Normal coordinates
View article
General formulation of vibronic spectroscopy in internal coordinates Open
Our general platform integrating time-independent and time-dependent evaluations of vibronic effects at the harmonic level for different kinds of absorption and emission one-photon, conventional and chiral spectroscopies has been extended …
View article
Vibrational Coupled Cluster Computations in Polyspherical Coordinates with the Exact Analytical Kinetic Energy Operator Open
We present the first use of curvilinear vibrational coordinates, specifically polyspherical coordinates, in combination with vibrational coupled cluster theory. The polyspherical coordinates are used in the context of both the adaptive den…
View article
Group-theoretical formulation of an Eckart-frame kinetic energy operator in curvilinear coordinates for polyatomic molecules Open
A new procedure is presented for building a general kinetic energy operator expressed as a polynomial series expansion of symmetry-adapted curvilinear coordinates for semirigid polyatomic molecules. As a starting point, the normal-mode Wat…
View article
Determining internal coordinate sets for optimal representation of molecular vibration Open
Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational …
View article
Lattice Boltzmann model in curvilinear coordinates for the study of the vibrational modes of a trumpet Open
Since its origins, lattice-Boltzmann methods have been restricted to rectangular coordinates, a fact which jeopardises the applications to problems with cylindrical or spherical symmetries and complicates the implementations with complex g…
View article
Probing vibrational coupling via a grid‐based quantum approach—an efficient strategy for accurate calculations of localized normal modes in solid‐state systems Open
In this work an approach to investigate the properties of strongly localized vibrational modes of functional groups in bulk material and on solid‐state surfaces is presented. The associated normal mode vectors are approximated solely on th…
View article
Toward Accurate Theoretical Vibrational Spectra: A Case Study for Maleimide Open
We employ and combine a number of recent developments in vibrational structure methods to push their current size limitations toward molecules with tens of modes and showcase their availability for the maleimide molecule. In particular, we…
View article
On the use of reduced-density matrices for the semi-automatic assignment of vibrational states Open
The use of one- and two-mode reduced-density matrices (RDM), and , respectively, and in particular the use of their diagonal elements, and , is suggested for the assignment of normal-mode-like quantum numbers to variationally computed vibr…
View article
Vibrationally correlated calculations in polyspherical coordinates: Taylor expansion-based kinetic energy operators Open
The efficiency of quantum chemical simulations of nuclear motion can in many cases greatly benefit from the application of curvilinear coordinate systems. This is rooted in the fact that a set of smartly selected curvilinear coordinates ma…
View article
Signatures of Duschinsky Rotation in Femtosecond Coherence Spectra Open
The motions of nuclei in a molecule can be mathematically described by using normal modes of vibration, which form a complete orthonormal basis. Each normal mode describes oscillatory motion at a frequency determined by the momentum of the…
View article
Supergravity scattering amplitudes Open
Supergravity theories with nonminimal Kähler potentials are characterized by a nontrivial field space manifold with corresponding nontrivial kinetic terms. The scattering amplitudes in these theories can be calculated at fixed background f…
View article
A quartic force field coordinate substitution scheme using hyperbolic sine coordinates Open
Quartic force fields (QFF) are currently the most cost‐effective method for the approximation of potential energy surfaces for the calculation of anharmonic vibrational energies. It is known, although, that its performance can be less than…
View article
On the role of intermolecular vibrational motions for ice polymorphs. IV. Anisotropy in the thermal expansivity and the nonaffine deformation for ice IX and III Open
We explore anisotropic properties in the thermal expansivities of hydrogen-ordered ice IX and its hydrogen-disordered counterpart, ice III. The free energies of these ice forms are calculated to obtain the lattice constants for the tetrago…
View article
Structural changes upon electronic excitation in 1,2-dimethoxybenzene from rotationally resolved electronic spectroscopy of various isotopologues Open
\n Contains fulltext :\n 201985.pdf (Publisher’s version ) (Open Access)\n
View article
Physics in precision-dependent normal neighborhoods Open
This dataset is associated with "Physics in Precision-Dependent Normal Neighborhoods", Bruno Hoegl, Stefan Hofmann, and Maximilian Koegler (2020) [https://arxiv.org/abs/2007.15717] It includes mathematica 11.0.1.0 notebooks to allow for th…
View article
