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On the basis of both experiment and theory, accurate rotational–vibrational line positions and energy levels, with associated critically reviewed labels and uncertainties, are reported for the ground electronic state of the H3+ molecular ion. An improved MARVEL algorithm is used to determine the validated experimental levels and their self-consistent uncertainties from a set of 1610 measured transitions and associated uncertainties, coming from 26 sources. 1410 transitions have been validated for ortho-H3+ and para-H3+, 78 belong to floating components of the spectroscopic network (SN) investigated and thus left unvalidated, while 122 measured transitions had to be excluded from the MARVEL analysis for one reason or another. The spectral range covered by the experiments is 7–16 506 cm–1 . Altogether 13 vibrational band origins are reported, the highest J value, where J stands for the rotational quantum number, for which energy levels are validated is 12. The MARVEL energy levels are checked against ones d...

A complex coordinate scaling (CCS) method is described allowing the quantum chemical computation of quasibound (also called resonance or metastable) rovibrational states of strongly bound triatomic molecules. The molecule chosen to test the method is H2 16O, for which an accurate global potential energy surface, a previous computation of a few resonance states via the complex absorbing potential (CAP) method, and some Feshbach (J = 0, where J is the quantum number characterising overall rotations of the molecule) and shape (J ≠ 0) resonances measured via a state-selective, triple-resonance technique are all available. Characterisation of the computed resonance states is performed via probability density plots based on CCS rovibrational wavefunctions. Such plots provide useful details about the physical nature of the resonance states. Based on the computations and the resonance plots, the following useful facts about the resonance states investigated are obtained: (a) Feshbach resonances are formed by accu...

Born−Oppenheimer equilibrium structure (r BO e) estimates are reported for benzene and all 12 possible fluorobenzenes, based on geometry optimizations performed at the coupled cluster level of electronic structure theory including single and double excitations augmented by a perturbational estimate of the effects of connected triple excitations [CCSD(T)] and Gaussian basis sets of at least triple zeta quality. Furthermore, accurate semiexperimental equilibrium (r SE e) structures are determined for C6H6, C6H5F, and 1,2- and 1,3-difluorobenzene. They are obtained through a least-squares structural refinement procedure based on equilibrium rotational constants of as many isotopologues as feasible, determined by correcting experimental vibrationally averaged ground-state rotational constants with computed ab initio vibration–rotation interaction constants and electronic g-factors, and using a few structural constraints based on the best r BO e estimates. The r BO e and r SE e equilibrium structures are in ex...

The current status of the W@DIS information system used for the systematization of spectroscopic data, including rovibronic transitions and energy levels, and data sources is reviewed, where the abbreviation W@DIS stands for Water Internet @ccesible Distributed Information System. Functionalities of W@DIS are outlined. The primary emphasis of W@DIS is on properties of data sources characterizing data quality. Several examples describe the interfaces used to create molecular spectral line lists and representation of binary relations between data sources and typical individuals of the ontology of information resources, states and transitions. The discussion employs the water molecule as an example.

Quantum mechanics builds large-scale graphs (networks): the vertices are the discrete energy levels the quantum system possesses, and the edges are the (quantum-mechanically allowed) transitions. Parts of the complete quantum mechanical networks can be probed experimentally via high-resolution, energy-resolved spectroscopic techniques. The complete rovibronic line list information for a given molecule can only be obtained through sophisticated quantum-chemical computations. Experiments as well as computations yield what we call spectroscopic networks (SN). First-principles SNs of even small, three to five atomic molecules can be huge, qualifying for the big data description. Besides helping to interpret high-resolution spectra, the network-theoretical view offers several ideas for improving the accuracy and robustness of the increasingly important information systems containing line-by-line spectroscopic data. For example, the smallest number of measurements necessary to perform to obtain the complete list of energy levels is given by the minimum-weight spanning tree of the SN and network clustering studies may call attention to "weakest links" of a spectroscopic database. A present-day application of spectroscopic networks is within the MARVEL (Measured Active Rotational-Vibrational Energy Levels) approach, whereby the transitions information on a measured SN is turned into experimental energy levels via a weighted linear least-squares refinement. MARVEL has been used successfully for 15 molecules and allowed to validate most of the transitions measured and come up with energy levels with well-defined and realistic uncertainties. Accurate knowledge of the energy levels with computed transition intensities allows the realistic prediction of spectra under many different circumstances, e.g., for widely different temperatures. Detailed knowledge of the energy level structure of a molecule coming from a MARVEL analysis is important for a considerable number of modeling efforts in chemistry, physics, and engineering.

The rovibrational eigenenergy set of molecular systems is a key feature needed to understand and model elementary chemical reactions. A unique class of molecular systems, represented by an ${}^{4}{A}^{\ensuremath{'}\ensuremath{'}}$ excited electronic state of the ${[\mathrm{H},\mathrm{S},\mathrm{N}]}^{\ensuremath{-}}$ system comprising several distinct dipole-bound isomers, is found to contain both bent and linear minima separated by relatively small barriers. Full-dimensional nuclear-motion computations performed in Jacobi coordinates using three-dimensional potential energy surfaces describing the stable isomers and the related transition states yield rovibrational eigenstates located both below and above the barriers. The rovibrational wave functions are well localized, regardless of whether the state's energy is below or above the barriers. We also show that the states preserve the memory of the isomeric forms they ``originate from,'' which is signature of a strong vibrational memory effect above isomerization barriers.

International audience; The variational nuclear-motion codes ElVibRot and GENIUSH have been used to compute rotational-vibrational states of the F-(H2O) anion and its deuterated isotopologue, F-(D2O), employing a full-dimensional, semiglobal potential energy surface (PES) called SLBCL, developed as part of this study for the ground electronic state of the complex. The PES is determined from all-electron, explicitly correlated coupled-cluster singles, doubles, and connected triples [CCSD(T)-F12a] computations with an atom-centered, fixed-exponent Gaussian basis set of cc-pCVTZ-F12 quality. The SLBCL PES accurately reproduces the two equivalent minima of the complex, the corresponding transition barrier of C2v point-group symmetry, as well as the proton transfer and the dissociation asymptotes towards the products HF + OH- and F- + H2O, respectively. The code ElVibRot has been updated so that it can use curvilinear internal coordinates corresponding to a reaction path. The variationally computed vibrational energy levels are compared to relevant experimental and previously determined first-principles results. The vibrational states reveal the presence of pronounced anharmonic effects and considerable intermode couplings resulting in strong resonances, involving in particular the HOH bend and ionic OH stretch motions. Tunneling results in particularly significant splittings for F-(H2O); as expected, the splittings are orders of magnitude smaller for the F-(D2O) molecule. The rovibrational energy levels reveal that, despite the large-amplitude vibrational motions, the rotations of F-(H2O) basically follow rigid-rotor characteristics.

