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The standard enthalpy of formation, ΔfH°, of 2Π3/2 SH has been determined at converged levels of ab initio electronic structure theory, including high-order coupled cluster and full configuration i...

The spectrum of water vapor is of fundamental importance for a variety of processes, including the absorption and retention of sunlight in Earth's atmosphere. Therefore, there has long been an urgent need for a robust and accurate predictive model for this spectrum. In our work on the high-resolution spectrum of water, we report first-principles calculations that approach experimental accuracy. To achieve this, we performed exceptionally large electronic structure calculations and considered a variety of effects, including quantum electrodynamics, which have routinely been neglected in studies of small many-electron molecules. The high accuracy of the resulting ab initio procedure is demonstrated for the main isotopomers of water.

The standard enthalpy of formation, Δ f H°, of 2 Π CH has been determined at converged levels of ab initio electronic structure theory, including high order coupled cluster and full configuration interaction benchmarks. The atomic Gaussian basis sets employed include the (aug)-cc-p(C)VXZ family with X = 3, 4, 5 and 6. Extrapolations to the complete one-particle basis set and the full configuration interaction limits, where appropriate, have been performed to reduce remaining computational errors. Additional improvements in the enthalpy of formation of 2 Π CH were achieved by appending the valence-only treatment with core-valence correlation, relativistic effects including spin-orbit correlation, and the diagonal Born-Oppenheimer correction. The recommended values for Δ f H° 0 and Δ f H° 2 9 8 of 2 Π CH are 592.48 + 0 . 4 7 - 0 . 5 6 kJ mol - 1 and 595.93 + 0 . 4 7 - 0 . 5 6 kJ mol - 1 , respectively.

Barriers of infinite (or very large) height prevent certain rearrangements of the atoms in a molecule from occurring and thus the complete nuclear permutation inversion (CNPI) group of the molecule can be reduced. Using the example of acetaldehyde molecule, it was pointed out that some barriers of infinite height, in addition to reducing the CNPI group, constrain torsional dynamics explicitly and influence how the torsional coordinate transforms under the MS group. It was proved that the symmetry properties of the torsional potential do not depend on the geometrical symmetry of either the top or the frame., The authors would like to thank Projects E-10/2001 of the Hungarian–Spanish Intergovernmental Cooperations on Science and Technology, BFM2000-1106 and BFM2001- 2315 of the Ministerio de Ciencia y Technologia (Spain), and Grant Nos. OTKA T034327 and T033074 for support.

Relativistic corrections beyond the simple one-electron mass–velocity–Darwin (MVD1) approximation to the ground-state electronic energy of H2S are determined at over 250 geometries. The corrections considered include the two-electron Darwin, the Gaunt and Breit corrections, and the one-electron Lamb shift. Fitted correction surfaces are constructed and used with an accurate ab initio nonrelativistic Born–Oppenheimer potential, determined previously (J. Chem. Phys. 115 (2001) 1229), to calculate vibrational and rotational levels for H232S. The calculations suggest that one- and two-electron relativistic corrections have a noticable influence on the levels of H2S. As for water, the effects considered have markedly different characteristics for the stretching and bending states.

Calculation of the rotation-vibration spectrum of H3+, as well as of its deuterated isotopologues, with near-spectroscopic accuracy requires the development of sophisticated theoretical models, methods, and codes. The present paper reviews the state-of-the-art in these fields. Computation of rovibrational states on a given potential energy surface (PES) has now become standard for triatomic molecules, at least up to intermediate energies, due to developments achieved by the present authors and others. However, highly accurate Born--Oppenheimer energies leading to highly accurate PESs are not accessible even for this two-electron system using conventional electronic structure procedures e.g., configuration-interaction or coupled-cluster techniques with extrapolation to the complete basis set limit). For this purpose highly specialized techniques must be used, e.g., those employing explicitly correlated Gaussians and nonlinear parameter optimizations. It has also become evident that a very dense grid of \ai\ points is required to obtain reliable representations of the computed points extending from the minimum to the asymptotic limits. Furthermore, adiabatic, relativistic, and QED correction terms need to be considered to achieve near-spectroscopic accuracy during calculation of the rotation-vibration spectrum of H3+. The remaining and most intractable problem is then the treatment of the effects of non-adiabatic coupling on the rovibrational energies, which, in the worst cases, may lead to corrections on the order of several \cm. A promising way of handling this difficulty is the further development of effective, motion- or even coordinate-dependent, masses and mass surfaces. Finally, the unresolved challenge of how to describe and elucidate the experimental pre-dissociation spectra of H$_3^+$ and its isotopologues is discussed., Topical review to be published in J Phys B: At Mol Opt Phys

A discrete-variable-representation-based symmetry adaptation algorithm is presented and implemented in the fourth-age quantum-chemical rotational-vibrational code GENIUSH. The utility of the symmetry-adapted version of GENIUSH is demonstrated by the computation of seven-dimensional bend-only vibrational and rovibrational eigenstates of the highly fluxionally symmetric C H 5 + molecular ion, a prototypical astructural system. While the numerical results obtained and the symmetry labels of the computed rovibrational states of C H 5 + are of considerable utility by themselves, it must also be noted that the present study confirms that the nearly unconstrained motion of the five hydrogen atoms orbiting around the central carbon atom results in highly complex rotational-vibrational quantum dynamics and renders the understanding of the high-resolution spectra of C H 5 + extremely challenging.

