Near-equilibrium Potential Energy Surface Research Articles

Transfer Learning to CCSD(T): Accurate Anharmonic Frequencies from Machine Learning Models.

The calculation of the anharmonic modes of small- to medium-sized molecules for assigning experimentally measured frequencies to the corresponding type of molecular motions is computationally challenging at sufficiently high levels of quantum chemical theory. Here, a practical and affordable way to calculate coupled-cluster quality anharmonic frequencies using second-order vibrational perturbation theory (VPT2) from machine-learned models is presented. The approach, referenced as "NN + VPT2", uses a high-dimensional neural network (PhysNet) to learn potential energy surfaces (PESs) at different levels of theory from which harmonic and VPT2 frequencies can be efficiently determined. The NN + VPT2 approach is applied to eight small- to medium-sized molecules (H2CO, trans-HONO, HCOOH, CH3OH, CH3CHO, CH3NO2, CH3COOH, and CH3CONH2) and frequencies are reported from NN-learned models at the MP2/aug-cc-pVTZ, CCSD(T)/aug-cc-pVTZ, and CCSD(T)-F12/aug-cc-pVTZ-F12 levels of theory. For the largest molecules and at the highest levels of theory, transfer learning (TL) is used to determine the necessary full-dimensional, near-equilibrium PESs. Overall, NN + VPT2 yields anharmonic frequencies to within 20 cm-1 of experimentally determined frequencies for close to 90% of the modes for the highest quality PES available and to within 10 cm-1 for more than 60% of the modes. For the MP2 PESs only ∼60% of the NN + VPT2 frequencies were within 20 cm-1 of the experiment, with outliers up to ∼150 cm-1, compared to the experiment. It is also demonstrated that the approach allows to provide correct assignments for strongly interacting modes such as the OH bending and the OH torsional modes in formic acid monomer and the CO-stretch and OH-bend mode in acetic acid.

Coupled cluster spectroscopic properties of the coinage metal nitrosyls, M–NO (M = Cu, Ag, Au)

Ab initio near-equilibrium potential energy and dipole moment surfaces for the bent CuNO, AgNO, and AuNO molecules have been calculated under the Feller–Peterson–Dixon (FPD) composite framework at the coupled cluster level of theory including complete basis set extrapolation, outer-core correlation, scalar relativistic effects, and spin–orbit coupling. The Brueckner coupled cluster doubles with perturbative triples method, BCCD(T), was used to greatly improve upon CCSD(T), which was particularly problematic for CuNO. In the latter case, the BCCD(T) vibrational frequencies showed significant differences compared to CCSD(T), e.g., nearly 65 cm−1 for the NO stretching frequency, and BCCD(T) also resulted in much better agreement with the available experimental frequencies. A full range of ro-vibrational spectroscopic constants are given for all three molecules of this study using the accurate composite potential energy functions and employing second-order vibrational perturbation theory.

Accurate ab initio vibronic spectroscopy of the CCP and CCAs radicals

Explicitly correlated MRCI-f12 calculations have been carried out for the CCP and CCAs radicals with systematic sequences of correlation consistent basis sets to determine the accurate near-equilibrium potential energy surface. The Feller-Peterson-Dixon methodology is applied to rule out significant possible errors and provide high-level theoretical results. The spin-orbit coupling effect is taken consideration explicitly to observe its interaction with the Renner-Teller effect. The anharmonic constants are calculated for the first time and make it able to compare directly with the experimental values.

Accurate characterization of the lowest triplet potential energy surface of SO2 with a coupled cluster method.

The near-equilibrium potential energy surface (PES) of the ã 3B1 state of SO2 is developed from explicitly correlated spin-unrestricted coupled cluster calculations with single, double, and perturbative triple excitations with an augmented triple-zeta correlation-consistent basis set. The lowest-lying ro-vibrational energy levels of several sulfur isotopologues have been determined using this PES. It is shown that the new ab initio PES provides a much better description of the low-lying vibrational states than a previous PES determined at the multi-reference configuration interaction level. In particular, the theory-experiment agreement for the three lowest-lying vibrational transitions is within 1-3 cm-1.

Ab initio ro-vibronic spectroscopy of the Π2 PCS radical and Σ+1PCS- anion.