The molecular ion is the simplest polyatomic and poly-electronic molecular system, and its spectrum constitutes an important benchmark for which precise answers can be obtained ab initio from the equations of quantum mechanics. Significant progress in the computation of the ro–vibrational spectrum of is discussed. A new, global potential energy surface (PES) based on ab initio points computed with an average accuracy of 0.01 cm −1 relative to the non-relativistic limit has recently been constructed. An analytical representation of these points is provided, exhibiting a standard deviation of 0.097 cm −1 . Problems with earlier fits are discussed. The new PES is used for the computation of transition frequencies. Recently measured lines at visible wavelengths combined with previously determined infrared ro–vibrational data show that an accuracy of the order of 0.1 cm −1 is achieved by these computations. In order to achieve this degree of accuracy, relativistic, adiabatic and non-adiabatic effects must be properly accounted for. The accuracy of these calculations facilitates the reassignment of some measured lines, further reducing the standard deviation between experiment and theory.

Based on a sample of 38 molecules, 47 accurate equilibrium CO bond lengths have been collected and analyzed. These ultimate experimental ( r e EX ) , semiexperimental ( r e SE ) , and Born–Oppenheimer ( r e BO ) equilibrium structures are compared to r e BO estimates from two lower-level techniques of electronic structure theory, MP2(FC)/cc-pVQZ and B3LYP/6-311+G(3df,2pd). A linear relationship is found between the best equilibrium bond lengths and their MP2 or B3LYP estimates. These (and similar) linear relationships permit to estimate the CO bond length with an accuracy of 0.002 A within the full range of 1.10–1.43 A, corresponding to single, double, and triple CO bonds, for a large number of molecules. The variation of the CO bond length is qualitatively explained using the Atoms in Molecules method. In particular, a nice correlation is found between the CO bond length and the bond critical point density and it appears that the CO bond is at the same time covalent and ionic. Conditions which permit the computation of an accurate ab initio Born–Oppenheimer equilibrium structure are discussed. In particular, the core–core and core–valence correlation is investigated and it is shown to roughly increase with the bond length.

When determining energy levels from several, in cases many, measured and assigned high-resolution molecular spectra according to the Ritz principle, it is advantageous to investigate the spectra via the concept of spectroscopic networks (SNs). Experimental SNs are finite, weighted, undirected, multiedge, rooted graphs, whereby the vertices are the energy levels, the edges are the transitions, and the weights are provided by transition intensities. A considerable practical problem arises from the fact that SNs can be very large for isotopologues of molecules widely studied; for example, the experimental dataset for the H2 16O molecule contains some 160,000 measured transitions and 20,000 energy levels. In order to treat such large SNs and extract the maximum amount of information from them, sophisticated algorithms are needed when inverting the transition data. To achieve numerical effectiveness, we found the following efficient algorithms applicable to very large SNs: reading the input data employs hash codes, building the components of the SN utilizes a recursive depth-first search algorithm, solving the linear least-squares problem is via the conjugate gradient method, and determination of the uncertainties of the energy levels takes advantage of the robust reweighting algorithm.

Given the large energy required for its electronic excitation, the most important properties of the water molecule are governed by its ground potential energy surface (PES). Novel experiments are now able to probe this surface over a very extended energy range, requiring new theoretical procedures for their interpretation. As part of this study, a new, accurate, global spectroscopic-quality PES and a new, accurate, global dipole moment surface are developed. They are used for the computation of the high-resolution spectrum of water up to the first dissociation limit and beyond as well as for the determination of Stark coefficients for high-lying states. The water PES has been determined by combined ab initio and semi-empirical studies. As a first step, a very accurate, global, ab initio PES was determined using the all-electron, internally contracted multi-reference configuration interaction technique together with a large Gaussian basis set. Scalar relativistic energy corrections are also determined in order to move the energy determinations close to the relativistic complete basis set full configuration interaction limit. The electronic energies were computed for a set of about 2500 geometries, covering carefully selected configurations from equilibrium up to dissociation. Nuclear motion computations using this PES reproduce the observed energy levels up to 39 000 cm −1 with an accuracy of better than 10 cm −1 . Line positions and widths of resonant states above dissociation show an agreement with experiment of about 50 cm −1 . An improved semi-empirical PES is produced by fitting the ab initio PES to accurate experimental data, resulting in greatly improved accuracy, with a maximum deviation of about 1 cm −1 for all vibrational band origins. Theoretical results based on this semi-empirical surface are compared with experimental data for energies starting at 27 000 cm −1 , going all the way up to dissociation at about 41 000 cm −1 and a few hundred wavenumbers beyond it.

Due to its crucial importance, numerous studies have been conducted to determine the enthalpy difference between the conformers of butane. However, it is shown here that the most reliable experimental values are biased due to the statistical model utilized during the evaluation of the raw experimental data. In this study, using the appropriate statistical model, both the experimental expectation values and the associated uncertainties are revised. For the 133-196 and 223-297 K temperature ranges, 668 ± 20 and 653 ± 125 cal mol(-1), respectively, are recommended as reference values. Furthermore, to show that present-day quantum chemistry is a favorable alternative to experimental techniques in the determination of enthalpy differences of conformers, a focal-point analysis, based on coupled-cluster electronic structure computations, has been performed that included contributions of up to perturbative quadruple excitations as well as small correction terms beyond the Born-Oppenheimer and nonrelativistic approximations. For the 133-196 and 223-297 K temperature ranges, in exceptional agreement with the corresponding revised experimental data, our computations yielded 668 ± 3 and 650 ± 6 cal mol(-1), respectively. The most reliable enthalpy difference values for 0 and 298.15 K are also provided by the computational approach, 680.9 ± 2.5 and 647.4 ± 7.0 cal mol(-1), respectively.

Equilibrium structures, r(e), of the heterocyclic molecules oxirane, furazan, furan, ethylene ozonide, and 1,3,4-oxadiazole have been determined using three different, somewhat complementary techniques: a completely experimental technique (r(m)), a semiexperimental technique (r(e)(SE), whereby equilibrium rotational constants are derived from experimental effective ground-state rotational constants and corrections based principally on an ab initio cubic force field), and an ab initio technique (r(e)(BO), whereby geometry optimizations are usually performed at the coupled cluster level of theory including single and double excitations augmented by a perturbational estimate of the effects of connected triple excitations [CCSD(T)] using quadruple-ζ Gaussian basis sets). All these molecules are asymmetric tops with the moment of inertia I(c) much larger than the other two moments of inertia, I(a) and I(b). Molecules of this shape experience a large rotation of the principal axis system upon certain isotopic substitutions. For such isotopologues it is difficult to obtain a good structural fit to the semiexperimental moments of inertia I(a) and I(b), which may significantly reduce the accuracy of the r(e)(SE) structural parameters. The origin of this difficulty is explained. For the heavy-atom skeleton of these molecules it was possible to determine a rather accurate empirical mass-dependent structure without a priori knowledge of the equilibrium structure.

