation of the hyperfine effects and ortho-para transitions in H$_2$$^{16}$O due to nuclear-spin-rotation and spin-spin interactions. We also present the details of our newly developed general variational approach to the simulation of hyperfine effects in polyatomic molecules. Our results for water suggest that the strongest ortho-para transitions with room-temperature intensities on the order of $10^{-31}$ cm/molecule are about an order of magnitude larger than previously predicted values and should be detectable in the mid-infrared $ν_2$ and near-infrared $2ν_1+ν_2$ and $ν_1+ν_2+ν_3$ bands by current spectroscopy experiments.

physics.atom-ph↗

arXiv2022

Picosecond pulse-shaping for strong three-dimensional field-free alignment of generic asymmetric-top molecules

Fixing molecules in space is a crucial step for the imaging of molecular structure and dynamics. Here, we demonstrate three-dimensional (3D) field-free alignment of the prototypical asymmetric top molecule indole using elliptically polarized, shaped, off-resonant laser pulses. A truncated laser pulse is produced using a combination of extreme linear chirping and controlled phase and amplitude shaping using a spatial-light-modulator (SLM) based pulse shaper of a broadband laser pulse. The angular confinement is detected through velocity-map imaging of H$^+$ and C$^{2+}$ fragments resulting from strong-field ionization and Coulomb explosion of the aligned molecules by intense femtosecond laser pulses. The achieved three-dimensional alignment is characterized by comparing the result of ion-velocity-map measurements for different alignment directions and for different times during and after the alignment laser pulse to accurate computational results. The achieved strong three-dimensional field-free alignment of $\langle \cos^{2}δ\rangle=0.89$ demonstrates the feasibility of both, strong three-dimensional alignment of generic complex molecules and its quantitative characterization.

physics.atm-clus↗

arXiv2021

Calculation of Electric Quadrupole Linestrengths for Diatomic Molecules: Application to the H2, CO, HF and O2 Molecules

We present a unified variational treatment of the electric quadrupole (E2) matrix elements, Einstein coefficients, and line strengths for general open-shell diatomic molecules in the general purpose diatomic code \Duo. Transformation relations between the Cartesian representation (typically used in electronic structure calculations) to the tensorial representation (required for spectroscopic applications) of the electric quadrupole moment components are derived. The implementation has been validated against accurate theoretical calculations and experimental measurements of quadrupole intensities of $^1\text{H}_2$ available in the literature. We also present accurate electronic structure calculations of the electric quadrupole moment functions for the $X^1Σ^+$ electronic states of $\text{CO}$ and $\text{HF}$ at the CCSD(T) and MRCI levels of theory, respectively, as well for the $a^1Δ_g$ -- $b^1Σ_g^+$ quadrupole transition moment of $\text{O}_2$ with MRCI level of theory. Accurate infrared E2 line lists for $^{12}\text{C}^{16}\text{O}$ and $^1\text{H}^{19}\text{F}$ are provided. A demonstration of spectroscopic applications is presented by simulating E2 spectra for $^{12}\text{C}^{16}\text{O}$, $\text{H}^{19}\text{F}$ and $^{16}\text{O}_2$ (Noxon $a^1Δ_g$ -- $b^1Σ_g^+$ band).

physics.atm-clus↗

arXiv2021

Active learning of potential-energy surfaces of weakly-bound complexes with regression-tree ensembles

Several pool-based active learning algorithms (AL) were employed to model potential energy surfaces (PESs) with a minimum number of electronic structure calculations. Theoretical and empirical results suggest that superior strategies can be obtained by sampling molecular structures corresponding to large uncertainties in their predictions while at the same time not deviating much from the true distribution of the data. To model PESs in an AL framework we propose to use a regression version of stochastic query by forest, a hybrid method that samples points corresponding to large uncertainties while avoiding collecting too many points from sparse regions of space. The algorithm is implemented with decision trees that come with relatively small computational costs. We empirically show that this algorithm requires around half the data to converge to the same accuracy in comparison to the uncertainty-based query-by-committee algorithm. Moreover, the algorithm is fully automatic and does not require any prior knowledge of the PES. Simulations on a 6D PES of \pyrrolew show that $\mathord{<}15\,000$ configurations are enough to build a PES with a generalization error of 16~\invcm, whereas the final model with around 50\,000 configurations has a generalization error of 11~\invcm.