The quasi-variational quantum chemical protocol and code GENIUSH [E. Matyus et al., J. Chem. Phys. 130, 134112 (2009) and C. Fabri et al., J. Chem. Phys. 134, 074105 (2011)] has been augmented with the complex absorbing potential (CAP) technique, yielding a method for the determination of rovibrational resonance states. Due to the effective implementation of the CAP technique within GENIUSH, the GENIUSH-CAP code is a powerful tool for the study of important dynamical features of arbitrary-sized molecular systems with arbitrary composition above their first dissociation limit. The GENIUSH-CAP code has been tested and validated on the H2He+ cation: the computed resonance energies and lifetimes are compared to those obtained with a previously developed triatomic rovibrational resonance-computing code, D2FOPI-CCS [T. Szidarovszky and A. G. Csaszar Mol. Phys. 111, 2131 (2013)], utilizing the complex coordinate scaling method. A unique feature of the GENIUSH-CAP protocol is that it allows the simple implementation of reduced-dimensional dynamical models. To prove this, resonance energies and lifetimes of the H2⋅CO van der Waals complex have been computed utilizing a four-dimensional model (freezing the two monomer stretches), and a related potential energy surface, of the complex.

Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H3(+), for which a global adiabatic potential energy surface accurate to better than 0.1 cm(-1) exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D(3h) point-group symmetry is employed. The vibrational mass of the proton in H3(+) is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m(opt,p)((v))=m(nuc,p)+0.31224m(e). This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.

The H2O···X complexes, with X = F, Cl, Br, and I, show considerable viability with nonspin-orbit De(D0) dissociation energy values of 3.73(2.42), 3.60(2.68), 3.54(2.72), and 3.36(2.77) kcal mol(-1) for X = F, Cl, Br, and I, respectively, obtained at the CCSD(T)-F12b/aug-cc-pVTZ(-PP) level of theory using relativistic pseudopotentials (PPs) for Br and I. Spin-orbit (SO) corrections, computed with the Breit-Pauli operator in the interacting states approach at the all-electron MRCI+Q/aug-cc-pwCVTZ(-PP) level, are found to depend sensitively and unpredictably on the O···X separations. 96% (F), 87% (Cl), 54% (Br), and 30% (I) quenching of the SO corrections significantly reduces the dissociation energies of the H2O···X complexes, resulting in De(D0) values of 3.38(2.06), 2.86(1.94), 1.64(0.83), and 1.23(0.64) kcal mol(-1) for X = F, Cl, Br, and I, respectively.

For individual molecules quantum mechanics (QM) offers a simple, natural and elegant way to build large-scale complex networks: quantized energy levels are the nodes, allowed transitions among the levels are the links, and transition intensities supply the weights. QM networks are intrinsic properties of molecules and they are characterized experimentally via spectroscopy; thus, realizations of QM networks are called spectroscopic networks (SN). As demonstrated for the rovibrationalstates of H216O,the molecule governing the greenhouse effect on earth through hundreds of millions of its spectroscopic transitions (links), both the measured and firstprinciples computed one-photon absorption SNs containing experimentally accessible transitions appear to have heavy-tailed degree distributions. The proposed novel view of high-resolution spectroscopy and the observed degree distributions have important implications: appearance of a core of highly interconnected hubs among the nodes, a generally disassortative connection preference, considerable robustness and error tolerance, and an “ultra-small-world” property. The network-theoretical view of spectroscopy offers a data reduction facility via a minimum-weight spanning tree approach, which can assist high-resolution spectroscopists to improve the efficiency of the assignment of their measured spectra.

A grid-based method designed to refine adiabatic potential energy surfaces (PES) of molecules via minimizing a suitable objective function is described. The objective function contains deviations from the reference (experimental) (ro)vibrational energy levels and is based on PES correction values determined at the grid points within a discrete-variable-representation nuclear-motion algorithm and first-order perturbation theory (PT). The proposed PES refinement technique is tested on the ground electronic state of the MgH molecule. The large number of numerical test results obtained suggest the following: (1) first-order PT is able to yield accurate correction values at the grid points representing the PES, and for practical cases there seems to be no need to go to higher orders of PT; (2) with the number of grid points greatly exceeding the number of experimental energy levels included in the refinement procedure, terms additional to the "obs-calc" term, including numerical first and second derivatives of the correction surface, are necessary in the objective function to arrive at a physically meaningful, "smooth" correction surface; (3) for a given J rotational quantum number, the corrected PES is able to reproduce experimental (ro)vibrational energies to within tenths of cm(-1) if they are included in the refinement or interpolated between states that are involved in the optimization, whereas extrapolated states tend to have somewhat larger remaining discrepancies; (4) the PES refined only for the J = 0 states introduces a minor systematic error for J > 0 states, with discrepancies growing with J; (5) when the number of experimental energies included in the refinement greatly exceeds the number of grid points upon which the PES is optimized, the systematic error of treating states with different J rotational quantum numbers can be reduced and an impressive average accuracy can be achieved for all rovibrational states; and (6) in the case of quasibound (also known as resonance) rovibrational states, energies can be computed to accuracies similar to those of the bound states and excellent lifetimes (widths) can also be determined. Changes in thermochemical functions upon inclusion of quasibound states during direct summation is discussed.

