An accurate ab initio quartic force field and vibrational frequencies for CH4 and isotopomers

Exploring Expansions of the Potential and Dipole Surfaces Used for Vibrational Perturbation Theory

A scheme for evaluating expansions of the potential and dipole moment surfaces for vibrational perturbation theory is described. The approach is based on numerical differentiation of the Hessian in the coordinates of interest. It is shown that performing these calculations in internal coordinates generates expansions that are transferable among isotopologues of the molecule of interest. Additionally, re-expressing the expansion of the potential in terms of functions of the internal coordinates, for example, cosines of angles or exponential functions of the bond length displacements, provides expansions that can be used for higher-order perturbation theory calculations. The approach is explored and the results are discussed for water, HOD, ammonia, isomers of HNO₃, and halogenated methane.

Accurate Property Prediction by Second Order Perturbation Theory: The REMP and OO-REMP Hybrids

The prediction of molecular properties such as equilibrium structures or vibrationalwavenumbers is a routine task in computational chemistry. If very high accuracy is required, however, the use of computationally demanding ab initio wavefunction methods is mandatory. We present property calculations utilizing the REMP and OO-REMP hybrid perturbation theories showing that with the latter approach, very accurate results are obtained at second order in perturbation theory. Specifically, equilibrium structures and harmonic vibrational wavenumbers as well as dipole moments of closed and open shell molecules were calculated and compared to the best available experimental results or very accurate calculations.OO-REMP is capable of predicting bond lengths of small closed and open shell molecules with an accuracy of 0.2 pm and 0.5 pm, respectively, often within the range of experimental uncertainty. Equilibrium harmonic vibrational wavenumbers are predicted with an accuracy better than 20 cm−1 . Dipole moments of small closed and open shell molecules are reproduced with a relative error of less than 3 %. Across all investigated properties it turns out that a 20 %:80 % MP:RE mixing ratio consistently provides the best results. This is in line with our previous findings featuring closed and open shell reaction energies.

Learning the Quantum Centroid Force Correction in Molecular Systems: A Localized Approach

Molecular mechanics (MM) is a powerful tool to study the properties of molecular systems in the fields of biology and materials science. With the development of ab initio force field and the application of ab initio potential energy surface, the nuclear quantum effect (NQE) is becoming increasingly important for the robustness of the simulation. However, the state-of-the-art path-integral molecular dynamics simulation, which incorporates NQE in MM, is still too expensive to conduct for most biological and material systems. In this work, we analyze the locality of NQE, using both analytical and numerical approaches, and conclude that NQE is an extremely localized phenomenon in nonreactive molecular systems. Therefore, we can use localized machine learning (ML) models to predict quantum force corrections both accurately and efficiently. Using liquid water as example, we show that the ML facilitated centroid MD can reproduce the NQEs in both the thermodynamical and the dynamical properties, with a minimal increase in computational time compared to classical molecular dynamics. This simple approach thus largely decreases the computational cost of quantum simulations, making it really accessible to the studies of large-scale molecular systems.

Unsupervised Machine Learning Neural Gas Algorithm for Accurate Evaluations of the Hessian Matrix in Molecular Dynamics

The Hessian matrix of the potential energy of molecular systems is employed not only in geometry optimizations or high-order molecular dynamics integrators but also in many other molecular procedures, such as instantaneous normal mode analysis, force field construction, instanton calculations, and semiclassical initial value representation molecular dynamics, to name a few. Here, we present an algorithm for the calculation of the approximated Hessian in molecular dynamics. The algorithm belongs to the family of unsupervised machine learning methods, and it is based on the neural gas idea, where neurons are molecular configurations whose Hessians are adopted for groups of molecular dynamics configurations with similar geometries. The method is tested on several molecular systems of different dimensionalities both in terms of accuracy and computational time versus calculating the Hessian matrix at each time-step, that is, without any approximation, and other Hessian approximation schemes. Finally, the method is applied to the on-the-fly, full-dimensional simulation of a small synthetic peptide (the 46 atom N-acetyl-l-phenylalaninyl-l-methionine amide) at the level of DFT-B3LYP-D/6-31G* theory, from which the semiclassical vibrational power spectrum is calculated.

