A new six-dimensional ab initio potential energy surface and rovibrational spectra for the N2-CO2 complex

New six-dimensional ab initio potential energy surfaces (PESs) for the N2-CO2 complex, which involve the stretching vibration of N2 and the Q3 normal mode for the ν3 asymmetric stretching vibration of CO2, were constructed using the CCSD(T)-F12/AVTZ method with midpoint bond functions. Two vibrational averaged 4D interaction potentials were obtained by integrating over the two intramolecular coordinates. It was found that both PESs possess two equivalent T-shaped global minima as well as two in-plane and one out-of-plane saddle points. Based on these PESs, rovibrational bound states and energy levels were calculated applying the radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm. The splitting of the energy levels between oN2-CO2 and pN2-CO2 for the intermolecular vibrational ground state is determined to be only 0.000 09 cm-1 due to the higher barriers. The obtained band origin shift is about +0.471 74 cm-1 in the N2-CO2 infrared spectra with CO2 at the ν3 zone, which coincides with the experimental data of +0.483 74 cm-1. The frequencies of the in-plane geared-bending for N2-CO2 at the ν3 = 0 and 1 states of CO2 turn out to be 21.6152 and 21.4522 cm-1, the latter reproduces the available experimental 21.3793 cm-1 value with CO2 at the ν3 zone. The spectral parameters fitted from the rovibrational energy levels show that this dimer is a near prolate asymmetric rotor. The computed microwave transitions as well as the infrared fundamental and combination bands for the complex agree well with the observed data.

Unusual Dynamics and Vibrational Fingerprints of van der Waals Dimers Formed by Linear Molecules and Rare-Gas Atoms

Detailed structural, dynamical, and vibrational analyses have been performed for systems composed of linear triatomic molecules solvated by a single rare-gas atom, He, Ne, or Ar. Among the chromophores of these van der Waals (vdW) dimers, there are four neutral molecules (CO2, CS2, N2O, and OCS) and six molecular cations (HHe2+, HNe2+, HAr2+, HHeNe+, HHeAr+, and HNeAr+), both of apolar and polar nature. Following the exploration of bonding preferences, high-level four-dimensional (4D) potential energy surfaces (PESs) have been developed for 24 vdW dimers, keeping the two intramonomer bond lengths fixed. For these 24 complexes, over 1500 bound vibrational states have been obtained via quasi-variational nuclear-motion computations, employing exact kinetic-energy operators together with the accurate 4D PESs and their 2D/3D cuts. The reduced-dimensional (2D to 4D) dimer models have been compared with full-dimensional (6D) ones in the cases of the neutral CO2·Ar and charged HHe2+·He dimers, corroborating the high accuracy of the 2D to 4D vibrational energies. The reduced-dimensional models suggest that (a) while the equilibrium structures are T-shaped and planar, the effective ground-state structures are nonplanar, (b) certain bound states belong to collinear molecular structures, even when they are not minima, (c) the vdW vibrations are heavily mixed and many states have amplitudes corresponding to both the T-shaped and collinear structures, (d) there are a few dimers, for which even some of the vdW fundamentals lie above the first dissociation limit, and (e) the vdW vibrations are almost fully decoupled from the intramonomer bending motion.

An intramolecular vibrationally excited intermolecular potential energy surface and predicted 2OH overtone spectroscopy of H2O-Kr

A new five-dimensional potential energy surface (PES) for H2O-Kr which explicitly includes the intramolecular 2OH overtone state of the H2O monomer is presented. The intermolecular potential energies were evaluated using explicitly correlated coupled cluster theory [CCSD(T)-F12] with a large basis set. Four vibrationally averaged analytical intermolecular PESs for H2O-Kr with H2O molecules in its |00+〉, |02+〉, |02-〉, and |11+〉 states are obtained by fitting to the multi-dimensional Morse/Long-Range potential function form. Each vibrationally averaged PES fitted to 578 points has root-mean-square (RMS) deviations smaller than 0.14 cm-1 and requires only 58 parameters. The combined radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were employed to calculate the rovibrational energy levels for |00+〉, |02+〉, |02-〉, and |11+〉 states of the H2O-Kr complexes. The calculated |02-〉Πf/e(101) ← |00+〉Σe(000) and |02+〉Πf/e(110) ← |00+〉Σe(101) infrared transitions are in excellent agreement with the experimental values with RMS discrepancies being only 0.007 and 0.016 cm-1, respectively. These analytical PESs can be used to provide reliable theoretical guidance for future infrared overtone spectroscopy of H2O-Kr.

