Vibration-rotation Energy Levels Research Articles

Numerically constructed internal-coordinate Hamiltonian with Eckart embedding and its application for the inversion tunneling of ammonia

It is shown that the use of an Eckart-frame embedding with a kinetic energy operator expressed in curvilinear internal coordinates becomes feasible and straightforward to implement for arbitrary molecular compositions and internal coordinates if the operator is defined numerically over a (discrete variable representation) grid. The algorithm proposed utilizes the transformation method of Dymarsky and Kudin to maintain the rotational Eckart condition. In order to demonstrate the applicability and flexibility of our approach the non-rigid ammonia molecule is considered and the corresponding rotational–vibrational energy levels and wave functions are computed using kinetic energy operators with three different embeddings. Two of them fulfill the Eckart conditions corresponding to a trigonal pyramidal (C3v) and a trigonal planar (D3h) reference structure and the third one is a non-Eckart frame. The computed energy levels are, of course, identical, and the structure of the three different wave-function representations are analyzed in terms of the rigid rotor functions for a symmetric top. The possible advantages of one frame representation over another are discussed concerning the interpretation of the rovibrational states in terms of the traditional rigid rotor labels.

Calculation of Rotation–Vibration Energy Levels of the Water Molecule with Near-Experimental Accuracy Based on an ab Initio Potential Energy Surface

A recently computed, high-accuracy ab initio Born-Oppenheimer (BO) potential energy surface (PES) for the water molecule is combined with relativistic, adiabatic, quantum electrodynamics, and, crucially, nonadiabatic corrections. Calculations of ro-vibrational levels are presented for several water isotopologues and shown to have unprecedented accuracy. A purely ab initio calculation reproduces some 200 known band origins associated with seven isotopologues of water with a standard deviation (σ) of about 0.35 cm(-1). Introducing three semiempirical scaling parameters, two affecting the BO PES and one controlling nonadiabatic effects, reduces σ below 0.1 cm(-1). Introducing one further rotational nonadiabatic parameter gives σ better than 0.1 cm(-1) for all observed ro-vibrational energy levels up to J = 25. We conjecture that the energy levels of closed-shell molecules with roughly the same number of electrons as water, such as NH3, CH4, and H3O(+), could be calculated to this accuracy using an analogous procedure. This means that near-ab initio calculations are capable of predicting transition frequencies with an accuracy only about a factor of 5 worse than high resolution experiments.

Study of the vibrational characteristics of the homonuclear diatomic nuclear schrödinger equation with a numerov method using a number of empirical potential functions

Many empirical potential energy functions have been modeled to represent the potential energy function of a diatomic molecule along whole range of internuclear distance coordinate, whereby one can determine certain molecular constants. Here we employ various potential functions such as Morse, Rydberg, Varshni(II), Varshni(III), Varshni(VI), Poschl-Teller, Hulburt-Hirschfelder, Lippincott, Frost-Musulin, Linnet, and Rosen-Morse, and the Numerov method to solve the nuclear Schrodinger equation for F2, as an example of a homonuclear diatomic molecule. Herewith, the vibrational and vibration-rotation energy levels are obtained and excellent accuracy is achieved. The potential of employing the Numerov method in engineering physics computations is emphasized.

MARVEL analysis of the rotational–vibrational states of the molecular ions H2D+ and D2H+

Critically evaluated rotational-vibrational line positions and energy levels, with associated critically reviewed labels and uncertainties, are reported for two deuterated isotopologues of the H3(+) molecular ion: H2D(+) and D2H(+). The procedure MARVEL, standing for Measured Active Rotational-Vibrational Energy Levels, is used to determine the validated levels and lines and their self-consistent uncertainties based on the experimentally available information. The spectral ranges covered for the isotopologues H2D(+) and D2H(+) are 5.2-7105.5 and 23.0-6581.1 cm(-1), respectively. The MARVEL energy levels of the ortho and para forms of the ions are checked against ones determined from accurate variational nuclear motion computations employing the best available adiabatic ab initio potential energy surfaces of these isotopologues. The number of critically evaluated, validated and recommended experimental (levels, lines) are (109, 185) and (104, 136) for H2D(+) and D2H(+), respectively. The lists of assigned MARVEL lines and levels and variational levels obtained for H2D(+) and D2H(+) as part of this study are deposited in the ESI to this paper.