Molecular Dynamics Simulations of Energy Dissipation on Amorphous Solid Water: Testing the Validity of Equipartition

Many different molecular species have been observed in the interstellar medium. These range from simple diatomic species to saturated organic molecules with several carbon atoms. The latter molecules are assumed to be formed predominantely on the surface of interstellar dust grains. All surface reactions that can proceed under the low interstellar temperatures are exothermic. Their exothermicity can be as high as a few electron volts, which is considerable compared to the thermal energy of the molecules at 10 K. It is postulated that this exothermicity can be used for the desorption of reaction products from the grain. In previous studies, we have shown that translational excitation can lead to desorption, whereas vibrational and rotational excitations are much less efficient in the desorption of surface products. Vibrational excitation is however much more likely upon bond formation than translational excitation. The present study follows energy dissipation upon translational, vibrational, or rotational excitation of admolecules on a surface and its conversion, or lack thereof, to different energy contributions. To this end, thousands of molecular dynamics simulations were performed with an admolecule on top of a surface that received a fixed amount of energy, vibrational, rotational, or translational. Three different surface species have been considered, CO₂, H₂O, and CH₄, spanning a range in binding energies, the number of internal degrees of freedom, and molecular weights. A fast exchange of energy between vibrational stretches is observed, but only very limited exchange to rotational or translation excitation has been found. For the dissipation of energy to the surface, excitation of the surface-admolecule bond is critical. Astrochemical models often assume instantaneous equipartition of energy after a reaction process to estimate the amount of available energy for chemical desorption. Based on the present study, we conclude that this assumption is not justified.

General Perturb-Then-Diagonalize Model for the Vibrational Frequencies and Intensities of Molecules Belonging to Abelian and Non-Abelian Symmetry Groups

In this paper, we show that the standard second-order vibrational perturbation theory (VPT2) for Abelian groups can be used also for non-Abelian groups without employing specific equations for two- or threefold degenerate vibrations but rather handling in the proper way all the degeneracy issues and deriving the peculiar spectroscopic signatures of non-Abelian groups (e.g., l -doubling) by a posteriori transformations of the eigenfunctions. Comparison with the results of previous conventional implementations shows a perfect agreement for the vibrational energies of linear and symmetric tops, thus paving the route to the transparent extension of the equations already available for asymmetric tops to the energies of spherical tops and the infrared and Raman intensities of molecules belonging to non-Abelian symmetry groups. The whole procedure has been implemented in our general engine for vibro-rotational computations beyond the rigid rotor/harmonic oscillator model and has been validated on a number of test cases.

Highly-accurate quartic force fields for the prediction of anharmonic rotational constants and fundamental vibrational frequencies

The CcCR quartic force field (QFF) methodology is capable of computing B₀ and C₀ rotational constants to within 35 MHz (0.14%) of experiment for triatomic and larger molecules with at least two heavy atoms. Additionally, the same constants for molecules with four or more atoms agree to within 20 MHz (0.12%) of experiment for the current test set. This work also supports previous claims that the same QFF methodology can produce fundamental vibrational frequencies with a deviation less than 5.7 cm^-1 from experiment. Consequently, this approach of augmenting complete basis set extrapolated energies with treatments of core electron correlation and scalar relativity produces some of the most accurate rovibrational spectroscopic data available.

Quantification of the Role of Chemical Desorption in Molecular Clouds

ConspectusDark molecular clouds have low temperatures of approximately 10 K and experience very little UV irradiation. These clouds are the birthplace of new stars and consist of gas and dust particles. The latter can act as a meeting place to facilitate surface chemistry to form saturated molecules such as formaldehyde, methyl formate, and dimethyl ether. These complex organic molecules or COMs become encapsulated in the ice that forms on the dust grains, and these ices are the precursor for cometary ices and other icy bodies. They likely played a role in bringing material to the early earth.Although these COMs are likely formed on the surfaces of dust grains, several of them have been detected in the gas phase. This means that they have desorbed from the grain under these cold, dark conditions where thermal desorption and photodesorption are negligible. It has been speculated that reactive, or chemical, desorption is responsible for the high gas-phase abundance. After a surface reaction, its products might be vibrationally, translationally, and/or rotationally excited. Dissipation of the excess energy to translational energy can briefly increase the desorption rate, leading to chemical desorption. Astrochemical modellers have added terms to their rate equations to account for this effect. These terms, however, have had little experimental or theoretical verification.In this Account, we use classical molecular dynamics (MD) simulations to give adsorbed molecules a fixed amount of energy as a proxy for excess energy and to record whether this leads to desorption. The excitation energy can be varied freely while keeping all other variables constant. This allows for the study of trends rather than being limited to a single reaction and a single system. The focus is on the dependence of the chemical desorption on the excitation energy, excitation type, and binding energy. Rotational and vibrational excitation was explicitly taken into account. An analytical expression for the chemical desorption probability was obtained in this way. It depends on the binding energy and reaction enthalpy. This expression was then implemented in a gas-grain astrochemical code to simulate the chemical evolution of a dark molecular cloud, and the results were compared against observational abundances of COMs in three different molecular clouds. The results with our new expression based on the MD simulations show good agreement for all species except H2CO, which has both gas-phase and surface-formation routes. This is a significant improvement over models without chemical desorption or with other expressions for chemical desorption, as frequently used by other authors. It is encouraging to see that a general description with a firmer theoretical basis leads to a significant improvement. Understanding chemical desorption can help to explain the unexpectedly high gas-phase abundance of some COMs, and chemical desorption also provides a link between the gas phase and the ice mantle, and its understanding might help in creating a diagnostic tool to learn more about the ice composition.