Doped rare gas clusters up to completion of first solvation shell, CO2-(Rg)n, n = 3-17, Rg = Ar, Kr, Xe

Spectra of rare gas atom clusters containing a single carbon dioxide molecule are observed using a tunable mid-infrared (4.3 µm) source to probe a pulsed slit jet supersonic expansion. There are relatively few previous detailed experimental results on such clusters. The assigned clusters include CO₂-Ar_n with n = 3, 4, 6, 9, 10, 11, 12, 15, and 17, and CO₂-Kr_n and CO₂-Xe_n with n = 3, 4, and 5. Each spectrum has (at least) a partially resolved rotational structure, and each yields precise values for the shift of the CO₂ vibrational frequency (ν₃) induced by the nearby rare gas atoms, together with one or more rotational constants. These results are compared with theoretical predictions. The more readily assigned CO₂-Ar_n species tend to be those with symmetric structures, and CO₂-Ar₁₇ represents completion of a highly symmetric (D_5h) solvation shell. Those not assigned (e.g., n = 7 and 13) are probably also present in the observed spectra but with band structures that are not well-resolved and, thus, are not recognizable. The spectra of CO₂-Ar₉, CO₂-Ar₁₅, and CO₂-Ar₁₇ suggest the presence of sequences involving very low frequency (≈2 cm^-1) cluster vibrational modes, an interpretation which should be amenable to theoretical confirmation (or rejection).

MLRNet: Combining the Physics-Motivated Potential Models with Neural Networks for Intermolecular Potential Energy Surface Construction

A physics-based machine learning model called MLRNet has been developed to construct the high-accuracy two-body intermolecular potential energy surface (IPES). The outputs of the neural network are integrated into the physically realistic Morse/long-range (MLR) function, which ensures that the MLRNet has meaningful extrapolation at both short and long ranges and solves the asymptotic problem in common neural network potential (NNP) models. The neural network representation of the MLR parameters is more flexible and more efficient than the polynomial expansion in the conventional mdMLR model, especially for systems containing nonrigid monomer(s). The present work illustrates the basic framework of the current MLRNet model, including (i) how to combine the physically meaningful MLR function with different possible NN structures, (ii) the preservation of permutation symmetry, and (iii) the predetermination of the long-range function u_LR. We choose two realistic systems to demonstrate the performance of MLRNet: the three-dimensional IPES of CO₂-He including the CO₂ antisymmetric vibration Q₃ and the six-dimensional IPES of the H₂O-Ar system. In both cases, the fitting errors of the MLRNet are several times smaller than those of the conventional mdMLR model. Both short-range and long-range extrapolation tests were performed to illustrate the extrapolation ability of the MLRNet and its damping function version. Moreover, for the 6-D H₂O-Ar system, the MLRNet only needs 1596 trainable parameters, which is almost equal to the number needed for the 5-D mdMLR model (1509) and half that needed for the PIP-NN model (3501) within similar accuracy, which illustrates the model efficiency in high-dimensional IPES fitting.

Spectra of CO2-Rg2 and CO2-Rg-He trimers (Rg = Ne, Ar, Kr, and Xe): Intermolecular CO2 rock, vibrational shifts and three-body effects

Weakly bound CO2-Rg2 trimers are studied by high-resolution (0.002 cm−1) infrared spectroscopy in the region of the CO2 ν3 fundamental band (≈2350 cm−1), using a tunable optical parametric oscillator to probe a pulsed supersonic slit jet expansion with an effective rotational temperature of about 2 K. CO2–Ar2 spectra have been reported previously, but they are extended here to include Rg = Ne, Kr, and Xe as well as new combination and hot bands. For Kr and Xe, a unified scaled parameter scheme is used to account for the many possible isotopic species. Vibrational shifts of CO2-Rg2 trimers are compared to those of CO2-Rg dimers, and in all cases the trimer shifts are slightly more positive (blue-shifted) than expected on the basis of linear extrapolation from the dimer. Combination bands directly measure an intermolecular vibrational mode (the CO2 rock) and give values of about 32.2, 33.8, and 34.7 cm−1 for CO2–Ar2, –Kr2, and –Xe2. Structural parameters derived for CO2-Rg2 trimers are compared with those of CO2-Rg and Rg2 dimers. Spectra of the mixed trimers CO2-Rg-He are also reported.