Near-equilibrium potential energy surfaces have been calculated for both the PCS radical and its anion using a composite coupled cluster approach based on explicitly correlated F12 methods in order to provide accurate structures and spectroscopic properties. These transient species are still unknown and the present study provides theoretical predictions of the radical and its anion for the first time. Since these species are strongly suggested to play an important role as intermediates in the interstellar medium, the rotational and vibrational spectroscopic parameters are presented to help aid in the identification and assignment of these spectra. The rotational constants produced will aid in ground-based observation. Both the PCS radical and the PCS- anion are linear. In the PCS- anion, which has a predicted adiabatic electron binding energy (adiabatic electron affinity of PCS) of 65.6 kcal/mol, the P-C bond is stronger than the corresponding neutral radical showing almost triple bond character, while the C-S bond is weaker, showing almost single bond character in the anion. The PCS anion shows a smaller rotational constant than that of the neutral. The ω3 stretching vibrational frequencies of PCS- are red-shifted from the radical, while the ω1 and ω2 vibrations are blue-shifted with ω1 demonstrating the largest blue shift. The ro-vibronic spectrum of the PCS radical has been accurately calculated in variational nuclear motion calculations including both Renner-Teller (RT) and spin-orbit (SO) coupling effects using the composite potential energy near-equilibrium potential energy and coupled cluster dipole moment surfaces. The spectrum is predicted to be very complicated even at low energies due to the presence of a strong Fermi resonance between the bending mode and symmetric stretch, but also due to similar values of the bending frequency, RT, and SO splittings.

Non-Adiabatic Effects on Excited States of Vinylidene Observed with Slow Photoelectron Velocity-Map Imaging.

High-resolution slow photoelectron velocity-map imaging spectra of cryogenically cooled X̃2B2 H2CC- and D2CC- in the region of the vinylidene triplet excited states are reported. Three electronic bands are observed and, with the assistance of electronic structure calculations and quantum dynamics on ab initio-based near-equilibrium potential energy surfaces, are assigned as detachment to the [Formula: see text] 3B2 (T1), b̃ 3A2 (T2), and à 1A2 (S1) excited states of neutral vinylidene. This work provides the first experimental observation of the à singlet excited state of H2CC. While regular vibrational structure is observed for the ã and à electronic bands, a number of irregular features are resolved in the vicinity of the b̃ band vibrational origin. High-level ab initio calculations suggest that this anomalous structure arises from a conical intersection between the ã and b̃ triplet states near the b̃ state minimum, which strongly perturbs the vibrational levels in the two electronic states through nonadiabatic coupling. Using the adiabatic electron affinity of H2CC previously measured to be 0.490(6) eV by Ervin and co-workers [J. Chem. Phys. 1989, 91, 5974], term energies for the excited neutral states of H2CC are found to be T0(ã 3B2) = 2.064(6), T0(b̃ 3A2) = 2.738(6), and T0(à 1A2) = 2.991(6) eV.

High-level theoretical rovibrational spectroscopy beyond fc-CCSD(T): The C3 molecule

An accurate local (near-equilibrium) potential energy surface (PES) is reported for the C3 molecule in its electronic ground state (X̃(1)Σg (+)). Special care has been taken in the convergence of the potential relative to high-order correlation effects, core-valence correlation, basis set size, and scalar relativity. Based on the aforementioned PES, several rovibrational states of all (12)C and (13)C substituted isotopologues have been investigated, and spectroscopic parameters based on term energies up to J = 30 have been calculated. Available experimental vibrational term energies are reproduced to better than 1 cm(-1) and rotational constants show relative errors of not more than 0.01%. The equilibrium bond length has been determined in a mixed experimental/theoretical approach to be 1.294 07(10) Å in excellent agreement with the ab initio composite value of 1.293 97 Å. Theoretical band intensities based on a newly developed electric dipole moment function also suggest that the infrared active (1, 1(1), 0)←(0, 0(0), 0) combination band might be observable by high-resolution spectroscopy.

Theoretical rovibrational spectroscopy beyond fc-CCSD(T): the cation CNC+

An accurate near-equilibrium potential energy surface (PES) for CNC+ is constructed based on a high-level composite ab initio method. By combining explicitly correlated all-electron CCSD(T)-F12b with scalar relativistic effects and higher order correlation up to coupled cluster theory with singles, doubles, triples and quadruples (CCSDTQ) we achieve convergence in the wavenumbers of the fundamentals to ca. 1 cm−1. Rovibrational energies are calculated in a variational approach and vibrational term energies and rotational constants are in excellent agreement with available experimental data. Accurate values for centrifugal distortion constants of CNC+ in different vibrational states are predicted. Especially the centrifugal distortion constants in the vibrational ground state of D0 = 0.563 · 10−6 cm−1 and H0 = 0.188 · 10−10 cm−1 should be superior to experimentally derived values. Reassignments of some experimentally observed transitions are suggested based on a comparison of experimental and calculated term differences. The bending part of the PES appears to be almost quartic and the band origin of the bending vibration is predicted at 94.2 cm−1. Absolute line intensities are calculated for various transitions in CNC+. For the bending vibration, an intensity is predicted that is three orders of magnitude smaller than for the antisymmetric stretching vibration.