An anharmonic force field is defined as a higher-order Taylor-series expansion of the molecular potential energy surface (PES) around a reference geometry, usually chosen to be an equilibrium structure. Force field expansions provide excellent local approximations to PESs, one of the most important theoretical constructs of chemistry. This review deals principally with the definition and physical interpretation of anharmonic molecular force fields, their determination via techniques of electronic structure theory, their transformation among different rectilinear and curvilinear representations, and their utilization. Physical and technical factors leading to more precise and more accurate force fields are also discussed. © 2011 John Wiley & Sons, Ltd.

Several approximately variational grid-based representation techniques devised to solve the time-independent nuclear-motion Schrodinger equation share a similar behavior: while the computed eigenpairs, the only results which are of genuine interest, are accurate, many of the underlying Hamiltonian matrix elements are inaccurate, deviating substantially from their values in a variational basis representation. Examples are presented for the discrete variable representation and the Lagrange-mesh approaches, demonstrating that highly accurate eigenvalues and eigenfunctions can be obtained even if some or even all of the Hamiltonian matrix elements in these grid-based representations are inaccurate. It is shown how the apparent contradiction of obtaining accurate eigenpairs with far less accurate individual matrix elements can be resolved by considering the unitary transformation between the representations. Furthermore, the relations connecting orthonormal bases and the corresponding Lagrange bases are generalized to relations connecting nonorthogonal, regularized bases and the corresponding nonorthogonal, regularized Lagrange bases.

High-level ab initio electronic structure and variational nuclear motion computations are combined to simulate the spectrum of the water molecule at and above its first dissociation limit. Results of these computations are compared with the related state-selective multi-photon measurements of Grechko et al. [J. Chem. Phys. 138 (2010) 081 103]. Both measured and computed spectra show pronounced structures due to quasi-bound (resonance) states. Traditional resonance features associated with trapping of vibrational or rotational energy of the system are identified and assigned. A strong and broad feature observed slightly above dissociation is found to be associated with direct photodissociation into the continuum.

The principal purpose of this investigation is the determination of the tunneling half-lives of the trans-HCSH → H2CS and the trans-HCSeH → H2CSe unimolecular isomerization reactions at temperatures close to 0 K. To aid these determinations, accurate electronic structure computations were performed, with electron correlation treatments as extensive as CCSDT(Q) and basis sets as large as aug-cc-pCV5Z, for the isomers of [H,H,C,S] and [H,H,C,Se] on their lowest singlet surfaces and for the appropriate transition states yielding structural data for key stationary points characterizing the isomerization reactions. The computational results were subjected to a focal-point analysis (FPA) that yields accurate relative energies with uncertainty estimates. The tunneling half-lives were determined by a simple Eckart-barrier approach and via the more sophisticated though still one-dimensional Wentzel–Kramers–Brillouin (WKB) approximation. Only stationary-point information is needed for the former while an intrinsic reaction path (IRP) is necessary for the latter approach. Both protocols suggest that, unlike for the parent hydroxymethylene (HCOH), at the low temperatures of matrix isolation experiments no tunneling will be observable for the trans-HCSH and trans-HCSeH systems.

This is the second of a series of articles 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 article presents Preprint submitted to Journal of Quantitative Spectroscopy & Radiative Transfer10th June 2010 energy levels and line positions of the following singly deuterated isotopologues of water: HD16O, HD17O, and HD18O. 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 0–22 708, 0–1 674, and 0–12 105 cm−1 for HD16O, HD17O, and HD18O, respectively. For HD16O, 54 740 transitions were analyzed from 76 sources, the lines come from spectra recorded both at room temperature and from hot samples. These lines correspond to 36 690 distinct assignments and 8 818 energy levels. For HD17O, only 485 transitions could be analyzed from 3 sources; the lines correspond to 162 MARVEL energy levels. For HD18O, 8 729 transitions were analyzed from 11 sources and these lines correspond to 1 860 energy levels. The energy levels are checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators. This comparison shows that the measured transitions account for about 86 % of the anticipated absorbance of HD16O at 296 K and that the transitions predicted by the MARVEL energy levels account for essentially all the remaining absorbance. The extensive list of MARVEL lines and levels obtained are given in the Supplementary Material of this article, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved. In addition, the transition and energy level information for H2 17O and H2 18O, given in the first paper of this series [J. Quant. Spectr. Rad. Transfer 110 (2009) 573-596], has been updated. Key words: Water vapor, transition wavenumbers, atmospheric physics, energy levels, MARVEL, information system, database, W@DIS, infrared spectra, microwave spectra, HD16O, HD17O, HD18O

The two lowest-energy gas-phase conformers, Ala-I and Ala-IIA, of the natural amino acid L-alanine (Ala) have been investigated by means of rigorous ab initio computations. Born-Oppenheimer (BO) equilibrium structures (re ) were fully optimized at the coupled-cluster (CCSD(T)/cc-pVTZ) level of electronic structure theory. Corresponding semiexperimental (SE) equilibrium structures (re ) of each conformer were determined for the first time by least-squares refinement of 11-15 structural parameters on modified, experimental rotational constant data from 10 isotopologues. The SE equilibrium rotational constants were obtained by, first, refitting Fourier transform microwave spectra using the method of predicate observations and, second, correcting the resulting effective rotational constants with theoretical vibration-rotation interaction constants (Ri). Careful analysis is made of the procedures to account for vibrational distortion, which proves essential to defining precise structures in flexible molecules such as Ala. Because Ala possesses no symmetry, has several large-amplitude nuclear motions, and exhibits conformers with different hydrogen bonding patterns, it is one of the most difficult cases where reliable equilibrium structures have now been determined. The relative energy of the alanine conformers was pinpointed using first-principles composite focal point analyses (FPA), which employed extrapolations using basis sets as large as aug-cc-pV5Z and electron correlation treatments as extensive as CCSD(T). The FPA computations place the Ala-IIA equilibrium structure higher in energy than that of Ala-I by a mere 0.45 kJ mol -1 (38 cm -1 ), showing that the two lowest-lying conformers of alanine are nearly isoenergetic; inclusion of zero-point vibrational energy increases the relative energy to 2.11 kJ mol -1 (176 cm -1 ). The yet unobserved Ala-IIB conformer is found to be separated from Ala-IIA by a vibrationally adiabatic isomerization barrier of only 16 cm -1 .