Research of Water Response under the Action of the Infrared Human Body Radiation by Water Conductometric Sensors

Non-equilibrium thermal and biothermal radiation generated by heated solid materials and hematothermal living organisms are studied by water conductometric sensors. Engineering aspects and physical features of developed water conductometric sensors are given. Procedure and measuring technique are described. Our experiments show the anomalous behavior of water conductivity and associated differential parameters under water heating by biological objects compared with traditional heating sources. Water response to human action strongly depends on psychophysiological and psychoemotional state of the person. Moreover the responses to the action by left and right human hands are substantially different and as a rule are specific to the gender. The possible physicochemical mechanisms of such anomalous water behavior are studied. It is suggested that the observed effects are associated with resonant excitation of vibration-rotation energy levels of water under the influence of bioradiation generated by human organism consisting of approximately 70% water. The results obtained have good perspectives for future applications in different fields of human activity.

IUPAC critical evaluation of the rotational–vibrational spectra of water vapor, Part III: Energy levels and transition wavenumbers for H216O

This is the third of a series of articles reporting critically evaluated rotational–vibrational line positions, transition intensities, and energy levels, with associated critically reviewed labels and uncertainties, for all the main isotopologues of water. This paper presents experimental line positions, experimental-quality energy levels, and validated labels for rotational–vibrational transitions of the most abundant isotopologue of water, H216O. The latest version of the MARVEL (Measured Active Rotational–Vibrational Energy Levels) line-inversion procedure is used to determine the rovibrational energy levels of the electronic ground state of H216O from experimentally measured lines, together with their self-consistent uncertainties, for the spectral region up to the first dissociation limit. The spectroscopic network of H216O containstwo components, an ortho (o) and a para (p) one. For o-H216O and p-H216O, experimentally measured, assigned, and labeled transitions were analyzed from more than 100 sources. The measured lines come from one-photon spectra recorded at room temperature in absorption, from hot samples with temperatures up to 3000K recorded in emission, and from multiresonance excitation spectra which sample levels up to dissociation. The total number of transitions considered is 184667 of which 182156 are validated: 68027 between para states and 114129 ortho ones. These transitions give rise to 18486 validated energy levels, of which 10446 and 8040 belong to o-H216O and p-H216O, respectively. The energy levels, including their labeling with approximate normal-mode and rigid-rotor quantum numbers, have been checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators as well as against previous compilations of energy levels. The extensive list of MARVEL lines and levels obtained are deposited in the supplementary data of this paper, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved.

Accurate ab initio potential energy surface and vibration‐rotation energy levels of hydrogen peroxide

The accurate ground-state potential energy surface of hydrogen peroxide, H(2)O(2), has been determined from ab initio calculations using the coupled-cluster approach in conjunction with the correlation-consistent basis sets up to septuple-zeta quality. Results obtained with the conventional and explicitly correlated coupled-cluster methods were compared. The core-electron correlation, scalar relativistic, and higher-order valence-electron correlation effects were taken into account. The adiabatic effects were also discussed. The vibration-rotation energy levels of the H(2)O(2), D(2)O(2), and HOOD isotopologues were predicted, and the experimental vibrational fundamental wavenumbers were reproduced to 1 cm(-1) ("spectroscopic") accuracy.