The Production and Potential Detection of Hexamethylenetetramine-Methanol in Space

Numerous laboratory studies of astrophysical ice analogues have shown that their exposure to ionizing radiation leads to the production of large numbers of new, more complex compounds, many of which are of astrobiological interest. We show here that the irradiation of astrophysical ice analogues containing H₂O, CH₃OH, CO, and NH₃ yields quantities of hexamethylenetetramine-methanol (hereafter HMT-methanol; C₇N₄H₁₄O) that are easily detectible in the resulting organic residues. This molecule differs from simple HMT, which is known to be abundant in similar ice photolysis residues, by the replacement of a peripheral H atom with a CH₂OH group. As with HMT, HMT-methanol is likely to be an amino acid precursor. HMT has tetrahedral (T_d) symmetry, whereas HMT-methanol has C₁ symmetry. We report the computed expected infrared spectra for HMT and HMT-methanol obtained using ab initio quantum chemistry methods and show that there is a good match between the observed and computed spectra for regular HMT. Since HMT-methanol lacks the high symmetry of HMT, it produces rotational transitions that could be observed at longer wavelengths, although establishing the exact positions of these transitions may be challenging. It is likely that HMT-methanol represents an abundant member of a larger family of functionalized HMT molecules that may be present in cold astrophysical environments.

Decomposing anharmonicity and mode-coupling from matrix effects in the IR spectra of matrix-isolated carbon dioxide and methane

A combined experimental and computational approach revealed similarities and differences in the vibrational signature of matrix-isolated carbon dioxide and methane.

Spectroscopic investigation of [Al,N,C,O] refractory molecules

As of yet, unexamined aluminum bearing molecules may help elucidate aluminum chemistry and associated refractory atom reactions in the interstellar medium. The flexibility of modern quantum chemistry in the construction and analysis of novel molecules makes it perfectly suited to analyze molecules of astrochemical significance. In this paper, high level ab initio electronic structure calculations using the coupled cluster CCSD(T) and explicitly correlated coupled cluster CCSD(T)-F12 methods with large basis sets extrapolated to the complete basis set limit have been performed on the various [Al,N,C,O] isomers. The anharmonic rotational and vibrational spectroscopic parameters for all isomers are produced with these same levels of theory via quartic force fields and vibrational perturbation theory in order to aid in their potential laboratory or even astrophysical identification. The most stable isomer is determined here to be the aluminum isocyanate radical with linear equilibrium geometry AlNCO (X¹Σ⁺). The NCO antisymmetric stretch of AlNCO has an intensity of 1500 km/mol, which should greatly aid in its infrared detection in the region around 2305 cm^-1. Additionally, the AlOCN isomer is relatively low lying, possesses a 5.12 D dipole moment, and has a notable kinetic stability, making it a viable candidate for astronomical observation. All isomers are characterized by small frequencies, which indicates that these are floppy molecules. Isomers with a terminal aluminum atom are especially floppy, with bending modes less than 100 cm^-1.

Improved semiclassical dynamics through adiabatic switching trajectory sampling

We introduce an improved semiclassical dynamics approach to quantum vibrational spectroscopy. In this method, a harmonic-based phase space sampling is preliminarily driven toward non-harmonic quantization by slowly switching on the actual potential. The new coordinates and momenta serve as initial conditions for the semiclassical dynamics calculation, leading to a substantial decrease in the number of chaotic trajectories to deal with. Applications are presented for model and molecular systems of increasing dimensionality characterized by moderate or high chaoticity. They include a bidimensional Henon-Heiles potential, water, formaldehyde, and methane. The method improves accuracy and precision of semiclassical results and it can be easily interfaced with all pre-existing semiclassical theories.

