The case of the weak N-X bond: Ab initio, semi-experimental, and experimental equilibrium structures of XNO (X = H, F, Cl, OH) and FNO2

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 .     

Molecular structures of the two most stable conformers of free glycine

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.     

Equilibrium structures of heterocyclic molecules with large principal axis rotations upon isotopic substitution

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.     

Microwave spectra and molecular structures of (Z)-pent-2-en-4-ynenitrile and maleonitrile.

Accurate equilibrium structures have been determined for (Z)-pent-2-en-4-ynenitrile (8) and maleonitrile (9) by combining microwave spectroscopy data and ab initio quantum chemistry calculations. The microwave spectra of 10 isotopomers of 8 and 5 isotopomers of 9 were obtained using a pulsed nozzle Fourier transform microwave spectrometer. The ground-state rotational constants were adjusted for vibration-rotation interaction effects calculated from force fields obtained from ab initio calculations. The resultant equilibrium rotational constants were used to determine structures that are in very good agreement with those obtained from high-level ab initio calculations (CCSD(T)/cc-pVTZ). The geometric parameters in 8 and 9 are very similar; they also do not differ significantly from the all-carbon analogue, (Z)-hex-3-ene-1,5-diyne (7), the parent molecule for the Bergman cyclization. A small deviation from linearity about the alkyne and cyano linkages is observed for 7-9 and several related species where accurate equilibrium parameters are available. The data on 7-9 should be of interest to radioastronomy and may provide insights on the formation and interstellar chemistry of unsaturated species such as the cyanopolyynes.     

Molecular structure of proline

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.     

N-Methyl inversion and structure of six-membered heterocyclic rings: rotational spectrum of 1-methyl-4-piperidone

The conformational and structural properties of the six-membered heterocyclic ring of 1-methyl-4-piperidone have been observed in a jet-cooled supersonic expansion using Fourier transform microwave spectroscopy (FT-MW). The rotational spectrum evidenced two different conformations originated by nitrogen inversion, with the N-methyl group in either equatorial (most stable) or axial position. Additional observation of the rotational spectra for all possible carbon, nitrogen, and oxygen monosubstituted species (4 × (13)C, (15)N, (18)O) in natural abundance allowed us to determine substitution (r(s)) and effective structures (r(0)) for the equatorial conformer. Additional ab initio and DFT calculations provided comparative rotational parameters, structural data, conformational energies, and the axial-equatorial interconversion barrier. The structural data were compared with the related azabicycle of tropinone, revealing the molecular changes and structural relaxation associated with the presence of the two-carbon bridge in the latter molecule.     

Equilibrium structure and spectroscopic constants of maleic anhydride

The quadratic, cubic, and semi-diagonal quartic force fields of maleic anhydride have been calculated at the MP2 level of theory employing the cc-pVTZ basis set. The spectroscopic constants derived from the force field are in excellent agreement with the corresponding experimental values. The semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational corrections calculated from the cubic force field. This semi-experimental equilibrium structure is in excellent agreement with the ab initio structures computed at the CCSD(T) level of theory and it is closer to the ab initio structure than the purely experimental (or empirical) structures r ₀, r _m⁽¹⁾, and r _m⁽²⁾ obtained by microwave spectroscopy as well as the equilibrium structure derived from gas-phase electron diffraction data.     

Equilibrium structure of sulfuric acid

The equilibrium structure of the more stable conformer of H2SO4, of C2 symmetry, has been calculated ab initio using the CCSD(T) method and taking into account the core correlation correction. The accuracy of this structure has been checked by comparing it to that of similar molecules and by estimating the effects of basis set enlargement and of diffuse functions. Furthermore, the quadratic, cubic, and quartic force fields have been calculated at the MP2 level of theory using a basis set of triple-zeta quality. The spectroscopic constants derived from the force field are in satisfactory agreement with the experimental ones. The resulting band origins are compared to literature infrared values, including those for overtone and combination bands. Normal modes of vibration are pictured. Using this force field, semiexperimental equilibrium rotational constants are determined which allows us to check the accuracy of the ab initio structure and to refine it using a mixed regression method.     