Ab initio calculation of the rotational spectrum of methane vibrational ground state

In a previous article we have introduced an alternative perturbation scheme to the traditional one starting from the harmonic oscillator, rigid rotator Hamiltonian, to find approximate solutions of the spectral problem for rotation-vibration molecular Hamiltonians. The convergence of our method for the methane vibrational ground state rotational energy levels was quicker than that of the traditional method, as expected, and our predictions were quantitative. In this second article, we study the convergence of the ab initio calculation of effective dipole moments for methane within the same theoretical frame. The first order of perturbation when applied to the electric dipole moment operator of a spherical top gives the expression used in previous spectroscopic studies. Higher orders of perturbation give corrections corresponding to higher centrifugal distortion contributions and are calculated accurately for the first time. Two potential energy surfaces of the literature have been used for solving the anharmonic vibrational problem by means of the vibrational mean field configuration interaction approach. Two corresponding dipole moment surfaces were calculated in this work at a high level of theory. The predicted intensities agree better with recent experimental values than their empirical fit. This suggests that our ab initio dipole moment surface and effective dipole moment operator are both highly accurate.

Global Multi-isotopologue fit of measured rotation and vibration–rotation line positions of CO in X1Σ+ state and new set of mass-independent Dunham coefficients

A set of mass-independent Umj and Δmj parameters globally describing vibration–rotation energy levels of the CO molecule in the X1Σ+ ground electronic state was fitted to more than 19,000 transitions of 12C16O, 13C16O, 14C16O, 12C17O, 13C17O, 12C18O, and 13C18O isotopologues collected from the literature. The maximal values of the vibrational V and the rotational J quantum numbers included in the fit was 41 and 128, respectively. The weighted standard deviation of the fit is .66. Fitted parameters were used for calculation of Dunham coefficients Ymj for nine isotopologues 12C16O, 13C16O, 14C16O, 12C17O, 13C17O, 14C17O, 12C18O, 13C18O, and 14C18O. Calculated transition frequencies based on the fitted parameters were compared with previously reported. A critical analysis of the CO HITRAN and HITEMP data is also presented.

Absorption spectrum of deuterated water vapor enriched by 18O between 6000 and 9200 cm−1

The absorption spectrum of water vapor enriched by deuterium and oxygen-18 is analyzed in the 6000–9200cm−1 region. The spectrum has been recorded at room temperature with a Bruker IFS 120h Fourier transform spectrometer. More than 14,000 absorption lines were measured in the recorded spectrum. The vibration–rotation assignments were performed on the basis of previously published experimental energies and of variational calculations. Nine water species (H216O, HD16O, D216O, H218O, HD18O, D218O, H217O, HD17O and D217O) were found to contribute to the observed absorption. More than 3600 lines of 19 vibrational bands of D218O and about 4700 lines of 16 bands of HD18O with J as high as 19 and Ka as high as 11 were assigned. The main part of the HD18O and D218O lines and all lines of HD17O and D217O were observed in the laboratory for the first time. The obtained vibration–rotation energy levels are compared with previous experimental studies and the results of variational calculations.

Local modes in vibration–rotation spectroscopy

AbstractThe present paper is concerned with the description of highly excited rotational and/or vibrational states of molecules in terms of localized vibrations or local modes. Local mode effects are most common in molecules with multiple equivalent H–X bonds, which give rise to equivalent H–X local mode stretching vibrations, and the theory is outlined for the simplest such case, that of an H2X molecule. In the local mode picture of molecular vibration, experimentally observed, initially unexpected near‐degeneracies of vibrational states at high vibrational excitation, and of rotation–vibration states at high rotational excitation, can be explained in a relatively straightforward manner. The local mode theory predicts relations between the conventional rotation–vibration parameters whose values are determined in least‐squares fittings to observed rotation–vibration transition frequencies or wavenumbers. It should be emphasized, however, that such relations are valid only for particular forms of the effective rotation–vibration Hamiltonian used in the spectral analysis. We illustrate the theory with examples of experimental spectroscopic work where local mode effects play an important role in the interpretation of the experimental findings. The fact that local mode vibrations not only cause clustering of highly excited vibrational energy levels, but also of highly rotationally excited rotation–vibration energy levels, has been understood fairly recently. We outline the theoretical background for this phenomenon and relate it to the existing experimental work. © 2012 John Wiley & Sons, Ltd.This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy

MARVEL: Measured active rotational–vibrational energy levels. II. Algorithmic improvements

When determining energy levels from several, in cases many, measured and assigned high-resolution molecular spectra according to the Ritz principle, it is advantageous to investigate the spectra via the concept of spectroscopic networks (SNs). Experimental SNs are finite, weighted, undirected, multiedge, rooted graphs, whereby the vertices are the energy levels, the edges are the transitions, and the weights are provided by transition intensities. A considerable practical problem arises from the fact that SNs can be very large for isotopologues of molecules widely studied; for example, the experimental dataset for the H216O molecule contains some 160,000 measured transitions and 20,000 energy levels. In order to treat such large SNs and extract the maximum amount of information from them, sophisticated algorithms are needed when inverting the transition data. To achieve numerical effectiveness, we found the following efficient algorithms applicable to very large SNs: reading the input data employs hash codes, building the components of the SN utilizes a recursive depth-first search algorithm, solving the linear least-squares problem is via the conjugate gradient method, and determination of the uncertainties of the energy levels takes advantage of the robust reweighting algorithm.

The ab initio ground-state potential energy function of beryllium monohydride, BeH

The accurate ground-state potential energy function of beryllium monohydride, BeH, has been determined from large-scale ab initio calculations using the multi-reference averaged coupled-pair functional (MR-ACPF) method in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. The effects of electron correlation beyond the MR-ACPF level of approximation were taken into account. The scalar relativistic and adiabatic (the diagonal correction) effects, as well as some of the nonadiabatic effects, were also discussed. The vibration-rotation energy levels of three isotopologues, BeH, BeD, and BeT, were predicted to sub-cm(-1) accuracy.

Accurate partition function for acetylene, 12C2H2, and related thermodynamical quantities

The internal partition function (Q(int)) of ethyne (acetylene), (12)C(2)H(2), is calculated by explicit summation of the contribution of all individual vibration-rotation energy levels up to 15,000 cm(-1). The corresponding energies are predicted from a global model and constants reproducing within 3σ all 18,415 published vibration-rotation lines in the literature involving vibrational states up to 8900 cm(-1), as produced by Amyay et al. [J. Mol. Spectrosc. 267, 80 (2011)]. Values of Q(int), with distinct calculations for para and ortho species are provided from 1 to 2000 K, in step of 1 K. The total internal partition function at 298.15 K is 104.224387(47) or 416.89755(19), with the nuclear degeneracy spin factors taken as 1/4:3/4 (astronomer convention) or 1:3 (atmospheric convention), respectively, for para:ortho species. The Helmholtz function, Gibbs enthalpy function, entropy, and specific heat at constant pressure are also calculated over the same temperature range. Accuracies as well as the missing contribution of the vinylidene isomer of acetylene in the calculations are discussed.

The role of intensities in determining characteristics of spectroscopic networks

Abstract Spectroscopic networks (SNs) are large, finite, weighted, undirected, rooted graphs, where the vertices are discrete energy levels, the edges are transitions, and the weights are transition intensities. While first-principles SNs are “deterministic” by definition, if a realistic transition intensity cut-off is employed during the construction of these SNs, a certain randomness (“stochasticity”) is introduced. Experiments naturally build random graphs. It is shown on the example of the HD 16 O isotopologue of the water molecule how intensities, in the present case one-photon absorption intensities, determine the structure as well as the degree distribution and edge density of SNs. The degree distribution of realistic computed SNs can be described as scale free, with the usual and well known consequences. Experimental SNs, based on measured and assigned transitions, also turn out to be scale free. The graph-theoretical view of high-resolution molecular spectra offers several new ideas for improving the accuracy and robustness of information systems containing spectroscopic data. For example, it is shown that most all rotational–vibrational energy levels are involved in at least a few relatively strong transitions suggesting that an almost complete coverage of experimental quality energy levels can be deduced from measurements.