A new potential energy surface and rovibrational spectra of the CO-CO2 complex: Dependence on the antisymmetric stretching vibration of CO2

We present a new ab initio five-dimensional potential energy surface for the CO-CO2 complex containing the Q3 normal mode for the ν3 asymmetric stretching vibration of the CO2 unit. The potential was calculated by supermolecular approach at the CCSD(T)-F12 level with aug-cc-pVTZ basis set plus midpoint bond functions. Two vibrationally averaged four-dimensional potentials for CO-CO2 with CO2 in the ground and ν3 excited states were generated by the integration of the five-dimensional potential over the Q3 intramolecular coordinate. Each potential displays a T-shaped global minimum with the C end in the CO unit pointing toward the C atom in the CO2 unit and a T-shaped local minimum but with the CO monomer rotated by 180º. The rovibrational bound states and energy levels for the CO-CO2 dimer were obtained employing the radial discrete variable representation (DVR)/angular finite basis representation (FBR) method in conjunction with the Lanczos algorithm. The vibrational ground and some lower excited states for CO-CO2 are localized around the global minimum because of the higher potential barriers. The band origin is blueshifted by 0.2089 cm-1 for CO-CO2 in the CO2 ν3 range, which is consistent with the experimental result of 0.211 cm-1. The geared bending vibrational frequencies for CO-CO2 are 24.7101 and 24.5549 cm-1 at the ground and ν3 excited states of CO2, respectively. The predicted rovibrational frequencies as well as spectral constants coincide with the available observations, and these parameters show the CO-CO2 complex is a nearly prolate asymmetric rotor.

Rotational excitation of CO2 induced by He: New potential energy surface and scattering calculations

The CO2 molecule is of great interest for astrophysical studies since it can be found in a large variety of astrophysical media where it interacts with the dominant neutral species, such as He, H2, or H2O. The CO2–He collisional system was intensively studied over the last two decades. However, collisional data appear to be very sensitive to the potential energy surface (PES) quality. Thus, we provide, in this study, a new PES of the CO2–He van der Waals complex calculated with the coupled-cluster method and a complete basis set extrapolation in order to provide rotational rate coefficients that are as accurate as possible. The PES accuracy was tested through the calculations of bound state transition frequencies and pressure broadening coefficients that were compared to experimental data. An excellent agreement was globally found. Then, revised collisional data were provided for the 10–300 K temperature range. Rate coefficients were compared to previously computed ones and are found to be up to 50% greater than previously provided ones. These differences can induce non-negligible consequences for the modeling of CO2 abundance in astrophysical media.

Multi-channel distorted-wave Born approximation for rovibrational transition rates in molecular collisions

Modeling protoplanetary disks and other interstellar media that are not in local thermal equilibrium require the knowledge of rovibrational transition rate coefficients of molecules in collision with helium and hydrogen. We present a computational method based on the numerically exact coupled-channel (CC) method for rotational transitions and a multi-channel distorted-wave Born approximation (MC-DWBA) for vibrational transitions to calculate state-to-state rate coefficients. We apply this method to the astrophysically important case of CO₂-He collisions, using newly computed ab initio three-dimensional potential energy surfaces for CO₂-He with CO₂ distorted along the symmetric and asymmetric stretch (ν₁ and ν₃) coordinates. It is shown that the MC-DWBA method is almost as accurate as full CC calculations, but more efficient. We also made computations with the more approximate vibrational coupled-channel rotational infinite-order sudden method but found that this method strongly underestimates the vibrationally inelastic collision cross sections and rate coefficients for both CO₂ modes considered.