A simple and fast, weighted, linear least-squares refinement protocol and code is presented for inverting the information contained in a network of quantum chemically computed 0 K reaction enthalpies. This inversion yields internally consistent 0 K enthalpies of formation for the species of the network. The refinement takes advantage of the fact that the accuracy of computed enthalpies depends strongly on the quantum-chemical protocol employed for their determination. Different protocols suffer from different sources of error; thus, the reaction enthalpies computed by them have "random" residual errors. Since it is much more natural for quantum-chemical energy and enthalpy results, including reaction enthalpies, to be based on the electronic ground states of the atoms and not on the historically preferred elemental states, and since these two possible protocols can be converted into each other straightforwardly, it is proposed that first-principles thermochemistry should employ the ground electronic states of atoms. In this scheme, called atom-based thermochemistry (AT), the enthalpy of formation of a gaseous compound corresponds simply to the total atomization energy of the species; it is always positive, and it reflects the bonding strength within the molecule. The inversion protocol developed and based on AT is termed NEAT, which represents the fact that the protocol proceeds from a network of computed reaction enthalpies toward atom-based thermochemistry, most directly to atom-based enthalpies of formation. After assembling a database that consisted of 361 ab initio reactions and reaction enthalpies involving 188 species, collected from 31 literature sources, the following dependable 0 K atom-based enthalpies of formation, Delta(f)${H{{{\rm AT}\hfill \atop 0\hfill}}}$, all in kJ mol(-1), have been obtained by means of NEAT: H(2)=432.07(0), CH=334.61(15), NH=327.69(25), OH=425.93(21), HF=566.13(31), CO=1072.08(28), O(2)=493.51(34), CH(2)=752.40(21), H(2)O=918.05(20), HO(2)=694.53(32), CO(2)=1597.77(40), CH(3)=1209.64(29), NH(3)=1157.44(33), C(2)H(2)=1625.78(40), and CH(4)=1641.68(40), in which the uncertainty values given in parentheses represent 95 % confidence intervals. The average deviation of these values from the well-established active thermochemical tables (ATcT) values is a mere 0.25 kJ mol(-1), with a maximum deviation of 0.7 kJ mol(-1). This shows that the use of a large number of ab initio reaction enthalpies within a NEAT-type protocol has considerable advantages over the sequential utilization of the ab initio information.

The Born–Oppenheimer (BO) equilibrium molecular structure (r BO e )o fcis-methyl formate has been determined at the CCSD(T) level of electronic structure theory using Gaussian basis sets of at least quadruple-f quality and a core correlation correction. The quadratic, cubic and semi-diagonal quartic force field in normal coordinates has also been computed at the MP2 level employing a basis set of triple-f quality. A semi-experimental equilibrium structure (r SE e ) has been derived from experimental ground-state rotational constants and the lowest-order rovibrational interaction parameters calculated from the ab initio cubic force field. To determine r SE e structures, it is important to start from accurate ground-state rotational constants. Different spectroscopic methods, applicable in the presence of internal rotation and used in the literature to obtain ‘‘unperturbed” rotational constants from the analysis and fitting of the spectrum, are reviewed and compared. They are shown to be compatible though their precision may be different. The r BO e and r SE e structures are in good agreement showing that, in the particular case of cis-methyl formate, the methyl torsion can still be treated as a small-amplitude vibration. The best equilibrium structure obtained for cis-methyl formate is: r(Cm–O) = 1.434 A, r(O–Cc) = 1.335 A, r(Cm–Hs) = 1.083 A, r(Cm– Ha) = 1.087 A, r(Cc–H) = 1.093 A, r(C@O) = 1.201 A, \(COC) = 114.4, \(CCHs) = 105.6, \(CCHa) = 110.2, \(OCH) = 109.6, \(OCO) = 125.5, and s(HaCOC) = 60.3. The accuracy is believed to be about 0.001 A for the bond lengths and 0.1 for the angles.

We estimated the post-Born–Oppenheimer (post-BO) contribution to electric dipole moments by finite-field derivatives of the diagonal Born–Oppenheimer correction computed with correlated electronic wave functions. The new method is used to examine the effect of isotopic substitution on the dipole moments of the HD, LiH, LiD, and H2 16O molecules. The non-zero dipole moment of HD is solely due to the post-BO effect and is predicted within a few percent of the best experimental and theoretical results. The post-BO contribution to the dipole moment in LiH and LiD is comparable in magnitude to that in HD, but the difference in total adiabatic dipole moments of LiH and LiD is dominated by the vibrationally averaged BO contribution, and the post-BO contribution is relatively unimportant. However, the post-BO contribution to the dipole moment in H2O is much larger than the vibrationally averaged BO contribution determined by Lodi et al. [J. Chem. Phys. 128, 044304 (2008)] and is twice as large as the discrepancy ...

Following an extensive search on the potential energy surfaces (PES) of the natural amino acid L-threonine (Thr) and its allotropic form L-allo-threonine (aThr), 56 and 61 conformers of Thr and aThr, respectively, have been located with the help of density functional theory (DFT). Accurate structures, relative energies, rotational as well as quartic and sextic centrifugal distortion constants, dipole moments, 14N nuclear quadrupole coupling constants, anharmonic vibrational frequencies and double-harmonic infrared intensities have been determined from ab initio electronic structure calculations for the five most stable Thr and aThr conformers. The global minimum, Thr-I, has a cyclic triple H-bond motif with strong OH ··· N, C=O ··· HO, and a weaker NH ··· OH H-bond, where the latter two involves the side chain OH, and an energetically unfavourable trans-COOH arrangement. The best relative energies of the conformers, accurate within ±1 kJ mol−1, have been determined through the first-principles composite f...

The proton affinity and the enthalpy of formation of the prototypical carbonyl, formaldehyde, have been determined by the first-principles composite focal-point analysis (FPA) approach. The electronic structure computations employed the all-electron coupled-cluster method with up to single, double, triple, quadruple, and even pentuple excitations. In these computations the aug-cc-p(C)VXZ [X = 2(D), 3(T), 4(Q), 5, and 6] correlation-consistent Gaussian basis sets for C and O were used in conjunction with the corresponding aug-cc-pVXZ (X = 2–6) sets for H. The basis set limit values have been confirmed via explicitly correlated computations. Our FPA study supersedes previous computational work for the proton affinity and to some extent the enthalpy of formation of formaldehyde by accounting for (a) electron correlation beyond the “gold standard” CCSD(T) level; (b) the non-additivity of core electron correlation effects; (c) scalar relativity; (d) diagonal Born–Oppenheimer corrections computed at a correlated level; (e) anharmonicity of zero-point vibrational energies, based on global potential energy surfaces and variational vibrational computations; and (f) thermal corrections to enthalpies by direct summation over rovibrational energy levels. Our final proton affinities at 298.15 (0.0) K are ΔpaHo (H2CO) = 711.02 (704.98) ± 0.39 kJ mol−1. Our final enthalpies of formation at 298.15 (0.0) K are ΔfHo (H2CO) = −109.23 (−105.42) ± 0.33 kJ mol−1. The latter values are based on the enthalpy of the H2 + CO H2CO reaction but supported by two further reaction schemes, H2O + C H2CO and 2H + C + O H2CO. These values, especially ΔpaHo (H2CO), have better accuracy and considerably lower uncertainty than the best previous recommendations and thus should be employed in future studies. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Converged first-principles proton affinities (PA) of ammonia and carbon monoxide have been determined by the focal-point analysis (FPA) approach, thus fixing the high and low ends of the molecular proton affinity scale. The electronic structure computations employed the all-electron (AE) coupled-cluster (CC) method up to single, double, triple, quadruple, and pentuple excitations. Aug-cc-pCVXZ [X = 2(D), 3(T), 4(Q), 5, and 6] correlation-consistent (cc) Gaussian basis sets for C, N, and O were used in conjunction with the corresponding aug-cc-pVXZ (X = 2-6) sets for H. Our FPA study supersedes previous computational work by accounting for (a) electron correlation beyond the "gold standard" CCSD(T) level; (b) the nonadditivity of core electron correlation effects; (c) scalar relativity; (d) diagonal Born-Oppenheimer corrections (DBOC); (e) anharmonicity of zero-point vibrational energies, based on accurate AE-CCSD(T)/cc-pCVQZ internal coordinate quartic force fields and fully variational vibrational computations; and (f) thermal corrections to enthalpies by direct summation over rovibrational energy levels. Our final proton affinities at 298.15(0.0) K are ΔpaH°(NH3) = 852.6(846.4) ± 0.3 kJ mol(-1) and ΔpaH°(CO) = 592.4(586.5) ± 0.2 kJ mol(-1). These values have better accuracy and considerably lower uncertainty than the best previous recommendations and thus anchor the proton affinity scale of molecules for future use.