physics.chem-ph↗

arXiv2021

Electric quadrupole transitions in carbon dioxide

Recent advances in the high sensitivity spectroscopy have made it possible, in combination with accurate theoretical predictions, to observe for the first time very weak electric quadrupole transitions in a polar polyatomic molecule of water. Here we present accurate theoretical predictions of the complete quadrupole ro-vibrational spectrum of a non-polar molecule CO$_2$, important in atmospheric and astrophysical applications. Our predictions are validated by recent cavity enhanced absorption spectroscopy measurements and are used to assign few weak features in the recent ExoMars ACS MIR spectroscopic observations of the martian atmosphere. Predicted quadrupole transitions appear in some of the mid-infrared CO$_2$ and water vapor transparency regions, making them important for detection and characterization of the minor absorbers in water- and CO$_2$-rich environments, such as present in the atmospheres of Earth, Venus and Mars.

physics.atom-ph↗

arXiv2021

Controlling rotation in the molecular-frame with an optical centrifuge

We computationally demonstrate a new method for coherently controlling the rotation-axis direction in asymmetric top molecules with an optical centrifuge. Appropriately chosen electric-field strengths and the centrifuge's acceleration rate allow to generate a nearly arbitrary rotational wavepacket. For D$_2$S and 2H-imidazole (C$_3$H$_4$N$_2$) we created wavepackets at large values of the rotational quantum number $J$ with the desired projections of the total angular momentum onto two of the molecules' principal axes of inertia. One application of the new method is three-dimensional alignment with a molecular axis aligned along the laser's wave vector, which is important for the three-dimensional imaging of molecules yet not accessible in standard approaches. The simultaneous orientation of the angular momentum in the laboratory frame and in the molecular frame could also be used in robust control of scattering experiments.

physics.chem-ph↗

arXiv2021

Detecting handedness of spatially oriented molecules by Coulomb explosion imaging

We present a new technique for detecting chirality in the gas phase: Chiral molecules are spatially aligned in three-dimensions by a moderately strong elliptically-polarized laser field. The momentum distributions of the charged fragments, produced by laser-induced Coulomb explosion, show distinct three-dimensional orientation of the enantiomers, when the laser polarization ellipse is rotated by a non-right angle with respect to the norm vector of the detector plane. The resulting velocity-map-image asymmetry is directly connected to the enantiomeric excess and to the absolute handedness of molecules. We demonstrated our scheme computationally for camphor (C10H16O), with its methyl-groups as marker fragments, using quantum-mechanical simulations geared toward experimentally feasible conditions. Computed sensitivity to enantiomeric excess is comparable to other modern chiroptical approaches. The present method can be readily optimized for any chiral molecule with an anisotropic polarizability tensor by adjusting the polarization state and intensity profile of the laser field.

physics.chem-ph↗

arXiv2020

The effect of nuclear-quadrupole coupling in the laser induced alignment of molecules

We present a theoretical study of the time-dependent laser alignment of molecules taking into account the hyperfine coupling due to nuclear-quadrupole interactions. The coupling of nuclear spins to the overall angular momentum of molecules significantly influences their rotational dynamics. Here, we systematically analyze the impact of the nuclear-quadrupole coupling on the rotational dynamics of the linear $\text{I}_2$ and the asymmetric-top diiodobenzene molecule induced by external laser fields. We explore different regimes of pulse shapes and laser-pulse intensities and detail under which conditions the quadrupole coupling cannot be neglected in the description of the laser alignment of molecules.

physics.chem-ph↗