Semiclassical vibrational spectroscopy with Hessian databases

We report on a new approach to ease the computational overhead of ab initio "on-the-fly" semiclassical dynamics simulations for vibrational spectroscopy. The well known bottleneck of such computations lies in the necessity to estimate the Hessian matrix for propagating the semiclassical pre-exponential factor at each step along the dynamics. The procedure proposed here is based on the creation of a dynamical database of Hessians and associated molecular geometries able to speed up calculations while preserving the accuracy of results at a satisfactory level. This new approach can be interfaced to both analytical potential energy surfaces and on-the-fly dynamics, allowing one to study even large systems previously not achievable. We present results obtained for semiclassical vibrational power spectra of methane, glycine, and N-acetyl-L-phenylalaninyl-L-methionine-amide, a molecule of biological interest made of 46 atoms.

Highly excited vibrational levels of methane up to 10 300 cm-1: Comparative study of variational methods

In this work, we report calculated vibrational energy levels of the methane molecule up to 10 300 cm^-1. Two potential energy surfaces constructed in quite different coordinate systems with different analytical representations are employed in order to evaluate the uncertainty of vibrational predictions. To calculate methane energy levels, we used two independent techniques of the variational method. One method uses an exact kinetic energy operator in internal curvilinear coordinates. Another one uses an expansion of Eckart-Watson nuclear motion Hamiltonian in rectilinear normal coordinates. In the Icosad range (up to five vibrational quanta bands-below 7800 cm^-1), the RMS standard deviations between calculated and observed energy levels were 0.22 cm^-1 and 0.41 cm^-1 for these two quite different approaches. For experimentally well-known 3v₃ sub-levels, the calculation accuracy is estimated to be ∼1 cm^-1. In the Triacontad range (7660-9188 cm^-1), the average error of the calculation is about 0.5 cm^-1. The accuracy and convergence issues for higher energy ranges are discussed.

Understanding global infrared opacity and hot bands of greenhouse molecules with low vibrational modes from first-principles calculations: the case of CF4

Fluorine containing molecules have a particularly long atmospheric lifetime and their very big estimated global warming potentials are expected to rapidly increase in the future. This work is focused on the global theoretical prediction of infrared spectra of the tetrafluoromethane molecule that is considered as a potentially powerful greenhouse gas having the largest estimated lifetime of over 50 000 years in the atmosphere. The presence of relatively low vibrational frequencies makes the Boltzmann population of the excited levels important. Consequently, the "hot bands" corresponding to transitions among excited rovibrational states contribute significantly to the CF4 opacity in the infrared even at room temperature conditions but the existing laboratory data analyses are not sufficiently complete. In this work, we construct the first accurate and complete ab initio based line lists for CF4 in the range 0-4000 cm-1, containing rovibrational bands that are the most active in absorption. An efficient basis set compression method was applied to predict more than 700 new bands and subbands via variational nuclear motion calculations. We show that already at room temperature a quasi-continuum of overlapping weak lines appears in the CF4 infrared spectra due to the increasing density of bands and transitions. In order to converge the infrared opacity at room temperature, it was necessary to include a high rotational quantum number up to J = 80 resulting in 2 billion rovibrational transitions. In order to make the cross-section simulation faster, we have partitioned our data into two parts: (a) strong & medium line lists with lower energy levels for calculation of selective absorption features that can be used at various temperatures and (b) compressed "super-line" libraries of very weak transitions contributing to the quasi-continuum modelling. Comparisons with raw previously unassigned experimental spectra showed a very good accuracy for integrated absorbance in the entire range of the reported spectra predictions. The data obtained in this work will be made available through the TheoReTS information system (http://theorets.univ-reims.fr, http://theorets.tsu.ru) that contains ab initio born line lists and provides a user-friendly graphical interface for a fast simulation of the CF4 absorption cross-sections and radiance under various temperature conditions from 80 K to 400 K.

"Divide and conquer" semiclassical molecular dynamics: A practical method for spectroscopic calculations of high dimensional molecular systems

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto, and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits us to perform spectroscopic calculations of high-dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows us to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra.