Singlet carbenes exhibit a divalent carbon atom whose valence shell contains only six electrons, four involved in bonding to two other atoms and the remaining two forming a non-bonding electron pair. These features render singlet carbenes so reactive that they were long considered too short-lived for isolation and direct characterization. This view changed when it was found that attaching the divalent carbon atom to substituents that are bulky and/or able to donate electrons produces carbenes that can be isolated and stored. N-heterocyclic carbenes are such compounds now in wide use, for example as ligands in metathesis catalysis. In contrast, oxygen-donor-substituted carbenes are inherently less stable and have been less studied. The pre-eminent case is hydroxymethylene, H-C-OH; although it is the key intermediate in the high-energy chemistry of its tautomer formaldehyde, has been implicated since 1921 in the photocatalytic formation of carbohydrates, and is the parent of alkoxycarbenes that lie at the heart of transition-metal carbene chemistry, all attempts to observe this species or other alkoxycarbenes have failed. However, theoretical considerations indicate that hydroxymethylene should be isolatable. Here we report the synthesis of hydroxymethylene and its capture by matrix isolation. We unexpectedly find that H-C-OH rearranges to formaldehyde with a half-life of only 2 h at 11 K by pure hydrogen tunnelling through a large energy barrier in excess of 30 kcal mol(-1).

The protocol MARVEL, standing for measured active rotational–vibrational energy levels, is used to study high-accuracy measurements of rotational lines of four isotopologues of water, H 2 16 O , H 2 17 O , H 2 18 O , and D 2 16 O , obtained by spectroscopy in the far-infrared (FIR) region of 15–170 cm−1 by Matsushima et al. [Matsushima F, Odashima H, Iwasaki T, Tsunekawa S, Takagi K. Frequency measurement of pure rotational transitions of H2O from 0.5 to 5 THz. J Mol Struct 1995; 352/353, 371–8; Matsushima F, Nagase H, Nakauchi T, Odashima H, Takagi K. Frequency measurement of pure rotational transitions of H 2 17 O and H 2 18 O from 0.5 to 5 THz. J Mol Spectrosc 1999;193: 217–23; Matsushima F, Matsunaga M, Qian GY, Ohtaki Y, Wang RL, Takagi K. Frequency measurement of pure rotational transitions of D2O from 0.5 to 5 THz. J Mol Spectrosc 2001;206: 41–6; Matsushima F, Tomatsu N, Nagai T, Moriwaki Y, Takagi K. Frequency measurement of pure rotational transitions in the v2=1 state of H2O. J Mol Spectrosc 2006;235: 190–5]. MARVEL validates the high accuracy of most of the measured line positions. It results in a considerable number of energy levels with an average internal uncertainty of only 40 kHz (2σ). It also supports serious inaccuracy problems when Watson-type A-reduced Hamiltonians are used for predicting the highly accurate rotational measurements for water. Finally, MARVEL suggests a large number of para-water levels, for example 41 for H 2 16 O , which are candidates for becoming frequency standards in the FIR region of 15–170 cm−1 (the 0.5–5 THz window) when an accuracy of about 0.1 MHz is deemed to be sufficient.

An algorithm is proposed, based principally on an earlier proposition of Flaud and co-workers [Mol. Phys. 32 (1976) 499], that inverts the information contained in uniquely assigned experimental rotational–vibrational transitions in order to obtain measured active rotational–vibrational energy levels (MARVEL). The procedure starts with collecting, critically evaluating, selecting, and compiling all available measured transitions, including assignments and uncertainties, into a single database. Then, spectroscopic networks (SN) are determined which contain all interconnecting rotational–vibrational energy levels supported by the grand database of the selected transitions. Adjustment of the uncertainties of the lines is performed next, with the help of a robust weighting strategy, until a self-consistent set of lines and uncertainties is achieved. Inversion of the transitions through a weighted least-squares-type procedure results in MARVEL energy levels and associated uncertainties. Local sensitivity coefficients could be computed for each energy level. The resulting set of MARVEL levels is called active as when new experimental measurements become available the same evaluation, adjustment, and inversion procedure should be repeated in order to obtain more dependable energy levels and uncertainties. MARVEL is tested on the example of the H2 17 O isotopologue of water and a list of 2736 depend

A list of proteins is given for which spatial structures, with a resolution better than 2.5 A, are known from entries in the Protein Data Bank (PDB) and isotropic chemical shift (ICS) values are known from the RefDB database related to the Biological Magnetic Resonance Bank (BMRB) database. The structures chosen provide, with unknown uncertainties, dihedral angles φ and ψ characterizing the backbone structure of the residues. The joint use of experimental ICSs of the same residues within the proteins, again with mostly unknown uncertainties, and ab initio ICS(φ,ψ) surfaces obtained for the model peptides For–(l-Ala) n –NH2, with n = 1, 3, and 5, resulted in so-called empirical ICS(φ,ψ) surfaces for all major nuclei of the 20 naturally occurring α-amino acids. Out of the many empirical surfaces determined, it is the $$^{13}\hbox{C}^{\alpha}$$ ICS(φ,ψ) surface which seems to be most promising for identifying major secondary structure types, α-helix, β-strand, left-handed helix (αD), and polyproline-II. Detailed tests suggest that Ala is a good model for many naturally occurring α-amino acids. Two-dimensional empirical $$^{13}\hbox{C}^{\alpha}$$ – $$^{1}\hbox{H}^{\alpha}$$ ICS(φ,ψ) correlation plots, obtained so far only from computations on small peptide models, suggest the utility of the experimental information contained therein and thus they should provide useful constraints for structure determinations of proteins.