Equilibrium structure of gas phase o-benzyne

An equilibrium structure has been derived for o-benzyne from experimental rotational constants of seven isotopomers and vibration–rotation constants calculated from MP2 (full)/6-31G(d) quadratic and cubic force fields. In the case of benzene, this method yields results that are in excellent agreement with those obtained from high quality ab initio force fields. The ab initio-calculated vibrational averaging corrections were applied to the measured A₀, B₀ and C₀ rotational constants and the resulting experimental, near-equilibrium, rotational constants were used in a least squares fit to determine the approximate equilibrium structural parameters. The C–C bond lengths for this equilibrium structure of o-benzyne are, beginning with the formal triple bond (C₁–C₂): 1.255, 1.383, 1.403 and 1.405 Å. The bond angles obtained are in good agreement with most of the recent ab initio predictions.     

The ground state energy levels and molecular structure of jet-cooled HGeCl and DGeCl from single vibronic level emission spectroscopy

Single vibronic level dispersed fluorescence spectra of jet-cooled HGeCl and DGeCl have been recorded by laser excitation of selected bands of the A 1A"-X 1A' electronic transition. Twenty-six ground state vibrational levels of HGeCl and 42 of DGeCl were measured, assigned, and fitted to standard anharmonicity expressions, which allowed all the harmonic frequencies to be determined for both isotopomers. A normal coordinate least squares analysis obtained by fitting the harmonic frequencies yielded reliable values for five of the six force constants. The ground state effective rotational constants and force field data were combined to calculate average (rz) and approximate equilibrium (re z) structures, with re z(GeH)=1.586(1) A, re z(GeCl)=2.171(2) A, and the bond angle fixed at our CCSD(T)/aug-cc-pVTZ ab initio value of 93.9 degrees . Comparisons show that the derived bond lengths are consistent with those of the appropriate diatomic molecules in their ground electronic states and the bond angle is similar to that of germylene (GeH2). A Franck-Condon simulation of the vibrational intensities in the 0(0) (0) band emission spectrum of HGeCl using ab initio force field data shows good agreement with experiment, lending credence to the vibrational analysis of the observed spectra.     

Semiexperimental equilibrium structure for cis,trans-1,4-difluorobutadiene by the mixed estimation method

The available experimental rotational constants of cis,trans-1,4-difluorobutadiene do not permit a determination of a complete structure. However, this problem, rather frequent in finding structures, may be solved by the mixed estimation method. The experimental ground state rotational constants are corrected for the rovibrational contribution calculated from an ab initio force field. These semiexperimental data are supplemented by structural parameters from ab initio calculations and a weighted least-squares fit allows us to obtain a reasonable structure. The accuracy of the fitted parameters is checked by optimizing a structure at the coupled cluster level. A good agreement is found between the two methods, validating our procedure.     

The chiral molecule CHClFI: first determination of its molecular parameters by Fourier transform microwave and millimeter-wave spectroscopies supplemented by ab initio calculations

The rotational spectrum of chlorofluoroiodomethane (CHClFI) has been investigated. Because its rotational spectrum is extremely crowded, extensive ab initio calculations were first performed in order to predict the molecular parameters. The low J transitions were measured using a pulsed-molecular-beam Fourier transform spectrometer, and the millimeter-wave spectrum was measured to determine accurate centrifugal distortion constants. Because of the high resolution of the experimental techniques, the analysis yielded accurate rotational constants, centrifugal distortion corrections, and the complete quadrupole coupling tensors for the iodine and chlorine nuclei, as well as the contribution of iodine to the spin-rotation interaction. These molecular parameters were determined for the two isotopologs CH35ClFI and CH37ClFI. They reproduce the observed transitions within the experimental accuracy. Moreover, the ab initio calculations have provided a precise equilibrium molecular structure. Furthermore, the ab initio molecular parameters are found in good agreement with the corresponding experimental values.     