Spectroscopy and Scattering Studies Using Interpolated Ab Initio Potentials

The Born-Oppenheimer potential energy surface (PES) has come a long way since its introduction in the 1920s, both conceptually and in predictive power for practical applications. Nevertheless, nearly 100 years later-despite astonishing advances in computational power-the state-of-the-art first-principles prediction of observables related to spectroscopy and scattering dynamics is surprisingly limited. For example, the water dimer, (H₂O)₂, with only six nuclei and 20 electrons, still presents a formidable challenge for full-dimensional variational calculations of bound states and is considered out of reach for rigorous scattering calculations. The extremely poor scaling of the most rigorous quantum methods is fundamental; however, recent progress in development of approximate methodologies has opened the door to fairly routine high-quality predictions, unthinkable 20 years ago. In this review, in relation to the workflow of spectroscopy and/or scattering studies, we summarize progress and challenges in the component areas of electronic structure calculations, PES fitting, and quantum dynamical calculations.

Analytic intermolecular potential energy surface and first-principles prediction of the rotational profiles for a symmetric top ion-atom complex: A case study of H3O+-Ar

We presented the first three-dimensional (3D) ab initio intermolecular potential energy surface (PES) for the H₃O⁺-Ar complex. The electronic structure computations were carried out at the explicitly correlated coupled cluster theory-F12 with an augmented correlation-consistent triple zeta basis set. Analytic 3D PES was obtained by least-squares fitting the multi-dimensional Morse/Long-Range (mdMLR) potential model to interaction energies, where the mdMLR function form was applied to the nonlinear ion-atom case for the first time. The 3D PES fitting to 1708 points has root-mean-square deviations of 0.19 cm^-1 with only 108 parameters for interaction energies less than 500 cm^-1. With the 3D PES of the H₃O⁺-Ar complex, we employed the combined radial discrete variable representation/angular finite basis representation method and Lanczos algorithm to calculate rovibrational energy levels. The rotational profiles of the O-H anti-stretching vibrational bands of v₃ ⁺(S)←0⁺ and v₃ ^-(A)←0^- for the H₃O⁺-Ar complex were predicted and were in good agreement with the experimental results.

Suppression of Parahydrogen Superfluidity in a Doped Nanoscale Bose Fluid Mixture

Helium (^{4}He) nanodroplets provide a unique environment to observe the microscopic origins of superfluidity. The search for another superfluid substance has been an ongoing quest in the field of quantum fluids. Nearly two decades ago, experiments on doped parahydrogen (p-H_{2}) clusters embedded in ^{4}He droplets displayed anomalous spectroscopic signatures that were interpreted as a sign of the superfluidity of p-H_{2} [S. Grebenev et al., Science 289, 1532 (2000)SCIEAS0036-807510.1126/science.289.5484.1532]. Here, we observe, using first-principles quantum Monte Carlo simulations, a phase separation between a symmetric and localized p-H_{2} core and ^{4}He shells. The p-H_{2} core has minimal superfluid response. These findings are consistent with the recorded spectra but not with their original interpretation, and lead us to conclude that doped p-H_{2} clusters form a nonsuperfluid core in ^{4}He droplets.

Theoretical calculation of a full-dimensional ab initio potential energy surface and prediction of infrared spectra for Xe-CS2

An effective four-dimensional (4D) ab initio potential energy surface (PES) for Xe-CS2 which explicitly involves the intramolecular Q 1 symmetric stretching and Q 3 antisymmetric stretching vibrational coordinates of CS2 is constructed. The computations are carried out employing single- and double-excitation coupled-cluster theory with a non-iterative perturbation treatment of triple excitations [CCSD(T)] method with a large basis set. Two vibrationally averaged potentials at the ground and ν 1 + ν 3 (ν 1 = 1, ν 3 = 1) excited states are obtained by integrating the 4D potentials over the Q 1 and Q 3 coordinates. The potentials have a T-shaped global minimum and two equivalent linear local minima. The radial discrete variable representation/angular finite basis representation and the Lanczos algorithm are employed to calculate the rovibrational energy levels for Xe-CS2. The infrared band origin shift associated with the fundamental band of CS2 is predicted, which is red-shifted by -1.996 cm-1 in the ν 1 + ν 3 region. In addition, we further predict the spectroscopic parameters for the ground and the ν 1 + ν 3 excited states of Xe-CS2. Compared with the previous Rg-CS2 (Rg = He, Ne, Ar, Kr) complexes, we found that the complexes of the rare gas atoms with CS2 display obvious regularities.