Fully variational energies and structures are obtained for the few-electron prototypical atomic and molecular systems H þ ,H 2, HHe + , H þ , Be, and LiH at the Hartree–Fock basis-set limit (HFL). The HFL computations are made possible by a global optimization technique employing analytic derivatives of the energy with respect to nuclear centers as well as to positions and exponents of Gaussian-type basis functions (GTF). The efficiency of the procedure presented means that the HFL structure and energy of few-electron systems can be obtained even with a few-dozen distributed s-type GTFs. � 2007 Elsevier B.V. All rights reserved.

The equilibrium molecular structures of the two lowest-energy conformers of glycine, Gly-Ip and Gly-IIn, have been characterized by high-level ab initio electronic structure computations, including all-electron cc-pVTZ CCSD(T) geometry optimizations and 6-31G* MP2 quartic force fields, the latter to account for anharmonic zero-point vibrational effects to isotopologic rotational constants. Based on experimentally measured vibrationally averaged effective rotational constant sets of several isotopologues and our ab initio data for structural constraints and zero-point vibrational shifts, least-squares structural refinements were performed to determine improved Born-Oppenheimer equilibrium (r(e)) structures of Gly-Ip and Gly-IIn. Without the ab initio constraints even the extensive set of empirical rotational constants available for 5 and 10 isotopologues of Gly-Ip and Gly-IIn, respectively, cannot satisfactorily fix their molecular structure. Excellent agreement between theory and experiment is found for the rotational constants of both conformers, the rms residual of the final fits being 7.8 and 51.6 kHz for Gly-Ip and Gly-IIn, respectively. High-level ab initio computations with focal point extrapolations determine the barrier to planarity separating Gly-IIp and Gly-IIn to be 20.5 +/- 5.0 cm(-1). The equilibrium torsion angle tau(NCCO) of Gly-IIn, characterizing the deviation of its heavy-atom framework from planarity, is (11 +/- 2) degrees. Nevertheless, in the ground vibrational state the effective structure of Gly-IIn has a plane of symmetry.

Complete nuclear magnetic resonance (NMR) chemical-shielding tensors, sigma, have been computed at different levels of density-functional theory (DFT), within the gauge-including atomic orbital (GIAO) formalism, for the atoms of the peptide model For-L-Ala-NH2 as a function of the backbone dihedral angles phi and psi by employing a dense grid of 10 degrees. A complete set of rigorously orthogonal symmetric tensor invariants, {sigma iso, rho, tau}, is introduced, where sigma iso is the usual isotropic chemical shielding, while the newly introduced rho and tau parameters describe the magnitude and the orientation/shape of the chemical-shielding anisotropy (CSA), respectively. The set {sigma iso, rho, tau} is unaffected by unitary transformations of the symmetric part of the shielding tensor. The mathematically and physically motivated {rho, tau} anisotropy pair is easily connected to more traditional shielding anisotropy measures, like span (Omega) and skew (kappa). The effectiveness of the different partitions of the CSA information in predicting conformations of peptides and proteins has been tested throughout the Ramachandran space by generating theoretical NMR anisotropy surfaces for our For-L-Ala-NH2 model. The CSA surfaces, including Omega(phi, psi), kappa(phi, psi), rho(phi, psi), and tau(phi, psi) are highly structured. Individually, none of these surfaces is able to distinguish unequivocally between the alpha-helix and beta-strand secondary structural types of proteins. However, two- and three-dimensional correlated plots, including Omega versus kappa, rho versus tau, and sigma iso versus rho versus tau, especially for 13Calpha, have considerable promise in distinguishing among all four of the major secondary structural elements.

Accurate, experimental rotational-vibrational energy levels determined via the MARVEL (Measured Active Rotational-Vibrational Energy Levels) algorithm and published recently for the symmetric-top (14)NH3 molecule in J. Quant. Spectrosc. Radiat. Transfer, 2015, 116, 117-130 are analyzed to unravel the promoting and inhibiting effects of vibrations and rotations on the tunneling splittings of the corresponding symmetric (s) and antisymmetric (a) rovibrational energy level pairs. The experimental transition data useful from the point of view of the present analysis cover the range 0.7-7000 cm(-1), sufficiently detailed rovibrational energy sets worth analyzing are available for 20 vibrational bands. The highest J value, where J stands for the rotational quantum number, within the experimental dataset employed is 30. Coupling of the "umbrella" motion of (14)NH3 with other vibrational degrees of freedom has only a minor effect on the a-s tunneling splitting characterizing the ground vibrational state, 0.79436(70) cm(-1). In the majority of the cases rotation around the C3 axis increases, while rotation around the two perpendicular axes decreases the tunneling splittings. For example, for the pair of vibrational ground states, 0(+) and 0(-), the tunneling splitting basically disappears at around J = 25 for the (J,K) = (J,1) states, where K = |k| is the usual quantum number characterizing the projection of the rotational angular momentum on the principal axis. The tunneling splittings, defined as energy differences E(a) - E(s) of corresponding energy level pairs, as a function of J and K show a very regular behavior for the ground state (GS) and the nν2 bands. For the other bands investigated exceptions from a regular behavior do occur, especially for bands characterized by degenerate vibrations, and occasionally the data available are not sufficient to arrive at definitive conclusions. The most irregular behavior is observed for rotational states characterized by the k - l = 3n rule (l is the vibrational angular momentum quantum number), with n = 0, 1, 2,… High-quality, variationally computed rovibrational data support all the conclusions of this study based on experimental energy levels.

Structures, accurate relative energies, equilibrium and vibrationally averaged rotational constants, quartic and sextic centrifugal distortion constants, dipole moments, (14)N nuclear quadrupole coupling constants, anharmonic vibrational frequencies, and double-harmonic infrared intensities have been determined from ab initio electronic structure computations for conformers of the neutral form of the natural amino acid l-cysteine (Cys). A systematic scan located 71 unique conformers of Cys using the MP2(FC)/cc-pVTZ method. The large number of structurally diverse low-energy conformers of Cys necessitates the highest possible levels of electronic structure theory to determine their relative energies with some certainty. For this reason, we determined the relative energies of the lowest-energy eleven conformers, accurate within a standard error (1σ) of about 0.3 kJ mol(-1), through first-principles composite focal-point analyses (FPA), which employed extrapolations using basis sets as large as aug-cc-pV(5+d)Z and correlation treatments as extensive as CCSD(T). Three and eleven conformers of l-cysteine fall within a relative energy of 6 and 10 kJ mol(-1), respectively. The vibrationally averaged rotational constants computed in this study agree well with Fourier-transform microwave spectroscopy results. The effects determining the relative energies of the low-energy conformers of cysteine are analyzed in detail on the basis of hydrogen bond additivity schemes and natural bond orbital analysis.