High-level theoretical spectroscopic parameters for three ions of astrochemical interest

The equilibrium geometry and rovibrational spectroscopic parameters of the three astrochemical ions l-C3H+, l-SiC2H+, and C3N− and some of their isotopologues are obtained from high-level quantum chemical calculations. A composite approach based on the explicitly correlated coupled-cluster method CCSD(T)-F12b, that further includes core correlation, scalar-relativistic effects and most importantly higher order correlation beyond CCSD(T) is used to set-up the near-equilibrium potential energy surface (PES). The spectroscopic parameters of these linear tetra-atomic ions are then extracted from these PESs by vibrational perturbation theory of second order (VPT2). Calculation of absolute intensities is also carried out for the stretching frequencies of the cations in order to identify the bands that are most likely to be detected. The importance of the accurate calculation of the rotational constants B0 and D0 for astrochemistry is discussed as well as the limits of VPT2 in this context and reasons for these limitations.

Rovibrational states of [formula omitted] isotopologues: Theory and experiment

Near-equilibrium potential energy surfaces for HBF+ isotopologues, obtained from high-level calculations beyond fc-CCSD (T), are employed in variational calculations for many rovibrational states. Calculated effective spectroscopic parameters are in excellent agreement with available experimental data and many predictions are being made, also for line intensities. The band origin of the bending vibration of H11BF+ is predicted at 730.7cm-1. Combining a difference-frequency system with glow discharge and a discharge modulation scheme, six and seven lines of the ν1 bands for H11BF+ and H10BF+, respectively, were observed. Together with data obtained from microwave spectroscopy the spectroscopic constants of ν1 could be derived through least-squares fitting.

Rovibrational States of N3– and CO2 Up to High J: A Theoretical Study Beyond fc-CCSD(T)

An accurate near-equilibrium potential energy surface (PES) has been constructed for the azide ion (N(3)(-)) on the basis of coupled cluster calculations up to CCSDTQ (Kállay, M.; Surján, P. R. J. Chem. Phys. 2001, 115, 2945.), with contributions from inner-shell correlation and special relativity being taken into account as well. A larger number of rovibrational states has been investigated by variational calculations with Watson's isomorphic Hamiltonian for linear molecules. Analogous calculations for CO2 demonstrate the high quality of this type of calculations. The G(v) values of the symmetric stretching and bending vibration of 14N(3)(-) are predicted to be ν1 = 1307.9 cm(-1) and ν2 = 629.3 cm(-1), with an uncertainty of ca. 1 cm(-1). Fermi resonance is less pronounced for the lower polyads of 14N(3)(-) compared with 12C16O2 but is as strong as in CO2 for the lowest diad of isotopologue 15-14-15. The band origin of the antisymmetric stretching vibration of 14N(3)(-) is calculated to be ν3 = 1986.4 cm(-1), only 0.1 cm(-1) lower than the experimental value. The corresponding vibrational transition dipole moment is predicted to be as large as μ = 0.476 D, 46% higher than calculated for CO2. The perturbed combination tone (01(1)1), which was accessible through diode laser IR spectroscopy, undergoes anharmonic interaction with at least two other vibrational states.

Accurate ab initio ro-vibronic spectroscopy of the $\tilde X^2 \Pi$X̃2Π CCN radical using explicitly correlated methods

Explicitly correlated CCSD(T)-F12b calculations have been carried out with systematic sequences of correlation consistent basis sets to determine accurate near-equilibrium potential energy surfaces for the X(2)Π and a(4)Σ(-) electronic states of the CCN radical. After including contributions due to core correlation, scalar relativity, and higher order electron correlation effects, the latter utilizing large-scale multireference configuration interaction calculations, the resulting surfaces were employed in variational calculations of the ro-vibronic spectra. These calculations also included the use of accurate spin-orbit and dipole moment matrix elements. The resulting ro-vibronic transition energies, including the Renner-Teller sub-bands involving the bending mode, agree with the available experimental data to within 3 cm(-1) in all cases. Full sets of spectroscopic constants are reported using the usual second-order perturbation theory expressions. Integrated absorption intensities are given for a number of selected vibronic band origins. A computational procedure similar to that used in the determination of the potential energy functions was also utilized to predict the formation enthalpy of CCN, ΔH(f)(0K) = 161.7 ± 0.5 kcal/mol.