This paper is the fourth of a series of papers reporting critically evaluated rotational–vibrational line positions, transition intensities, pressure dependences, and energy levels, with associated critically reviewed assignments and uncertainties, for all the main isotopologues of water. This paper presents energy level and transition data for the following doubly and triply substituted isotopologues of water: D216O, D217O, and D218O. The MARVEL (Measured Active Rotational–Vibrational Energy Levels) procedure is used to determine the levels, the lines, and their self-consistent uncertainties for the spectral regions 0–14 016, 0–7969, and 0–9108 cm−1 for D216O, D217O, and D218O, respectively. For D216O, D217O, and D218O, 53 534, 600, and 12 167 lines are considered, respectively, from spectra recorded in absorption at room temperature and in emission at elevated temperatures. The number of validated energy levels is 12 269, 338, and 3351 for D216O, D217O, and D218O, respectively. The energy levels have been checked against the ones determined, with an average accuracy of about 0.03 cm−1, from variational rovibrational computations employing exact kinetic energy operators and an accurate potential energy surface. Furthermore, the rovibrational labels of the energy levels have been validated by an analysis of the computed wavefunctions using the rigid-rotor decomposition (RRD) scheme. The extensive list of MARVEL lines and levels obtained is deposited in the Supplementary Material of this paper, in a distributed information system applied to water, W@DIS, and on the official MARVEL website, where they can easily be retrieved.

The fourth-age quantum chemical code GENIUSH is used for the variational determination of rotational-vibrational energy levels corresponding to reduced- and full-dimensional models of H(+)(5), a molecular ion exhibiting several strongly coupled large-amplitude motions. The computations are supplemented with one- and two-dimensional analytic results which help to understand the peculiar rovibrational energy-level structure computed correctly for the first time. An unusual aspect of the results is that the canonical Eckart-embedding of molecule-fixed axes, a cornerstone of the computational spectroscopy of semirigid molecules, is found to be inadequate. Furthermore, it is shown that while the 1D "active torsion" model provides proper results when compared to the full, 9D treatment, models excluding the torsion have limited physical significance. The structure of the rovibrational energy levels of H(+)(5) proves that this is a prototypical astructural molecule: the rotational and vibrational level spacings are of the same order of magnitude and the level structure drastically deviates from that computed via perturbed rigid-rotor and harmonic-oscillator models.

The report of an IUPAC Task Group, formed in 2011 on "Intensities and line shapes in high-resolution spectra of water isotopologues from experiment and theory" (Project No. 2011-022-2-100), on line profiles of isolated high-resolution rotational-vibrational transitions perturbed by neutral gas-phase molecules is presented. The well-documented inadequacies of the Voigt profile (VP), used almost universally by databases and radiative-transfer codes, to represent pressure effects and Doppler broadening in isolated vibrational-rotational and pure rotational transitions of the water molecule have resulted in the development of a variety of alternative line-profile models. These models capture more of the physics of the influence of pressure on line shapes but, in general, at the price of greater complexity. The Task Group recommends that the partially Correlated quadratic-Speed-Dependent Hard-Collision profile should be adopted as the appropriate model for high-resolution spectroscopy. For simplicity this should be called the Hartmann--Tran profile (HTP). The HTP is sophisticated enough to capture the various collisional contributions to the isolated line shape, can be computed in a straightforward and rapid manner, and reduces to simpler profiles, including the Voigt profile, under certain simplifying assumptions., Comment: Accepted for publication in Pure and Applied Chemistry

The report and results of an IUPAC Task Group (TG) formed in 2004 on “A Database of Water Transitions from Experiment and Theory” (Project No. 2004-035-1-100) are presented. Energy levels and recommended labels involving exact and approximate quantum numbers for the main isotopologues of water in the gas phase, H2 16O, H2 18O, H2 17O, HD16O, HD18O, HD17O, D2 16O, D2 18O, and D2 17O, are determined from measured transition frequencies. The transition frequencies and energy levels are validated using first-principles nuclear motion computations and the MARVEL (measured active rotational–vibrational energy levels) approach. The extensive data including lines and levels are required for analysis and synthesis of spectra, thermochemical applications, the construction of theoretical models, and the removal of spectral contamination by ubiquitous water lines. These datasets can also be used to assess where measurements are lacking for each isotopologue and to provide accurate frequencies for many yet-to-be measured transitions. The lack of high-quality frequency calibration standards in the near infrared is identified as an issue that has hindered the determination of high-accuracy energy levels at higher frequencies. The generation of spectra using the MARVEL energy levels combined with transition intensities computed using high accuracy ab initio dipole moment surfaces are discussed. A recommendation of the TG is for further work to identify a single, suitable model to represent pressure- (and temperature-) dependent line profiles more accurately than Voigt profiles.

Ab initio semiglobal potential energy and dipole moment hypersurfaces for the isomerising HCN–HNC system are computed, using a grid of 242 points, principally at the all-electron cc-pCVQZ CCSD(T) level. Several potential energy hypersurfaces (PES) are presented including one which simultaneously fits 1527 points from earlier ab initio, smaller basis CCSD(T) calculations of Bowman et al. [J. Chem. Phys. 99, 308 (1993)]. The resulting potential is then morphed with 17 aug-cc-pCVQZ CCSD(T) points calculated at HNC geometries to improve the representation of the HNC part of the surface. The PES is further adjusted to coincide with three ab initio points calculated, at the cc-pCV5Z CCSD(T) level, at the critical points of the system. The final PES includes relativistic and adiabatic corrections. Vibrational band origins for HCN and HNC with energy up to 12 400 cm−1 above the HCN zero-point energy are calculated variationally with the new surfaces. Band transition dipoles for the fundamentals of HCN and HNC, and a few overtone and hot band transitions for HCN have been calculated with the new dipole surface, giving generally very good agreement with experiment. The rotational levels of ground and vibrationally excited states are reproduced to high accuracy.