Single vibronic level emission spectroscopic studies of the ground state energy levels and molecular structures of jet-cooled HGeBr, DGeBr, HGeI, and DGeI

Single vibronic level dispersed fluorescence spectra of jet-cooled HGeBr, DGeBr, HGeI, and DGeI have been obtained by laser excitation of selected bands of the A (1)A(")-X (1)A(') electronic transition. The measured ground state vibrational intervals were assigned and fitted to anharmonicity expressions, which allowed the harmonic frequencies to be determined for both isotopomers. In some cases, lack of a suitable range of emission data necessitated that some of the anharmonicity constants and vibrational frequencies be estimated from those of HGeClDGeCl and the corresponding silylenes (HSiX). Harmonic force fields were obtained for both molecules, although only four of the six force constants could be determined. The ground state effective rotational constants and force field data were combined to calculate average (r(z)) and approximate equilibrium (r(e) (z)) structures. For HGeBr r(e) (z)(GeH)=1.593(9) A, r(e) (z)(GeBr)=2.325(21) A, and the bond angle was fixed at our CCSD(T)/aug-cc-pVTZ ab initio value of 93.6 degrees . For HGeI we obtained r(e) (z)(GeH)=1.589(1) A, r(e) (z)(GeI)=2.525(5) A, and bond angle=93.2 degrees . Franck-Condon simulations of the emission spectra using ab initio Cartesian displacement coordinates reproduce the observed intensity distributions satisfactorily. The trends in structural parameters in the halogermylenes and halosilylenes can be readily understood based on the electronegativity of the halogen substituent.     

High-resolution microwave studies of ring-structured complexes between trifluoroacetic acid and water

The rotational spectra of the complexes between one trifluoroacetic acid molecule and up to three water molecules have been recorded using a pulsed nozzle Fourier transform microwave spectrometer. The unambiguous assignments of them are made on the basis of the agreement between the experimentally determined rotational constants and the theoretical predictions from ab initio calculations using MP2/6-311++G(2df,2pd). All the complexes exhibit hydrogen-bonded ring structures. The fine splittings observed in some of the a-type transitions of the trifluoroacetic acid-H2O dimer were analyzed in terms of the likely tunneling motions of the hydrogens in the H2O molecule. Further calculations of the equilibrium constants for these three hydrated complexes of trifluoroacetic acid were also made to evaluate their fractions against the trifluoroacetic acid monomer in the atmosphere.     

More user-friendly phosphines? Molecular structure of methylphosphine and its adduct with borane, studied by gas-phase electron diffraction and quantum chemical calculations

The molecular structures of methylphosphine (CH(3)PH(2)) and methylphosphine-borane (CH(3)PH(2).BH(3)) have been determined from gas-phase electron diffraction data and rotational constants, employing the SARACEN method. The experimental geometric parameters generally showed a good agreement with those obtained using ab initio calculations and previous microwave spectroscopy studies. In order to assess the accuracy of the calculated structures a range of ab initio methods were used, including the CCSD(T) method, with correlation-consistent basis sets. The structural environment around the phosphorus atom was found to change significantly upon complexation with borane, with the P-C bond length shortening and the bond angles widening.     

Fourier transform microwave spectroscopy and Fourier transform microwave-millimeter wave double resonance spectroscopy of the ClOO radical

Pure rotational spectra of the ClOO radical for the (35)Cl and (37)Cl isotopomers have been observed using Fourier transform microwave and Fourier transform microwave-millimeter wave double resonance spectroscopy. The rotational, centrifugal, spin-rotation coupling, and hyperfine coupling constants have been determined by least-squares fits of the observed transition frequencies. The molecular constants indicate that the electronic ground state is 2A". The r(0) structure is determined to be r(0)(ClO)=2.075 A, r(0)(OO)=1.227 A, and theta;(0)(ClOO)=116.4 degrees . Several highly accurate ab initio calculations have also been performed. Some of them turned out to be inaccurate because it is necessary to take into account both static and dynamic electronic correlations. Only multireference (single and double) configuration interaction calculations with large basis sets reproduce the present experimental results. The anharmonic force constants obtained by the ab initio calculations are used to determine the r(e) structure, r(e)(ClO)=2.084(1) A, r(e)(OO)=1.206(2) A, and theta;(e)(ClOO)=115.4(1) degrees . Unique features of the ClOO radical have become clear by the present experiment and the ab initio calculations.     