Threshold Photoelectron Spectroscopy of the Methyl Radical Isotopomers, CH3, CH2D, CHD2 and CD3: Synergy between VUV Synchrotron Radiation Experiments and Explicitly Correlated Coupled Cluster Calculations

Threshold photoelectron spectra (TPES) of the isotopomers of the methyl radical (CH(3), CH(2)D, CHD(2), and CD(3)) have been recorded in the 9.5-10.5 eV VUV photon energy range using third generation synchrotron radiation to investigate the vibrational spectroscopy of the corresponding cations at a 7-11 meV resolution. A threshold photoelectron-photoion coincidence (TPEPICO) spectrometer based on velocity map imaging and Wiley-McLaren time-of-flight has been used to simultaneously record the TPES of several radical species produced in a Ar-seeded beam by dc flash-pyrolysis of nitromethane (CH(x)D(y)NO(2), x + y = 3). Vibrational bands belonging to the symmetric stretching and out-of-plane bending modes have been observed and P, Q, and R branches have been identified in the analysis of the rotational profiles. Vibrational configuration interaction (VCI), in conjunction with near-equilibrium potential energy surfaces calculated by the explicitly correlated coupled cluster method CCSD(T*)-F12a, is used to calculate vibrational frequencies for the four radical isotopomers and the corresponding cations. Agreement with data from high-resolution IR spectroscopy is very good and a large number of predictions is made. In particular, the calculated wavenumbers for the out-of-plane bending vibrations, nu(2)(CH(3)(+)) = 1404 cm(-1), nu(4)(CH(2)D(+)) = 1308 cm(-1), nu(4)(CHD(2)(+)) = 1205 cm(-1), and nu(2)(CD(3)(+)) = 1090 cm(-1), should be accurate to ca. 2 cm(-1). Additionally, computed Franck-Condon factors are used to estimate the importance of autoionization relative to direct ionization. The chosen models globally account for the observed transitions, but in contrast to PES spectroscopy, evidence for rotational and vibrational autoionization is found. It is shown that state-selected methyl cations can be produced by TPEPICO spectroscopy for ion-molecule reaction studies, which are very important for the understanding of the planetary ionosphere chemistry.

Theoretical prediction of noble-gas compounds: Ng–Pd–Ng and Ng–Pt–Ng

Following our recent study on Ng-Pt-Ng (Ng=Ar,Kr,Xe) [J. Chem. Phys. 123, 204321 (2005)], the binding of noble-gas atoms with Pd atom has been investigated by the ab initio coupled cluster CCSD(T) method with counterpoise corrections, including relativistic effects. It is shown that two Ng atoms bind with Pd atom in linear geometry due to the s-d(sigma) hybridization in Pd where the second Ng atom attaches with much larger binding energy than the first. The binding energies are evaluated as 4.0, 10.2, and 21.5 kcalmol for Ar-Pd-Ar, Kr-Pd-Kr, and Xe-Pd-Xe, respectively, relative to the dissociation limit, Pd ((1)S)+2Ng. In the hybrid Ng complexes, the binding energies for XePd and Ng (=Ar,Kr) are evaluated as 4.0 and 6.9 kcalmol for XePd-Ar and XePd-Kr, respectively. The fundamental frequencies and low-lying vibrational-rotational energy levels are determined for each compound by the variational method, based on the three-dimensional near-equilibrium potential energy surface. Results of vibrational-rotational analyses for Ng-Pt-Ng (Ng=Ar,Kr,Xe) and Xe-Pt-Ng (Ng=He,Ne,Ar,Kr) compounds are also given.

The HCS∕HSC and HCS+∕HSC+ systems: molecular properties, isomerization, and energetics

The isomer pair HCSHSC and related cations have been studied by means of a highly accurate level of theory. For all the species investigated the near-equilibrium potential energy surface has been calculated using the coupled cluster method in conjunction with correlation consistent basis sets ranging in size from quadruple to sextuple zeta. After extrapolation to the complete basis set limit, additional corrections due to core-valence correlation and scalar relativistic effects have also been included. Consequently, the molecular and spectroscopic properties as well as the ionization potentials and dissociation energies have been predicted to high accuracy. Isomerization path and energy for both radical and cationic species have also been investigated. Finally, the anharmonic vibrational frequencies have been employed in order to obtain zero-point corrections to ionization potentials, dissociation energies, and isomerization barriers: IP0(HCS) = 7.57(4) eV and IP0(HSC) = 9.00(5) eV; D0(C-H) = 49.29(55) kcal/mol and D0(S-H) = 9.99(37) kcal/mol; deltaE0(HCSHSC) = 39.29(49) kcal/mol, and deltaE0(HCS+HSC+) = 72.24(75) kcal/mol.