Two-electron relativistic corrections to the ground-state electronic energy of water are determined as a function of geometry at over 300 points. The corrections include the two-electron Darwin term (D2) of the Coulomb–Pauli Hamiltonian, obtained at the cc-pVQZ CCSD(T) level of theory, as well as the Gaunt and Breit corrections, calculated perturbationally using four-component fully variational Dirac–Hartree–Fock (DHF) wavefunctions and two different basis sets. Based on the calculated energy points, fitted relativistic correction surfaces are constructed. These surfaces are used with a high-accuracy ab initio nonrelativistic Born–Oppenheimer (BO) potential energy hypersurface to calculate vibrational band origins and rotational term values for H 2 16 O . The calculations suggest that these two-electron relativistic corrections, which go beyond the usual kinetic relativistic effects and which have so far been neglected in rovibrational calculations on light many-electron molecular systems, have a substantial influence on the rotation–vibration levels of water. The three effects considered have markedly different characteristics for the stretching and bending levels, which often leads to fortuitous cancellation of errors. The effect of the Breit interaction on the rovibrational levels is intermediate between the effect of the kinetic relativistic correction and that of the one-electron Lamb-shift effect.

The basis-set convergence of singlet and triplet pair energies of coupled-cluster theory including single and double excitations is accelerated by means of extrapolations based on the distinct convergence behaviors of these pairs. The new extrapolation procedure predicts a nonrelativistic Born-Oppenheimer inversion barrier of 1767 ± 12 cm −1 for NH3 .A n effective one-dimensional, vibrationally averaged barrier of 2021 ± 20 cm −1 is obtained when relativistic effects (+20 cm −1 ), Born-Oppenheimer diagonal corrections (−10 cm −1 ), and zero-point vibrations (+244 cm −1 ) are accounted for. c � 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1306-1314, 2001

Potential energy hypersurfaces (PES) have been constructed for the ground electronic state of H2S utilizing results from state-of-the-art ab initio quantum chemical methods, most notably higher-order coupled cluster theory employing (core-polarized) correlation-consistent basis sets. Small corrections due to extrapolation to the complete basis set and full configuration interaction limits, core correlation, and relativistic corrections, as well as effects beyond the Born–Oppenheimer approximation have been investigated and incorporated into the final PES. Using the exact rovibrational kinetic energy operator rovibrational energy levels have been computed with the different PESs. The final converged ab initio PES of this study reproduces the available vibrational band origins of H2 32S, HD32S, D2 32S, and H2 34S with maximum deviations, gradually increasing for increased vibrational excitation, of 29(14 300), 10(3800), 7(4600), and 12(6400) cm−1, respectively, where the maximum energy above the zero-point ...

Employing introductory (3-21G RHF) and medium-size (6-311CCG B3LYP) ab initio calculations, complete conformational libraries, containing as many as 27 conformers, have been determined for diamide model systems incorporating the amino acids valine (Val) and phenylalanine (Phe). Conformational and energetic properties of these libraries were analyzed. For example, significant correlation was found between relative energies from 6-311CCG B3LYP and single-point B3LYP/6-311CCG//RHF/3-21G calculations. Comparison of populations of molecular conformations of hydrophobic aromatic and nonaromatic residues, based on their ab initio relative energies, with their natural abundance indicates that, at least for the hydrophobic core of proteins, the conformations of Val (Ile, Leu) and Phe (Tyr, Trp) are controlled by the local energetic preferences of the respective amino acids. c 2001 John Wiley & Sons, Inc. J Comput Chem 22: 732-751, 2001

A simple multiplicative approach is presented for approximating the full configuration interaction (FCI) limit at the complete basis set limit from the small basis set FCI and coupled cluster [most notably CCSD(T) and CCSDT] calculations. The proposed scaled higher-order correlation (SHOC) correction scheme is demonstrated to extrapolate CCSD(T) and CCSDT correlation energies for BH and AlH to the FCI limit with remarkable accuracy, and to correct the dissociation energies of [CN,C2,N2] computed at the CCSD(T) and CCSDT levels by [+1.4, +2.3, +1.5] kcal/mol, respectively, bringing them in much closer agreement with the best experimental values. The approach is also well suited for the generation of accurate potential energy hypersurfaces.

Chemical shielding anisotropy tensors have been determined for all twenty-seven characteristic conformers of For-L-Val-NH2 using the GIAO-RHF formalism with the 6-31+G* and TZ2P basis sets. The individual chemical shifts and their conformational averages have been compared to their experimental counterparts taken from the BioMagnetic Resonance Bank (BMRB). At the highest level of theory applied, for all nuclei but the amide proton, deviations between statistically averaged theoretical and experimental chemical shifts are as low as 1–3 %. Correlated chemical shift plots of selected nuclei, as function of the respective ϕ, ψ, χ1, and χ2 torsional angles, have been generated. On two-dimensional chemical shift–chemical shift plots, for example, 1HNH–15NNH and 15NNH–13Cα, regions corresponding to major conformational clusters have been identified, providing a basis for the quantitative identification of conformers from NMR shift data. Experimental NMR resonances of nuclei of valine residues have been deduced from 18 selected proteins, resulting in 93 1Hα–13Cα chemical shift pairs. These experimental results have been compared to relevant ab initio values revealing remarkable correlation between the two sets of data. Correlations of 1Hα and 13Cα values with backbone conformational parameters (ϕ and ψ) have also been found for all pairs (e.g. 1Hα/ϕ and 13Cα/ϕ) but 1Hα/ψ. Overall, the appealing idea of establishing backbone folding of proteins by employing chemical shift information alone, obtained from selected multiple-pulse NMR experiments (e.g. 2D-HSQC, 2D-HMQC, and 3D-HNCA), has received further support.