Analytic Morse/long-range potential energy surfaces and "adiabatic-hindered-rotor" treatment for a symmetric top-linear molecule dimer: A case study of CH3F-H2

A first effective six-dimensional ab initio potential energy surface (PES) for CH₃F-H₂ which explicitly includes the intramolecular Q₃ stretching normal mode of the CH₃F monomer is presented. The electronic structure computations have been carried out at the explicitly correlated coupled cluster level of theory [CCSD(T)-F12a] with an augmented correlation-consistent triple zeta basis set. Five-dimensional analytical intermolecular PESs for ν₃(CH₃F) = 0 and 1 are then obtained by fitting the vibrationally averaged potentials to the Morse/Long-Range (MLR) potential function form. The MLR function form is applied to the nonlinear molecule-linear molecule case for the first time. These fits to 25 015 points have root-mean-square deviations of 0.74 cm^-1 and 0.082 cm^-1 for interaction energies less than 0.0 cm^-1. Using the adiabatic hindered-rotor approximation, three-dimensional PESs for CH₃F-paraH₂ are generated from the 5D PESs over all possible orientations of the hydrogen monomer. The infrared and microwave spectra for CH₃F-paraH₂ dimer are predicted for the first time. These analytic PESs can be used for modeling the dynamical behavior in CH₃F-(H₂)_N clusters, including the possible appearance of microscopic superfluidity.

A new ab initio potential energy surface and infrared spectra for the Ar-CS₂ complex

We report a new three-dimensional potential energy surface for Ar-CS2 involving the Q3 normal mode for the υ3 antisymmetric stretching vibration of the CS2 molecule. The potential energies were calculated using the supermolecular method at the coupled-cluster singles and doubles level with noniterative inclusion of connected triples, using augmented correlation-consistent quadruple-zeta basis set plus midpoint bond functions. Two vibrationally averaged potentials with CS2 at both the ground (υ = 0) and the first excited (υ = 1)υ3 vibrational states were generated from the integration of the three-dimensional potential over the Q3 coordinate. Each potential was found to have a T-shaped global minimum and two equivalent linear local minima. The radial discrete variable representation /angular finite basis representation method and the Lanczos algorithm were applied to calculate the rovibrational energy levels. The calculated band origin shift of the complex (0.0622 cm(-1)) is very close to the observed one (0.0671 cm(-1)). The predicted infrared spectra and spectroscopic parameters based on the two averaged potentials are in excellent agreement with the available experimental data.

Theoretical prediction of the linear isomers for rare gas-carbon disulfide complexes: He-CS₂, Ne-CS₂, and Ar-CS₂

Theoretical studies of the potential energy surfaces (PESs) and bound states are performed for rare gas-carbon disulfide complexes, He-CS2, Ne-CS2, and Ar-CS2. Three two-dimensional intermolecular PESs are constructed from ab initio data points which are calculated at the CCSD(T) level with aug-cc-pVTZ basis set supplemented with bond functions. We find that the three PESs have very similar features and each PES can be characterized by a global T-shaped minimum, two equivalent local linear minima, and the saddle points between them. The T-shaped isomer is energetically more stable than the linear isomer for each complex. The linear isomers, which have not been observed in experiment so far, are predicted from our PESs and further identified by bound state calculations. Moreover, we assign several intermolecular vibrational states for both the T-shaped and linear isomers of the three complexes via the analysis of wavefunctions. The corresponding vibrational frequencies are calculated from the bound state energies for these assigned states. These frequencies could be helpful for further experimental studies, especially for the linear isomers. We also calculate the rovibrational transition frequencies for the three T-shaped isomers and the pure rotational transition frequencies for the linear isomers, respectively. The accuracy of the PESs is validated by the good agreement between theoretical and experimental results for the rovibrational transition frequencies and spectroscopic parameters.

