Near-equilibrium Potential Energy Research Articles

Variational rovibrational calculations for tetra atomic linear molecules using Watson’s isomorphic Hamiltonian: II. The B11244 story retold

A new six-dimensional near-equilibrium potential energy function for propynylidynium (l-C3H+) is developed based on a high-level composite ab initio method. The importance of higher-order correlation contributions to the composite potential is clearly demonstrated. Variational rovibrational calculations were performed using the new C8v4 program based on Watson’s isomorphic Hamiltonian and a basis of symmetrized harmonic oscillator/rigid rotor product wave functions. The results of these calculations employing the new composite potential as well as a previously constructed quartic force field rectify long-standing discrepancies between theory and experiment. Effective Hamiltonian fits yield a ground state rotational parameter within 5 MHz of the experimental result and a quartic centrifugal distortion constant in virtual agreement with experiment. Spectroscopic parameters for low-lying excited vibrational states are presented which should provide a starting point in forthcoming experimental studies on l-C3H+. A close relationship can be established by comparing the properties of l-C3H+ with floppy C3 from which follows that l-C3H+ behaves in many respects like a “protonated”, albeit more rigid, C3.

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.

Theoretical rovibrational spectroscopy of [formula omitted

Accurate near-equilibrium potential energy functions (PEFs) have been constructed for the nitronium ion (NO2+) by composite methods using either CCSD(T)-F12b or explicitly correlated multi-reference methods (MRCI-F12+Q or MRACPF-F12) as dominant contributions. Up to pentuple substitutions are required in the coupled-cluster based approach to reach convergence in the wavenumbers of the fundamentals to ca. 1cm−1. These are predicted to be ν1=1386.0cm-1,ν2=621.1cm−1 and ν3=2342.8cm−1. All values differ significantly from the results of previous studies by zero-kinetic energy (ZEKE) spectroscopy and reanalysis or remeasurement is suggested. Compared to neon-matrix IR spectroscopic work of Jacox and coworkers the present calculations yield smaller wavenumbers of Δν3=-5.4cm−1 and Δ(ν1+ν3)=-7.9cm−1 so that blueshifting is predicted for those absorptions. The calculated isotopic shifts for both bands are in excellent agreement with the corresponding experimental values. Accurate values for rotational and centrifugal distortion constants of NO2+ in different vibrational states are predicted which should be of help in the search for forthcoming high-resolution spectra of that cation.

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.

Correlation consistent, Douglas–Kroll–Hess relativistic basis sets for the 5p and 6p elements

New sets of all-electron correlation consistent triple- and quadruple-zeta basis sets have been developed for the 5p and 6p elements (In–Xe, Tl–Rn). For the 5p elements, the spin-free Douglas–Kroll–Hess (DKH) Hamiltonian truncated at second order was used, while for the 6p row, DKH3 was employed. The resulting cc-pVmZDK sets (m = T, Q) are designed to correlate the valence ns and np electrons, but both core–valence sets (cc-pwCVmZ-DK) for (n - 1)spd correlation and diffuseaugmented sets (aug-cc-pVmZ-DK) for weak interactions have also been included. Benchmark DKH CCSD(T) calculations were carried out on the atoms for their first ionization potentials and electron affinities. Coupled cluster calculations of the near-equilibrium potential energy functions of 18 selected diatomic molecules were also carried out to determine their spectroscopic and thermodynamic properties. These results are extensively compared to those obtained using the analogous aug-ccp( wC)VmZ-PP basis sets with their associated small-core pseudopotentials. For the quadruple-zeta quality basis sets, the mean unsigned differences were found to be just 1.4 mA for re, 0.7 cm-1 for xe, and 0.2 kcal/mol for De with corresponding maximum differences of 4.8 mA, 4.3 cm-1, and 0.7 kcal/mol, respectively. Using all-electron DKH calculations with the present basis sets as corrections to the pseudopotential approximation appears to be most accurate when (n - 1)d correlation is considered in both cases using aug-cc-pwCVQZ quality basis sets. The new DK basis sets exhibit similar basis set convergence toward the complete basis set (CBS) limit as the PP-based sets and hence should find utility in all-electron [T, Q] basis set extrapolations.

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.

Ab initio ro-vibrational spectroscopy of the group 11 cyanides: CuCN, AgCN, and AuCN

Accurate near-equilibrium potential energy and dipole moment functions have been calculated for the linear coinage-metal cyanides CuCN, AgCN, and AuCN using coupled cluster methods and sequences of correlation consistent basis sets. The explicitly correlated CCSD(T)-F12b method is used for the potential energy surfaces (PESs) with inclusion of core correlation, and is combined with contributions from molecular spin-orbit coupling, scalar relativity, and effects due to higher order electron correlation. The resulting composite PESs are used in both perturbative and variational calculations of the ro-vibrational spectra. In addition to accurate equilibrium geometries, the ro-vibrational spectra are predicted, which are found to be relatively intense in the 200-600 cm(-1) range due to the bending and metal-carbon stretching modes. The CN stretch near 2165 cm(-1) is also predicted to carry enough intensity to allow its observation by experiment. A strong Fermi-resonance is predicted between the first overtone of the bend and the fundamental of the metal-carbon stretch for both CuCN and AgCN. The heats of formation at 0 K are predicted from their calculated atomization energies to be 89.8, 88.6, and 104.5 kcal mol(-1) for CuCN, AgCN, and AuCN, respectively.