The triplet electronic states of isocyanic acid have been systematically investigated by means of state-of-the-art electronic structure methods, including various correlation techniques based on the coupled-cluster ansatz [CCSD, EOM-CCSD, CCSD(T), and BD(TQ)], second- through fifth-order Moller−Plesset perturbation theory (MP2-MP5), and the complete active space self-consistent field approach. The one-particle [(C,N,O)/H] basis sets for these studies ranged in quality from [4s2p1d/2s1p] to [7s6p5d4f3g2h1i/6s5p4d3f2g1h]. Vertical excitation energies were determined for the lowest 13 triplet states (5 valence, 8 Rydberg), and potential energy curves for bending to and from linearity were generated for 10 of these states, revealing intricate state interactions and numerous actual and avoided crossings. An extensive mapping was then executed for the interlocking a3A‘ ‘ and b3A‘ surfaces, which produced geometric structures, relative energies, harmonic vibrational frequencies, and selected large-amplitude vib...

High-quality ab initio quantum chemical methods, including higher-order coupled cluster (CC) and many-body perturbation (MP) theory, as well as full configuration interaction (FCI) benchmarks, with basis sets ranging from [S/H] [4s3p1d/2s1p] to [9s8p7d5f4g3h2i/7s6p5d4f3g2h] have been employed to obtain the best technically possible value for the barrier to linearity of hydrogen sulphide. Following careful extrapolations of MP2, CCSD and CCSD(T) energies to the complete basis set (CBS) limit and inclusion of small corrections due to scalar relativistic terms, core polarization and core correlation effects, and the diagonal Born–Oppenheimer correction (DBOC), the final electronic (vibrationless) extrapolated barrier height of this study is 24 423±75 cm −1 .

The full quartic force field of the ground electronic state of the silyl anion (SiH3−) has been determined at the CCSD(T)-R12 level employing a [Si/H]=[16s11p6d5f/7s5p4d] basis set. The vibrational energy levels, using the quartic force field as a representation of the potential energy hypersurface around equilibrium, have been determined by vibrational perturbation theory carried out to second, fourth, and sixth order. The undetected vibrational fundamental for the umbrella mode, ν2, is predicted to be 844 cm−1. High-quality ab initio quantum chemical methods, including higher-order coupled cluster (CC) and many-body perturbation (MP) theory with basis sets ranging from [Si/H] [5s4p2d/3s2p] to [8s7p6d5f4g3h/7s6p5d4f3g] have been employed to obtain the best possible value for the inversion barrier of the silyl anion. The rarely quantified effects of one- and two-particle relativistic terms, core correlation, and the diagonal Born–Oppenheimer correction (DBOC) have been included in the determination of the...

NMR chemical shielding anisotropy tensors have been computed, employing several basis sets and the GIAO-RHF and GIAO-MP2 formalisms of electronic structure theory, for all the atoms of the five and nine typical backbone conformers of For-Gly-NH2 and For-L-Ala-NH2, respectively. Multidimensional chemical shift plots, as a function of the respective backbone fold, have been generated for both peptide models. On the 2D 1 H NH - 15 N NH and 15 N NH - 13 C plots the most notable feature is that at all levels of theory studied the backbone conformers cluster in different regions. Computed chemical shifts, as well as their averages, have been compared to relevant experimental values taken from the BioMagnetic Resonance Bank (BMRB). At the highest levels of theory, for all nuclei but the amide protons, deviations between statistically averaged theoretical and experimental shifts are as low as 1-3%. These results indicate that chemical shift information from selected multiple-pulse NMR experiments (e.g., 2D-HSQC and 3D-HNCA) could directly be employed to extract folding information for polypeptides and proteins. c 2000 John Wiley & Sons, Inc. J Comput Chem 21: 882-900, 2000

Geometry optimizations were carried out for the (HF)2 ,( H 2O)2, and HF-H2O intermolecular complexes using the MP2/aug-cc-pVXZfXD 2, 3, 4, and 5g theoretical models on both the uncorrected and counterpoise (CP) corrected potential energy hypersurfaces (PES). Our results and the available literature data clearly show that extrapolation of intermolecular distances to the complete basis set (CBS) limit is satisfactory on PESs corrected for BSSE. On the other hand, one should avoid such extrapolations using data obtained from uncorrected PESs. Also, fixing intramolecular parameters at their experimental values could cause difficulties during the extrapolation. As the available literature data and our results clearly show, the MP2/aug-cc-pVXZfXD 2, 3, 4g data series of intermolecular distances obtained from the CP-corrected surfaces can be safely used for the purpose of CBS extrapolations. c 2000 John Wiley & Sons, Inc. J Comput Chem 22: 196-207, 2001

High-quality ab initio quantum chemical methods, including higher-order coupled cluster (CC) and many-body perturbation (MP) theory, explicitly correlated (linear R12) techniques, and full configuration interaction (FCI) benchmarks, with basis sets ranging from [O/H] [3s2p1d/2s1p] to [8s7p6d5f4g3h2i/7s6p5d4f3g2h] have been employed to obtain the best possible value for the barrier to linearity of water. Attention is given to the degree of accord among extrapolations of conventional MP2, CCSD, and CCSD(T) energies to the complete basis set (CBS) limit and corresponding linear R12 schemes for these correlation methods. Small corrections due to one- and two-particle relativistic terms, core correlation effects, and the diagonal Born–Oppenheimer correction (DBOC) have been incorporated. The final electronic (vibrationless) extrapolated barrier height of this study is 11 127±35 cm−1. Anharmonic force fields have been determined at the aug-cc-pCVTZ CCSD(T) level at equilibrium and at a linear reference geometry...