An ab initio study of the lowest electronic states of yttrium dicarbide, YC2

The low-lying electronic states of yttrium dicarbide have been calculated using highly correlated wave functions and systematic sequences of correlation consistent basis sets. For the (2)A(1) ground electronic state, the near-equilibrium potential energy surface (PES) has been calculated using the coupled cluster method in conjunction with basis sets ranging in size from double to quintuple zeta. The relativistic effects have been taken into account by using pseudopotentials for the Y atom. After extrapolation to the complete basis set limit, additional corrections due to core-valence correlation and spin-orbit effects have also been included. The same approach has been followed for the (2)B(1), (2)B(2), and (2)A(2) states but only the C(2V) PESs have been considered in these cases. For the two (2)A(1) electronic excited states and, for comparison purposes, for the ground state, the multireference configuration interaction (MRCI) approach has been used in conjunction with double-zeta and triple-zeta basis sets for the construction of the PES. The molecular and spectroscopic properties predicted for the ground and excited states investigated in this work compare well with the available experimental data, particularly for the ground electronic state. The 0 K dissociation enthalpy of YC(2), DeltaH(Y-C2)(0 K), and its atomization enthalpy, SigmaD(0), are predicted to be 148.4 and 291.5 kcal/mol, respectively.

Accurate theoretical near-equilibrium potential energy and dipole moment surfaces of HgClO and HgBrO.

The complexes HgBrO and HgClO have been previously determined by ab initio methods to be strongly bound and were suggested to be important intermediates during mercury depletions events observed in the polar troposphere. In the present work accurate near-equilibrium potential energy surfaces (PESs) of these species are reported. The PESs are determined using accurate coupled cluster methods and a series of correlation consistent basis sets with subsequent extrapolation to the complete basis set limit. Additive corrections for both core-valence correlation energy and relativistic effects are also included. The anharmonic ro-vibrational spectra of HgBrO and HgClO have been calculated in variational calculations. Strong infrared band strengths are predicted for all fundamentals in these species. The spin-orbit splitting dominates over the vibronic coupling effect in both HgClO and HgBrO. The Renner-Teller vibronic energy levels corresponding to the bending mode of these molecules are calculated via perturbation theory.

Theoretical determination of the spin-rovibronic spectrum of the [formula omitted] electronic transition of MgNC

The spin-rovibronic spectrum of the A ̃ 2 Π← X ̃ 2 Σ + electronic transition of MgNC has been determined variationally by RVIB3 [Mol. Phys. 98 (2000) 1697], based on the three-dimensional near-equilibrium potential energy surfaces of the 1 2 A ′ , 2 2 A ′ and 1 2 A″ states together with the transition moment functions between these electronic states. The theoretically determined spectrum is shown to be in very good agreement with the corresponding gas-phase high-resolution experimental spectrum.

Probing the B22–2A1 conically intersecting electronic states of ClO2 through photodetachment spectroscopy of its negative ion

The photodetachment spectroscopy of the ClO2− ion is studied theoretically with the aid of a time-dependent wave packet method. The theoretical findings in conjunction with the experimental observations unambiguously established the existence of a conical intersection in the excited B22–2A1 electronic manifold of ClO2. The highly diffused vibrational structure of this electronic manifold observed in the experimental recording is attributed to the nonadiabatic effects associated with this conical intersection. In our study we employed the near-equilibrium potential energy surfaces reported by Peterson and Werner [J. Chem. Phys. 96, 8948 (1992)] along the symmetric stretching and bending vibrations of ClO2. The potential energy surfaces along the asymmetric stretching vibration are assumed to be harmonic. The dynamics of the system is studied within a linear vibronic coupling scheme, and the strength of the coupling is explicitly determined by ab initio methods. The effect of the next higher A22 electronic state of ClO2 on the above photoelectron band is also discussed. The nonradiative decay dynamics of the system mediated by the vibronic coupling is examined, and the findings are correlated with the femtosecond time-resolved experiment.

A variational determination of spin-rovibronic energy levels of MgNC in the [formula omitted] state

The variational method is applied to determine the spin-rovibronic energy levels of MgNC in the A 2Π electronic state. The calculations are based on the three-dimensional near-equilibrium potential energy surfaces of the 1 2A″ and 2 2A ′ states determined by the multireference singles and doubles configuration interaction method. Results are presented for energies up to 1000 cm −1 , and compared with the corresponding values calculated by the perturbational method, as well as with gas-phase high resolution experimental results.