A new four-dimensional ab initio potential energy surface for N2O-He and vibrational band origin shifts for the N2O-He(N) clusters with N = 1-40

A new four-dimensional ab initio potential energy surface for N(2)O-He is constructed at the CCSD(T) level with an aug-cc-pVQZ basis set together with bond functions. The vibrational coordinates Q(1) and Q(3) of N(2)O are explicitly included, due to the strong coupling between the symmetric and asymmetric stretches of N(2)O. A global potential energy surface is obtained by fitting the original potential points to a four-dimensional Morse∕long range (MLR) analytical form. In the fitting, the ab initio noise in the long range region of the potential is smoothed over by theoretically fixed long range parameters. Two-dimensional intermolecular potentials for both the ground and the excited υ(3) states of N(2)O are then constructed by vibrationally averaging the four-dimensional potential. Based on the two-dimensional potentials, we use the path integral Monte Carlo algorithm to calculate the vibrational band origin shifts for the N(2)O-He(N) clusters using a first order perturbation theory estimate. The calculated shifts agree reasonably well with the experimental values and reproduce the evolution tendency from dimer to large clusters.

High resolution quantum cascade laser studies of the ν3 band of methyl fluoride in solid para-hydrogen

Spectra of solid para-H(2) doped with CH(3)F at 1.8 K are studied in the ν(3) region (~1040 cm(-1)) using a quantum cascade laser source. As shown previously, residual ortho-H(2) in the sample (~1000 ppm) gives rise to distinct spectral features due to clusters of the form CH(3)F-(ortho-H(2))(N), with N = 0, 1, 2, 3, etc. Brief annealing at 7 K is found to give narrower spectral lines (≥0.006 cm(-1)) than conventional (5 K) annealing, and causes the N = 3 and 4 lines to fragment into two or more components. The N = 3 line is observed to be particularly stable and persistent. The N = 0 line (no ortho-H(2) neighbors) is resolved into two closely spaced (≈0.007 cm(-1)) components which are assigned to the K = 0 and 1 states of CH(3)F rotating around its C(3v) symmetry axis (ortho- and para-CH(3)F, respectively). Similar K-structure is also evident for other lines. Weak but persistent features ("N = 1/2 lines") are observed mid way between N = 0 and 1.

Theoretical and experimental study of weakly bound CO2-(pH2)2 trimers

The infrared spectrum of CO(2)-(pH(2))(2) trimers is predicted by performing exact basis-set calculations on a global potential energy surface defined as the sum of accurately known two-body pH(2)-CO(2) (J. Chem. Phys. 2010, 132, 214309) and pH(2)-pH(2) potentials (J. Chem. Phys. 2008, 129, 094304). These results are compared with new spectroscopic measurements for this species, for which 13 transitions are now assigned. A reduced-dimension treatment of the pH(2) rotation has been employed by applying the hindered-rotor averaging technique of Li, Roy, and Le Roy (J. Chem. Phys. 2010, 133, 104305). Three-body effects and the quality of the potential are discussed. A new technique for displaying the three-dimensional pH(2) density in the body-fixed frame is used, and shows that in the ground state the two pH(2) molecules are localized much more closely together than is the case for the two He atoms in the analogous CO(2)-(He)(2) species. A clear tunneling splitting is evident for the torsional motion of the two pH(2) molecules on a ring about the CO(2) molecular axis, in contrast to the case of CO(2)-(He)(2) where a more regular progression of vibrational levels reflects the much lower torsional barrier.

A new potential energy surface and predicted infrared spectra of the Ar-CO(2) van der Waals complex

A new potential energy surface for Ar-CO(2) is constructed at the coupled-cluster singles and doubles with noniterative inclusion of connected triple [CCSD(T)] level with augmented correlation-consistent triple-zeta (aug-cc-pVTZ) basis set plus midpoint bond functions. The Q(3) normal mode for the v(3) antisymmetric stretching vibration of CO(2) is involved in the construction of the potential. Effective two-dimensional potentials with CO(2) in the ground and first excited v(3) vibrational states are obtained by averaging a three-dimensional potential for each case over the Q(3) asymmetric stretch vibrational coordinate. Both potentials have only a T-shaped minimum with a well depth of 200.97 and 201.37 cm(-1), respectively. No linear local minima are detected. The radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm are employed to calculate the related rovibrational energy levels. The calculated band origin shift of the complex agrees very well with the observed one (-0.474 versus -0.470 cm(-1)). In addition, the predicted infrared spectra based on the two averaged potentials are in excellent agreement with the available experimental data, which again testifies the accuracy of the new potentials.