The relativistic correction to the electronic energy of the water molecule is calculated as a function of geometry using . CCSD T wavefunctions and first-order perturbation theory applied to the one-electron mass-velocity and Darwin terms. Based on the calculated 324 energy points, a fitted relativistic correction surface is constructed. This surface is used with a high-accuracy ab initio non-relativistic Born-Oppenheimer potential energy surface to calculate the vibrational band origins and rotational term values for H 16 O. These calculations suggest that the relativistic correction, has a stronger influence on 2 the vibration-rotation levels of water than the Born-Oppenheimer diagonal correction. The effect is particularly marked for vibrational levels with bending excitation or rotational states with high K. q 1998 Elsevier Science B.V. All rights a reserved.

The convergence of ab initio predictions to the one- and n-particle limits has been systematically explored for several conformational energy prototypes: the inversion barriers of ammonia, water, and isocyanic acid, the torsional barrier of ethane, the E/Z rotamer separation of formic acid, and the barrier to linearity of silicon dicarbide. Explicit ab initio results were obtained with atomic-orbital basis sets as large as [7s6p5d4f3g2h1i/6s5p4d3f2g1h] and electron correlation treatments as extensive as fifth-order Mo/ller–Plesset perturbation theory (MP5), the full coupled-cluster method through triple excitations (CCSDT), and Brueckner doubles theory including perturbational corrections for both triple and quadruple excitations [BD(TQ)]. Subsequently, basis set and electron correlation extrapolation schemes were invoked to gauge any further variations in arriving at the ab initio limit. Physical effects which are tacitly neglected in most theoretical work have also been quantified by computations of non...

The millimeter-wave spectrum of P2O produced by reacting P-4 vapor with atomic or molecular oxygen directly inside the absorption cell has been observed in 13 vibrational states. Reliable identification of the various vibrationally excited states has been achieved with the help of high-level ab initio calculations resulting in accurate geometric data and an anharmonic force field. Careful analysis of the vibrational levels observed resulted in 13 sets of rotational and centrifugal distortion parameters, which have been used, in turn, to determine the equilibrium rotational, quartic centrifugal distortion, and rovibrational interaction constants of P2O. The 2 nu(1)-nu(3) Fermi resonance has been analyzed. (C) 1997 American Institute of Physics. [S0021-9606(97)01137-9].

The long-standing problem of the topography, energetics, and vibrational dynamics of the ground-state surface of SiC2 is systematically investigated by means of the gamut of state-of-the-art electronic structure methods, including single-reference correlation techniques as extensive as the coupled-cluster singles and doubles method augmented by a perturbative triples term [CCSD(T)], the Brueckner doubles method (BD) with analogous contributions from both triple and quadruple excitations [BD(TQ)], and second-through fifth-order Mo/ller–Plesset perturbation theory (MP2–MP5), as well as the multiconfigurational complete-active-space self-consistent-field [CASSCF(12,12)] approach. The one-particle basis sets for these studies ranged from Si[6s4p1d], C[4s2p1d] to Si[7s6p4d3f2g1h], C[6s5p4d3f2g1h]. The methodological analysis resolves the polytopism problem regarding the mercurial potential energy surface for the circumnavigation of Si+ about C2− in silicon dicarbide, whose topography is shown to exhibit almost...

Several quartic force fields and a full sextic anharmonic force field for H 2 O have been determined from high-quality ab initio calculations, the highest at the aug-cc-pVQZ CCSD(T) level of theory. These force fields have been used to determine vibrational excited state band origins up to 15000 cm −1 above the zero-point level, using both a perturbation-resonance approach and a variational approach. An optimised quartic force field has been obtained by least squares refinement of our best ab initio results to fit the observed overtone levels of 5 symmetrically substituted isotopomers of water (H 2 16 O, H 2 17 O, H 2 18 O, D 2 O, and T 2 O) with an rms error of less than 10 cm −1 , using the perturbation-resonance model for the vibrational calculation. Predicate least squares refinement was used to provide a loose constraint of the refined force field to the ab initio results. The results obtained prove the viability of the perturbation-resonance model for use in larger molecular systems and also highlight some of its weaknesses.

To help future structural characterization of gaseous P2S2 by experimental techniques, accurate relative energies, geometries, rotational, and quartic centrifugal distortion constants, dipole moments, harmonic vibrational frequencies, infrared intensities, and vertical ionization energies have been determined from ab initio calculations for several isomers of P2S2. There are at least five minima identified on the lowest singlet potential energy surface of P2S2. The energy results obtained indicate that a PP-bridged bicyclic (butterfly-type) isomer of C2v symmetry corresponds to the global minimum, while the planar cyclic 4-membered isomers of D2h and C2v symmetries are the second and third most stable isomers, respectively.