Molecular dynamics simulations of energy dissipation and non-thermal diffusion on amorphous solid water

Molecules in space are synthesized via a large variety of gas-phase reactions, and reactions on dust-grain surfaces, where the surface acts as a catalyst. Especially, saturated, hydrogen-rich molecules are formed through surface chemistry where the interstellar grains act as a meeting place and absorbing energy. Here we present the results of thousands of molecular dynamics simulations to quantify the outcome of an energy dissipation process. Admolecules on top of an amorphous solid water surface have been given translational energy between 0.5 and 5 eV. Three different surface species are considered, CO₂, H₂O and CH₄, spanning a range in binding energies, number of internal degrees of freedom and molecular weight. The results are compared against a previous study using a crystalline water ice surface. Possible outcomes of a dissipation process are adsorption - possibly after long-range diffusion-, desorption and desorption of a surface molecule. The three admolecules were found to bind at different locations on the surface, particularly in terms of height. Water preferably binds on top of the surface, whereas methane fills the nanopores on the surface. This has direct consequences for desorption, travelled distance, and kick-out probabilities. The admolecules are found to frequently travel several tens of angstroms before stabilizing on a binding site, allowing follow-up reactions en route. We present kick-out probabilities and we have been able to quantify the desorption probability which depends on the binding energy of the species, the translational excitation, and a factor that accounts for difference in binding site height. We provide expressions that can be incorporated in astrochemical models to predict grain surface formation and return into the gas phase of these products.

The importance of the pre-exponential factor in semiclassical molecular dynamics

This paper deals with the critical issue of approximating the pre-exponential factor in semiclassical molecular dynamics. The pre-exponential factor is important because it accounts for the quantum contribution to the semiclassical propagator of the classical Feynman path fluctuations. Pre-exponential factor approximations are necessary when chaotic or complex systems are simulated. We introduced pre-exponential factor approximations based either on analytical considerations or numerical regularization. The approximations are tested for power spectrum calculations of more and more chaotic model systems and on several molecules, for which exact quantum mechanical values are available. The results show that the pre-exponential factor approximations introduced are accurate enough to be safely employed for semiclassical simulations of complex systems.

Quartic force fields for excited electronic states: rovibronic reference data for the 1 (2)A' and 1 (2)A″ states of the isoformyl radical, HOC

Quartic force fields (QFFs) have been shown to be an effective, accurate, and relatively compact means of computing rovibrational spectroscopic data for numerous molecules with numerous applications. However, excited states have been nearly excluded from the this approach since most accurate QFFs are based on the "gold standard" coupled cluster singles, doubles, and perturbative triples [CCSD(T)] method which is not readily extended to excited states. In this work, rovibronic spectroscopic data is provided for the isoformyl radical, a molecule of significance in combustion and astrochemistry, both through the traditional means of variational access to excited states with CCSD(T) and in the novel extension of QFFs routinely to treat electronically excited states through the standard coupled cluster excited state approach, equation of motion (EOM) CCSD. It is shown here that the new EOM-based QFF provides structural parameters and rotational constants that are quite close to those from a related CCSD(T)-based QFF for the 1 (2)A(″) excited state of HOC. The anharmonic vibrational frequency percent differences between the two QFFs are less than 0.4% for the O-H stretch, less than 1.9% for the C-O stretch, and around 3.0% for the bend. Even so, the pure excited state EOM-QFF anharmonic frequencies are still very good abinitio representations that may be applied to systems where electronically excited states are not variationally accessible. Additionally, rovibrational spectroscopic data is provided for the 1 (2)A(') ground state of HOC and for both the ground and excited state of DOC.

Limited rotational and rovibrational line lists computed with highly accurate quartic force fields and ab initio dipole surfaces

In this work, computational procedures are employed to compute the rotational and rovibrational spectra and line lists for H2O, CO2, and SO2. Building on the established use of quartic force fields, MP2 and CCSD(T) Dipole Moment Surfaces (DMSs) are computed for each system of study in order to produce line intensities as well as the transition energies. The computed results exhibit a clear correlation to reference data available in the HITRAN database. Additionally, even though CCSD(T) DMSs produce more accurate intensities as compared to experiment, the use of MP2 DMSs results in reliable line lists that are still comparable to experiment. The use of the less computationally costly MP2 method is beneficial in the study of larger systems where use of CCSD(T) would be more costly.