The equilibrium structures of FNO, ClNO, HONO, and FNO2 have been determined using three different, somewhat complementary methods: a completely experimental, a semi-experimental (where the equilibrium rotational constants are derived from the experimental effective ground-state rotational constants and an ab initio cubic force field), and an ab initio, where geometry optimizations are usually performed at the coupled cluster level of nonrelativistic electronic structure theory using small to very large Gaussian basis sets. For the sake of comparison, the equilibrium structures of HNO and N2O have also been redetermined, confirming and extending earlier results. The semi-experimental method gives structural parameters in good agreement with the reliable experimental results for each compound investigated. Because of inadequate treatment of electron correlation, the single-reference CCSD(T) method gives N-X (X[double bond]F, Cl, OH) bonds that are too strong and associate bond lengths that are significantly too short. The discrepancy increases with increase in the size of the basis set. A much more elaborate treatment of electron correlation at the CCSDTQ level solves this problem and results in increased bond lengths, correctly representing the weakness of the N-X bond in these XNO and XNO2 species. The equilibrium structures determined are accurate to better than 0.001 A and 0.1 degrees .

The vibrational fundamentals and the rotational levels up to J=7 of the X ˜ 3 B 1 and a ˜ 1 A 1 electronic states of CH2 have been computed completely ab initio. The calculations were based on converged, variational nuclear motion calculations employing high-quality ab initio quartic force field approximations of the related potential energy surfaces (PES). The vibrational fundamentals obtained are compared to other computational results, namely those obtained from second-order vibrational perturbation theory (VPT2) and the nonrigid-rotation-large-amplitude-internal-motion Hamiltonian (NRLH) approach. The variationally computed rotational transitions are compared both to experimentally available results and to results obtained using empirical, fitted PESs. The comparisons suggest that while the fitted PESs of X ˜ 3 B 1 CH2 reproduce excellently the available rovibrational transition wavenumbers, the corresponding stretching fundamental term values, which have not been determined experimentally, are less accurate than the ab initio values obtained in the present study. This means that the zero-point energy (ZPE) computed ab initio in the present work is an improvement over that computed from the fitted PES of X ˜ 3 B 1 CH2. No similar problems are observed for the semirigid a ˜ 1 A 1 state of CH2, where the computed, the fitted, and the experimental results all agree with each other. The symmetric and antisymmetric stretching fundamentals of X ˜ 3 B 1 CH2 obtained in this study are 3035±7 and 3249±7 cm−1, respectively. The corresponding ZPE of X ˜ 3 B 1 is 3733±10 cm−1, while that of a ˜ 1 A 1 CH2 is 3605±15 cm−1.

Stability and structure of homo- and heterochiral protonated serine (Ser) dimers were investigated by a combination of mass spectrometry and ab initio quantum chemical calculations. This established that the energy difference between the most stable homo- and heterochiral forms is very small: tandem mass spectrometry with Cooks' kinetic method yielded a negligible difference in Gibbs free energy (0.2+/-0.2 kJ mol(-1)). The various isomeric forms of (Ser)2 H+ and their energetics were determined by extensive electronic-structure calculations, which yielded homo- and heterochiral forms of the isomers with distinctly different relative energies. The most stable homochiral isomer is stabilized by two hydrogen bonds and is far more stable than any other homochiral isomer. The most stable heterochiral isomer has completely different features, and it is characterized by a salt-bridge structure. This clearly shows that salt-bridge structures do exist in the gas phase even in comparatively small molecules and in the absence of particularly basic or acidic functional groups.

This is the first part of a series of articles reporting critically evaluated thermochemical properties of selected free radicals. The present article contains datasheets for 11 radicals: CH, CH2(triplet), CH2(singlet), CH3, CH2OH, CH3O, CH3CO, C2H5O, C6H5CH2, OH, and NH2. The thermochemical properties discussed are the enthalpy of formation, as well as the heat capacity, integrated heat capacity, and entropy of the radicals. One distinguishing feature of the present evaluation is the systematic utilization of available kinetic, spectroscopic and ion thermochemical data as well as high-level theoretical results.

Systematic quantum chemical calculations have been performed to obtain precise estimates of the equilibrium and vibrationally averaged molecular structure and electric dipole moment of vinylacetylene (VA, 1-buten-3-yne). Anharmonic (cubic and semi-diagonal quartic) MP2/cc-pVTZ force fields in normal coordinates were computed to account for anharmonic vibrational effects, including zero-point contributions to the rotational constants and the electric dipole moment. A simultaneous weighted least-squares structural refinement was performed, resulting in the best semispectroscopic estimate of the re structure of VA. The refinement was based on experimentally measured ground-state rotational constants of two isotopologs of VA corrected to equilibrium values using MP2/cc-pVTZ vibration-rotation interaction constants and all-electron CCSD(T)/aug-cc-pVTZ structural constraints. The semispectroscopic re structure of VA agrees excellently with the high-level CCSD(T)/aug-cc-pVTZ ab initio structure. The most dependable, CCSD(T)/cc-pVQZ//CCSD(T)/aug-cc-pVTZ equilibrium electric dipole moment of VA, in D, is mua= 0.4088, mub= 0.0004, and muc= 0. The vibrationally corrected a-component of 0.4214 D is in excellent agreement with one of the available experimental values. The present analysis shows that mub is negligible even after vibrational correction. A simple quantitative structure-property relationship (QSPR) model resulted in a highly similar estimate, 0.45 D, for the electric dipole moment of VA.

A simple variational procedure, termed DOPI for discrete variable representation—Hamiltonian in orthogonal coordinates—direct product basis–iterative diagonalization, is described and applied to compute low-lying vibrational band origins (VBOs) of the triatomic systems H2O, CO2, and N2O, employing published empirical and theoretical sextic force fields. While in these cases no difficulties arise when quartic potentials are used, the limited range of applicability of 6th-order potentials presents difficulties for the variational determination of VBOs, in particular for the higher-lying bending states. For H2O, transformation of quadratic and quartic force fields from simple bond stretching to Simons–Parr–Finlan (SPF) coordinates results in computed VBOs deviating less from experiment. This, however, does not hold for the VBOs computed from the transformed sextic force fields where the two representations provide highly similar results. While use of empirical quartic and sextic force fields result in a much...

The molecular structures of the two lowest-energy conformers of proline, Pro-I and Pro-II, have been characterized by ab initio electronic structure computations. An extensive MP2/6-31G* quartic force field for Pro-I, containing 62,835 unique elements in the internal coordinate space, was computed to account for anharmonic vibrational effects, including total zero-point contributions to isotopomeric rotational constants. New re and improved r0 least-squares structural refinements were performed to determine the heavy-atom framework of Pro-I, based on experimentally measured (A. Lesarri, S. Mata, E. J. Cocinero, S. Blanco, J. C. Lopez, J. L. Alonso, Angew. Chem. 2002, 114, 4867; Angew. Chem. Int. Ed. 2002, 41, 4673) rotational constant sets of nine isotopomers and our ab initio data for structural constraints and zero-point vibrational (ZPV) shifts. Without the ab initio constraints, even the extensive set of empirical rotational constants cannot satisfactorily fix the molecular structure of the most stable conformer of proline, a 17-atom molecule with no symmetry. After imposing the ab initio constraints, excellent agreement between theory and experiment is found for the heavy-atom geometric framework, the root-mean-square (rms) residual of the empirical rotational constant fit being cut in half by adding ZPV corrections. The most significant disparity, about 0.07 A, between the empirical and the best ab initio structures, concerns the r(N...H) distance of the intramolecular hydrogen bond. Some of the experimental quartic centrifugal distortion constants assigned to Pro-II have been corrected based on data obtained from a theoretical force field.