Equilibrium molecular structures accurate to 0.001 A and 0.2° have been determined for cis,cis- and trans,trans-1,4-difluorobutadiene by the semiexperimental mixed estimation method. In this method, structures are fitted concurrently to equilibrium rotational constants and bond parameters obtained from an intermediate level of electronic structure theory. The effect of fluorine substitution on the carbon backbone of butadiene is surprisingly small. Definitive energy differences for the ground states were computed, employing the focal-point analysis (FPA) technique, between the trans,trans and cis,cis isomers (ΔH°0 = 5.6(3) kJ mol(-1)) and the cis,trans and cis,cis isomers (ΔH°0 = 3.2(2) kJ mol(-1)) of 1,4-difluorobutadiene. These differences confirm the exceptional relationship that the trans,trans isomer has the highest energy and the cis,cis isomer the lowest energy, endorsing what was reported earlier on the basis of experimental observations in benzene solution.

Accurate equilibrium, re, structures of the monosubstituted benzene molecules benzonitrile, C6H5CN, and phenylacetylene, C6H5CCH, have been determined using two different, to some extent complementary techniques. The semiexperimental, r(e)(SE), structural parameters are the result of a least-squares fit to equilibrium rotational constants derived from experimental effective ground-state rotational constants and rovibrational corrections based principally on an ab initio cubic force field. The composite ab initio Born-Oppenheimer, r(e)(BO), structural parameters are obtained from frozen-core and all-electron MP2 and the CCSD(T) geometry optimizations using Gaussian basis sets up to quintuple-zeta quality. The DFT(B3LYP) method, with two different Gaussian basis sets, 6-31G* and 6-311+G(3df,2pd), was used to calculate the cubic force field employed during the r(e)(SE) structure determination. With the 6-31G* basis set, the error of the rovibrational correction is to a large extent random, whereas with the 6-311+G(3df,2pd) basis set it is mainly systematic. As shown here, systematic errors do not have a significant effect on the accuracy of the derived structure; the quality of the structural fit, however, is sensitive to the true accuracy of the ground-state rotational constants. An even more important general conclusion of this study is that the addition of extra rotational constants from multisubstituted species does not seem to improve the accuracy of the r(e)(SE) structures, quite in contrast to the highly desirable availability of data corresponding to all singly substituted species.

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

International audience; This is the third of a series of articles reporting critically evaluated rotational-vibrational line positions, transition intensities, and energy levels, with associated critically reviewed labels and uncertainties, for all the main isotopologues of water. This paper presents experimental line positions, experimental-quality energy levels, and validated labels for rotational-vibrational transitions of the most abundant isotopologue of water, H216O. The latest version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) line-inversion procedure is used to determine the rovibrational energy levels of the electronic ground state of H216O from experimentally measured lines, together with their self-consistent uncertainties, for the spectral region up to the first dissociation limit. The spectroscopic network of H216O containstwo components, an ortho (o) and a para (p) one. For o-H216O and p-H216O, experimentally measured, assigned, and labeled transitions were analyzed from more than 100 sources. The measured lines come from one-photon spectra recorded at room temperature in absorption, from hot samples with temperatures up to 3000 K recorded in emission, and from multiresonance excitation spectra which sample levels up to dissociation. The total number of transitions considered is 184 667 of which 182 156 are validated: 68 027 between para states and 114 129 ortho ones. These transitions give rise to 18 486 validated energy levels, of which 10 446 and 8040 belong to o-H216O and p-H216O, respectively. The energy levels, including their labeling with approximate normal-mode and rigid-rotor quantum numbers, have been checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators as well as against previous compilations of energy levels. The extensive list of MARVEL lines and levels obtained are deposited in the supplementary data of this paper, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved.

Variational rotational-vibrational quantum chemical computations are performed for the F(-)-CH4 and F(-)-CH2D2 anion complexes using several reduced-dimensional models in a curvilinear polyspherical coordinate system and utilizing an accurate ab initio potential energy surface (PES). The implementation of the models is made practical by using the general rovibrational code GENIUSH, which constructs the complicated form of the exact rovibrational kinetic energy operator in reduced and full dimensions in any user-specified coordinates and body-fixed frames. A one-dimensional CF stretch, 1D(RCF), a two-dimensional intermolecular bend, 2D(θ,φ), and a three-dimensional intermolecular, 3D(RCF,θ,φ), rigid methane model provide vibrational energies for the low-frequency, large-amplitude modes in good agreement with full-dimensional MCTDH results for F(-)-CH4. The 2D(θ,φ) and 3D(RCF,θ,φ) four-well computations, describing equally the four possible CH-F(-) bonds, show that the ground-state tunneling splitting is less than 0.01 cm(-1). For the hydrogen-bonded CH stretching fundamental a local-mode model is found to have almost spectroscopic accuracy, whereas a harmonic frequency analysis performs poorly. The 2D(θ,φ) and 3D(RCF,θ,φ) rotational-vibrational computations on the Td-symmetric four-well PES reveal that in most cases F(-)-CH4 behaves as a semirigid C3v symmetric top. For the degenerate intermolecular bending vibrational states substantial splittings of the rigid rotor levels are observed. For F(-)-CH2D2 the rotational levels guide the assignment of the vibrational states to either F(-)-H or F(-)-D connectivity.

The brace notation, introduced by Allen and Csaszar (1993, J. chem. Phys., 98 2983), provides a simple and compact way to deal with derivatives of arbitrary non-tensorial quantities. One of its main advantages is that it builds the permutational symmetry of the derivatives directly into the formalism. The brace notation is applied to formulate the general nth-order Cartesian derivatives of internal coordinates, and to provide closed forms for general, nth-order transformation equations of anharmonic force fields, expressed as Taylor series, from internal to Cartesian or normal coordinate spaces.