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.

A theoretical study of ZnH2: a case of very strong Darling–Dennison resonance

The metastable linear ZnH2 molecule in its X electronic ground state has been investigated by the coupled cluster method CCSD(T) in conjunction with a small-core pseudopotential for the zinc atom. Using three pieces of spectroscopic information for the most abundant isotopomer 64ZnH2, an accurate near-equilibrium potential energy function (PEF) has been constructed and used in variational calculations of rovibrational energies and wave functions. The ν1 and ν2 band origins (in cm−1) for 64ZnH2 and 64ZnD2 (in parentheses) are predicted at 1886.4(1349.7) and 635.1(459.8), respectively. 64ZnH2 is characterised by strong Darling–Dennison and l-type rotational resonances. Various perturbations are analysed in detail, partly making use of calculated expectation values of the vibrational quantum number |l|. Einstein coefficients of spontaneous emission are predicted for several transitions.

A theoretical study of the low-lying electronic states of OIO and the ground states of IOO and OIO−

Several low-lying electronic states of OIO were investigated at the multireference configuration interaction (MRCI) level of theory. The state, which is the origin of the absorption bands observed experimentally, is calculated to be bound with respect to dissociation to IO + O. A low barrier for dissociation to I + O2 is calculated for the state, which should lead to efficient I atom production. This indirect process would involve an initial spin–orbit interaction between the state and the nearby B2A1, followed by a strong vibronic interaction with the A2B2 state via an avoided crossing. Accurate near-equilibrium potential energy functions have also been determined for OIO, IOO, and OIO− using sequences of correlation consistent basis sets extrapolated to the complete basis set limit using MRCI or coupled cluster methods. These were then used to calculate rotational and vibrational spectroscopic constants. Accurate bond dissociation energies and enthalpies of formation have also been calculated. The use of additional tight functions in the iodine basis sets were found to be essential for both accurate energetics and structures, and in particular their use leads to a revision of a previously calculated dissociation energy of IO that is now also in near perfect agreement with experiment.

Accurate Potential Energy Surface and Calculated Spectroscopic Properties for CdH2 Isotopomers

Ab initio calculations employing the coupled cluster method CCSD(T), in conjunction with a small-core pseudopotential for the cadmium atom, have been employed to construct a near-equilibrium potential energy function (PEF) and an electric dipole moment function (EDMF) for CdH(2). The significance of the spin-orbit interaction was checked and found to be of minor importance. Making use of two pieces of experimental information for the most abundant isotopomer (114)CdH(2), we obtained a refined PEF, which, within variational calculations of rovibrational states and wave functions, reproduces all available experimental data (S. Yu, A.Shayesteh, and P. F. Bernath, J. Chem. Phys. 2005, 122, 194301) very well. In addition, numerous predictions are made. In particular, the nu(2) band origins for (114)CdH(2) and (114)CdD(2) are predicted at 605.9 and 436.9 cm(-1), respectively, and the state perturbing the e parity levels of the (0,0(0),1) state of (114)CdH(2) at J = 12-17 is identified as the (0,3(3),0) state. Assignments for further perturbations found in the emission spectra are given as well.

A theoretical study of the spectroscopic properties of the ground and first excited electronic state of HS 2

Accurate thermochemical and spectroscopic properties have been calculated for the X ∼ 2 A ″ and A ∼ 2 A ′ electronic states of the HS 2 radical using highly correlated coupled cluster methods with explicit basis set extrapolations. The heat of formation of HS 2 at 0 K is predicted to be 26.1 kcal/mol based in part on accurate benchmark calculations of SH and S 2. The equilibrium geometry of HS 2, which is estimated to be accurate to at least 0.002 Å, is predicted to be r e(SH) = 1.3482 Å, R e(SS) = 1.9608 Å, and θ e(HSS) = 101.52°. In addition to a set of centrifugal distortion constants, harmonic frequencies, and vibration–rotation coupling constants being calculated for both electronic states of HS 2 and DS 2 using second order perturbation theory, the anharmonic infrared band origins and A ∼ – X ∼ emission spectra were calculated variationally together with their intensities. These made use of accurate three-dimensional, near-equilibrium potential energy and dipole moment functions. The ν 3 fundamentals of both HS 2 and DS 2 are reproduced to better than 3 cm −1. Predictions are made for both the ground state infrared spectrum as well as the electronic spectrum. Two possible misassignments in the recently reported chemiluminescence spectra are noted.