Decoupled coordinates for precise molecular vibrational analysis by vibrational self-consistent-field and vibrational configuration interaction methods Open
Decoupled coordinates were developed to calculate precise molecular frequencies effectively by the vibrational self-consisted-field (VSCF) and vibrational configuration interaction (VCI) methods. Strong coupling between the normal modes of…
View article
On the Choice of Coordinates in Anharmonic Theoretical Vibrational Spectroscopy Open
By a suitable choice of coordinates,the computational effort required for calculations of anharmonic vibrational spectra can be reduced significantly. By using suitable localized-mode coordinates obtained from an orthogonal transformation …
View article
Expressing the curvature tensor and connection of a given metric in terms of those of another metric Open
Let $(M,g)$ be a Riemannian manifold, and $m$ be a second metric on $M$. We give expressions of $m$'s associated connection, and Riemann curvature tensor $R_m$, in terms of $R_g$ and certain combinations of covariant derivatives of $m$ (wi…
View article
Localized-Normal Mode DVR for Terminal Alkyne CC Stretch Vibrations Open
The terminal alkyne C≡C stretch has a large Raman scattering cross section in the “silent” region for biomolecules. This has led to many Raman tag and probe studies using molecules with this moiety. Computational investigation of these sys…
View article
Normal form for pseudo-Einstein contact forms and intrinsic CR normal coordinates Open
We give a normal form for pseudo-Einstein contact forms and apply it to construct intrinsic CR normal coordinates parametrized by the structure group of CR geometry. The proof is based on the construction of parabolic normal coordinates by…
View article
On the Choice of Coordinates in Anharmonic Theoretical Vibrational Spectroscopy Open
By a suitable choice of coordinates,the computational effort required for calculations of anharmonic vibrational spectra can be reduced significantly. By using suitable localized-mode coordinates obtained from an orthogonal transformation …
View article
Development of accurate anharmonic vibrational state theory using a novel vibrational coordinate based on backflow transformation Open
Synopsis The anharmonic vibrational state theory based on quantum Monte Carlo method is one of the most accurate methods to solve a vibrational Schrödinger equation of molecular systems. In anharmonic vibrational state analyses, one should…
View article
Analysis, Calculation and Understanding of Molecular Vibrations Open
The idea of molecular dynamics seems intuitively simple,that atoms should move through space on complex but well defined trajectories that reflect the chemical interactions between them.Unfortunately,atoms are quantum ob- jects therefore t…
View article
Orthogonal coordinates on 4 dimensional Kähler manifolds Open
The existence of orthogonal local coordinates is a generalization of the manifold being conformally flat. It is always possible to construct orthogonal coordinates on 2-manifolds, using geometric normal coordinates or isothermal coordinate…
View article
New form of the Kerr-Newman solution Open
A new form of the Kerr-Newman solution is presented. The solution involves a time coordinate which represents the local proper time for a charged massive particle released from rest at spatial infinity. The chosen coordinates ensure that t…
View article
Variational vibrational states of HCOOH Open
Vibrational states of the formic acid molecule are converged using the GENIUSH-Smolyak approach and the potential energy surface taken from [D. Tew and W. Mizukami, J. Phys. Chem. A 120, 9815 (2016)]. The quantum nuclear motion is describe…
View article
Cosmology in Painleve-Gullstrand coordinates Open
Cosmology is most typically analyzed using standard co-moving coordinates, in which the galaxies are (on average, up to presumably small peculiar velocities) "at rest", while "space" is expanding. But this is merely a specific coordinate c…
View article
Lattice Boltzmann model for the simulation of the wave equation in curvilinear coordinates Open
Since its origins, lattice-Boltzmann methods have been restricted to rectangular coordinates, a fact which jeopardises the applications to problems with cylindrical or spherical symmetries and complicates the implementations with complex g…
View article
MOLECULAR SYMMETRY ANALYSIS OF LOW-ENERGY TORSIONAL AND VIBRATIONAL STATES IN THE S0 AND S1 STATES OF p-XYLENE TO INTERPRET THE REMPI SPECTRUM Open
The electronic transition $S_{1}$ $leftarrow$ $S_{0}$ of $p$-xylene (pXyl) has been observed by REMPI spectroscopy.footnote{AM Gardner, WD Tuttle, P. Groner, TG Wright, J. Chem. Phys., submitted Dec 2016} Its analysis required a detailed i…
View article
Supergravity Scattering Amplitudes Open
Supergravity theories with non-minimal Kähler potentials are characterized by a non-trivial field space manifold with corresponding non-trivial kinetic terms. The scattering amplitudes in these theories can be calculated at fixed backgroun…