State of the art ab initio techniques of molecular electronic structure theory have been employed to investigate different structural aspects of the electronic states of ketene. Vertical excitation energies of more than 40 singlet and triplet states have been determined from equation‐of‐motion coupled cluster singles and doubles (EOM‐CCSD) and configuration interaction singles (CIS) calculations employing extended basis sets. Most importantly, all singlet and triplet electronic states below 70 000 cm−1, close to the first ionization potential of ketene, 77 500 cm−1 have been determined. Only four pure excited valence states have been identified: the 1 3A1, 2 3A1, 1 3A2, and 1 1A2 states. Vertical ionization energies have also been determined at the EOM‐CCSD level. They are found to be in nice accord with the available experimental results. All lower‐lying members of the Rydberg series of ketene terminating at 77 500 cm−1 are assigned based on theoretical data, symmetry considerations, and use of the Rydberg formula and the available experimental results. High‐quality estimates are given for the possible occurrence of fluorescence emission from the first singlet state of ketene.

Accurate geometries, relative energies, rotational and quartic centrifugal distortion constants, dipole moments, harmonic vibrational frequencies, and infrared intensities have been determined from...

Forms for the exact non-relativistic quantum mechanical vibrational (J = 0) kinetic energy operators for sequentially bonded (A-B-C-D-E) and (A,B)-C-D-E-type penta-atomic molecules, expressed in valence internal coordinates, are presented. As advocated earlier (Handy, N. C., 1987, Molec. Phys., 61, 207), computer algebra has been employed during the derivation. The suggested use of these operators in calculations for vibrational energy levels of interesting penta-atomic molecules (e.g., C3O2, and H2CCO) is outlined.

$Q_{\rm int}$($T$), of the H$_2$$^{16}$O molecule is reported for temperatures between 0 and 6000 K. Determination of $Q_{\rm int}$($T$) is principally based on the direct summation technique involving all accurate experimental energy levels known for H$_2$$^{16}$O (almost 20~000 rovibrational energies including an almost complete list up to a relative energy of 7500 \cm), augmented with a less accurate but complete list of first-principles computed rovibrational energy levels up to the first dissociation limit, about 41~000 \cm\ (the latter list includes close to one million bound rovibrational energy levels up to $J = 69$, where $J$ is the rotational quantum number). Partition functions are developed for {\it ortho}- and {\it para}-H$_2$$^{16}$O as well as for their equilibrium mixture. Unbound rovibrational states above the first dissociation limit are considered using an approximate model treatment. The effect of the excited electronic states on the thermochemical functions is neglected, as their contribution to the thermochemical functions is negligible even at the highest temperatures considered. Based on the high-accuracy $Q_{\rm int}$($T$) and its first two moments, definitive results, in 1~K increments, are obtained for the following thermochemical functions: Gibbs energy, standardized enthalpy, entropy, and isobaric heat capacity. Reliable approximately two standard deviation uncertainties, as a function of temperature, are estimated for each quantity determined. These uncertainties emphasize that the present results are the most accurate ideal-gas thermochemical functions ever produced for H$_2$$^{16}$O. It is recommended that the new value determined for the standard molar enthalpy increment at 298.15~K, $9.90404 \pm 0.00001$ kJ~mol$^{-1}$, should replace the old CODATA datum, $9.905 \pm 0.005$ kJ~mol$^{-1}$., J. Phys. Chem. Ref. Data (in press)

The full nonrelativistic quantum mechanical vibrational (J=0) kinetic energy operator for sequentially bonded N‐atom molecules, expressed in valence stretch, bend, and torsion internal coordinates, is explicitly given. Certain properties of the operator and its possible applications are discussed.

Variational nuclear motion computations, employing an exact kinetic energy operator and two different potential energy surfaces, are performed to study the first 60 vibrational states of the molecular ion H5 (+)≡ [H2-H-H2](+) and all of its deuterated isotopologues and isotopomers, altogether 12 species. Detailed investigation of the vibrational wavefunctions mostly results in physically intuitive labels not only for the fundamentals but also for the overtone and combination states computed. The torsional motion associated with the left and right diatomics appears to be well separated from the other vibrational degrees of freedom for all species. The unusual structure of the higher-lying bending states and the heavy mixing of the internal motions is partly due to the astructural character of all these molecular ions. The existence of distinct isotopomers in the H5-nDn (+), n = 1-4 cases, in the energy range studied, is confirmed. Two rules determine the stability order of the isotopomers: first, when possible, H prefers to stay in the middle of the ions rather than at the sides, and, second, the isotopomer with a homonuclear diatomic at the side is always lower in energy. The large number of precise vibrational energies of the present study, as well as the detailed assignment of the states, should serve as benchmarks for future studies by more approximate nuclear-motion treatments, such as diffusion Monte Carlo and multiconfiguration time-dependent Hartree.

Correlated-level ab initio calculations, including large basis set MP2, have been performed for several conformers of the neutral forms of the amino acids glycine and α-alanine. These calculations resulted in accurate geometric structures and relative energies for the conformers considered. The structural results obtained support the rotational constants measured for the lowest-lying two conformers of both glycine and α-alanine. Energetic and structural results, however, indicate necessary model improvements for existing gas-phase electron diffraction studies of these simplest amino acids. The calculations performed also reveal that, in contrast to what has recently been suggested for this class of compound (R.F. Frey, J. Coffin, S.Q. Newton, M. Ramek, V.K.W. Cheng, F.A. Momany and L. Schafer, J. Am. Chem. Soc., 114 (1992) 5369), correlated-level geometry optimizations can usually be avoided even if nearly quantitative accuracy is sought in relative energy predictions for the conformers.