Rotating full- and reduced-dimensional quantum chemical models of molecules

A flexible protocol, applicable to semirigid as well as floppy polyatomic systems, is developed for the variational solution of the rotational-vibrational Schrödinger equation. The kinetic energy operator is expressed in terms of curvilinear coordinates, describing the internal motion, and rotational coordinates, characterizing the orientation of the frame fixed to the nonrigid body. Although the analytic form of the kinetic energy operator might be very complex, it does not need to be known a priori within this scheme as it is constructed automatically and numerically whenever needed. The internal coordinates can be chosen to best represent the system of interest and the body-fixed frame is not restricted to an embedding defined with respect to a single reference geometry. The features of the technique mentioned make it especially well suited to treat large-amplitude nuclear motions. Reduced-dimensional rovibrational models can be defined straightforwardly by introducing constraints on the generalized coordinates. In order to demonstrate the flexibility of the protocol and the associated computer code, the inversion-tunneling of the ammonia ((14)NH(3)) molecule is studied using one, two, three, four, and six active vibrational degrees of freedom, within both vibrational and rovibrational variational computations. For example, the one-dimensional inversion-tunneling model of ammonia is considered also for nonzero rotational angular momenta. It turns out to be difficult to significantly improve upon this simple model. Rotational-vibrational energy levels are presented for rotational angular momentum quantum numbers J = 0, 1, 2, 3, and 4.

Optimized semiempirical potential energy surface for H2 16O up to 26000 cm−1

A semiempirical potential energy surface is obtained for the major isotopologue of the water molecule H216O that allows the vibration-rotation energy levels in the range of 0–26000 cm−1 to be calculated with an accuracy almost equal to the average experimental accuracy of measurements in the infrared and visible ranges. Variational calculations using this potential energy surface reproduce the experimental energy values of more than 1500 vibration-rotation levels of H216O with the total angular momentum quantum number J = 0, 2, and 5 in the indicated range with a standard deviation of 0.022 cm−1. The potential was obtained by optimizing a starting ab initio surface using a combination of two approaches, i.e., (1) the multiplication of the starting ab initio surface by a morphing function whose parameters were optimized and (2) the optimization of parameters of the ab initio surface using both the experimental values of energy levels and the results of quantum-chemical electronic structure calculations.

Calculation of hydrogen molecule energy levels using the moment constant summability method with specialized weight

The moment constant summability method with specialized weight for the summation of divergent series of the perturbation theory is considered in this work. The method is applied to the calculation of vibrational-rotational energy levels of a two-atom hydrogen molecule. It was tested earlier only on model problems. Some energy levels obtained by the Pade, Pade-Borel, and Pade-Hermit methods and ab initio are considered for comparison. The calculations have been carried out for the ground state and first ten excited vibrational states.

The ground-state potential energy function of a beryllium dimer determined using the single-reference coupled-cluster approach

The accurate ground-state potential energy function of the beryllium dimer, Be(2), has been determined from large-scale ab initio calculations using the single-reference coupled-cluster approach in conjunction with the correlation-consistent core-valence basis sets up to septuple-zeta quality. Results obtained with the conventional and explicitly-correlated coupled-cluster methods were compared. The scalar relativistic and adiabatic (the diagonal correction) effects were also discussed. The vibration-rotation energy levels of Be(2) were predicted and found to be as accurate as those determined from the empirical potential energy function [J. M. Merritt et al., Science, 2009, 324, 1548]. The potential energy function of Be(2) was determined in this study to have a minimum at 2.444 Å and the well depth of 935 cm(-1).

On the relationship between molecular spectroscopy and statistical mechanics: Calculation of vibrational-rotational energy levels and partition functions in the ground electronic state of BC2

The results of extensive ab initio calculations of the vibrational- rotational energy spectrum in the ground electronic state of the BC2 molecule are presented. These data were employed to discuss the evaluation of the corresponding partition functions. Special attention was paid to the problems connected with the calculation of the partition functions for the bending vibrations and rotations about the axis corresponding to the smallest moment of inertia.