Nuclear magnetic resonance isotropic chemical shift (ICS) surfaces have been generated for all the atoms of the central Ala residue of the peptide models For–(L–Ala)n–NH2, n=1, 3, and 5, at the GIAO-B3LYP/TZ2P level at a grid of 10° in the backbone dihedral angles φ and ψ for n=1 and at a grid of 30° for the larger models. The resulting periodic 3D ICS(φ,ψ) surfaces were fitted employing a number of suitable mathematical functions. A cosine expansion provided the most accurate and compact representation of the highly structured ICS surfaces. At 10th order, involving 66 coefficients, the mean errors in the 13Cα and 1Hα ICS predictions for the For–L–Ala–NH2 model are 0.33 and 0.034 ppm, respectively. Similar fitting residues were found for other nuclei, as well. The computed surfaces are compared to results corresponding to an experimental database. The changes in chemical shifts due to the increase in the model size are investigated in detail.

A theoretical estimation of the enthalpy of formation for the hydroperoxyl radical is presented. These results are based on CCSD(T)/aug-cc-pCV5Z calculations extrapolated to the basis-set limit with additional corrections. Anharmonic vibrational zero-point energies, scalar relativistic, spin -orbit coupling, and diagonal BornOppenheimer corrections are further used to correct the extrapolated term energies, as well as various empirical corrections that account for correlation effects not treated at the CCSD(T) level. We estimate that ¢fH° ) 3.66 ( 0.10 kcal mol -1 (¢fH° ) 2.96 ( 0.10 kcal mol -1 ) using several reaction schemes. Significantly, it appears to be necessary to include effects of connected pentuple excitations in order to achieve an uncertainty of ca. 0.1 kcal mol -1 .

Highly accurate equilibrium molecular structures have been determined for the molecules cyclobutene, 1,2-difluorocyclobutene, 1,2-dicyanocyclobutene, trans-3,4-difluorocyclobutene, 1,4,4-trifluoroc...

The method of discrete variable representation (DVR) is based on standard orthogonal polynomial bases and the associated Gaussian quadratures. General basis functions correspond either to nonpolynomial expressions or to nonstandard orthogonal polynomials. Although one cannot directly relate any Gaussian quadrature to general basis functions, the DVR-like representation derivable with such basis sets via the transformation (diagonalization) method is, as proved here, of Gaussian quadrature accuracy. The optimal generalized DVR (GDVR) is an alternative to and entirely different from this DVR-like representation. Yet, when built from the same general basis functions and the corresponding quadrature points obtained by the diagonalization method, the two representations are found to give almost identical numerical results. The intricate relationship between the optimal GDVR and the transformation method is discussed.

High-quality ab initio quantum chemical methods, including higher-order coupled cluster and full configuration interaction benchmarks, with basis sets ranging from [C/H] [4s3p1d/2s1p] to [9s8p7d5f4g3h2i/7s6p5d4f3g2h] have been employed to obtain the best technically possible value for the standard enthalpy of formation of X 3B1 CH2 and a 1A1 CH2. Careful extrapolations of finite basis MP2, CCSD, CCSD(T), and CCSDT energies to the complete basis set full configuration interaction limit plus inclusion of small corrections owing to relativistic effects, core correlation, and the diagonal Born–Oppenheimer correction results in the final extrapolated enthalpies of formation of this study, ΔfH0o(X 3B1 CH2)=390.45−0.64+0.68 kJ mol−1 and ΔfH0o(a 1A1 CH2)=428.10−0.64+0.68 kJ mol−1. The computed value for X 3B1 CH2 is in between the best two experimental results of 389.87±0.86 and 390.73±0.66 kJ mol−1. The elaborate calculations leading to these enthalpies of formation also resulted in accurate estimates of the singlet-triplet splitting, T0(a 1A1 CH2)=37.54−0.29+0.41 kJ mol−1, in excellent agreement with the best empirical value of 37.65±0.06 kJ mol−1, of the total atomization enthalpy, D0(X 3B1 CH2)=753.03−0.62+0.43 kJ mol−1, in excellent agreement with the best experimental value of 753.3 kJ mol−1, of the bond dissociation energy, DU1o(0 K)(CH–H)=417.85±0.35 kJ mol−1, and of the quartic force field representations of the potentials of the two states around their respective minima.

The rho-axis system and the rho-axis-system Hamiltonian were devised and formulated to describe the rotational–internal–rotational motion of molecules possessing certain local geometrical symmetries. Nevertheless, they were employed to molecules without the required symmetries and apparently lying outside the range of their applicability. To justify such applications and to facilitate first-principles calculation of the corresponding spectroscopic parameters, the rho-axis-system and the rho-axis system Hamiltonian must be derived without assuming or imposing symmetry constraints. A derivation satisfying this requirement is described, and the rho-axis method is extended to molecules having a large amplitude internal motion of any kind.

NMR chemical shielding anisotropy tensors have been computed by employing a medium size basis set and the GIAO-DFT(B3LYP) formalism of electronic structure theory for all of the atoms of type I and type II beta-turn models. The models contain all possible combinations of the amino acid residues Gly, Ala, Val, and Ser, with all possible side-chain orientations where applicable in a dipeptide. The several hundred structures investigated contain either constrained or optimized phi, psi, and chi dihedral angles. A statistical analysis of the resulting large database was performed and multidimensional (2D and 3D) chemical-shift/chemical-shift plots were generated. The (1)H(alpha-13)C(alpha), (13)C(alpha-1)H(alpha-13)C(beta), and (13)C(alpha-1)H(alpha-13)C' 2D and 3D plots have the notable feature that the conformers clearly cluster in distinct regions. This allows straightforward identification of the backbone and side-chain conformations of the residues forming beta-turns. Chemical shift calculations on larger For-(L-Ala)(n)-NH(2) (n=4, 6, 8) models, containing a single type I or type II beta-turn, prove that the simple models employed are adequate. A limited number of chemical shift calculations performed at the highly correlated CCSD(T) level prove the adequacy of the computational method chosen. For all nuclei, statistically averaged theoretical and experimental shifts taken from the BioMagnetic Resonance Bank (BMRB) exhibit good correlation. These results confirm and extend our previous findings that chemical shift information from selected multiple-pulse NMR experiments could be employed directly to extract folding information for polypeptides and proteins.