Femtosecond degenerate four-wave mixing of carbon disulfide: high-accuracy rotational constants

Femtosecond degenerate four-wave mixing (fs-DFWM) rotational coherence spectroscopy (RCS) has been used to determine the rotational and centrifugal distortion constants of the 00 (0)0 ground and 01 (1)0 vibrationally excited states of gas-phase CS(2). RCS transients were recorded over the 0-3300 ps optical delay range, allowing the observation of 87 recurrences. The fits yield rotational constants B(00 (0)0)=3.271 549 2(18) GHz for (12)C(32)S(2) and B(00 (0)0)=3.175 06(21) GHz for the (12)C(32)S(34)S isotopomer. The rotational constants of the degenerate 01 (1)0 bending level of (12)C(32)S(2) are B(01 (1)0)=3.276 72(40) and 3.279 03(40) GHz for the e and f substrates, respectively. These fs-DFWM rotational constants are ten times more accurate than those obtained by CO(2) laser/microwave heterodyne measurements and are comparable to those obtained by high-resolution Fourier transform infrared spectroscopy. Ab initio calculations were performed at two levels, second-order Moller-Plesset theory and coupled-cluster singles, doubles, and iterative triples [CCSD(T)]. The equilibrium and vibrationally averaged C=S distances were calculated using large Dunning basis sets. An extrapolation procedure combining the ab initio rotational constants with the experiment yields an equilibrium C=S bond length of 155.448 pm to an accuracy of +/-20 fm. The theoretical C=S bond length obtained by a complete basis set extrapolation at the CCSD(T) level is r(e)(C=S)=155.579 pm, or 0.13 pm longer than that in the experiment.     

Equilibrium structure and torsional barrier of BH3NH3

Born-Oppenheimer equilibrium structures, r(e)(BO), of the electronic ground state of the borazane (BH3NH3) molecule of C3v point-group symmetry are computed ab initio using the CCSD(T) method with basis sets up to quintuple-zeta quality. Inclusion of the counterpoise correction and extrapolation of the structural parameters to the complete basis set limit yield a best estimate of r(e)(BO) of BH3NH3. The anharmonic force field of BH3NH3, computed at the CCSD(T) level of theory with a basis set of triple-zeta quality, allows the determination of semi-experimental equilibrium rotational constants, which in turn result in a semi-experimental equilibrium structure, r(e)(SE). The r(e)(BO) and r(e)(SE) structures are in excellent agreement, indicating the validity of the methods used for their determination. The empirical mass-dependent structure, r(m)(1), of BH3NH3 is also determined. Although it is inferior in quality to the previous two structures, it is much more accurate than the standard empirical r0 and r(s) structures reported earlier for BH3NH3. The semi-experimental r(e)(SE) as well as the empirical r(m)(1) structures determined are based on experimental ground-state rotational constants available from the literature for nine isotopologues of borazane. The effective barrier to the internal rotation of BH3NH3, a molecule isoelectronic with CH3CH3, has been computed ab initio, employing the focal-point analysis (FPA) approach, to be 699 +/- 11 cm(-1). This compares favorably with an empirical redetermination of the effective barrier based on the above r(e)(SE) structure, V3 = 718(17) cm(-1).     

Monohydrates of cuprous chloride and argentous chloride: H2O⋅⋅⋅CuCl and H2O⋅⋅⋅AgCl characterized by rotational spectroscopy and ab initio calculations

Pure rotational spectra of the ground vibrational states of ten isotopologues of each of H(2)O???CuCl and H(2)O???AgCl have been measured and analyzed to determine rotational constants and hyperfine coupling constants for each molecule. The molecular structure and spectroscopic parameters determined from the experimental data are presented alongside the results of calculations at the CCSD(T) level. Both experiment and theory are consistent with structures that are nonplanar at equilibrium. The heavy atoms are collinear while the local C(2) axis of the water molecule intersects the axis defined by the heavy atoms at an angle, φ = 40.9(13)° for Cu and φ = 37.4(16)° for Ag. In the zero-point state, each molecule is effectively planar, undergoing rapid inversion between two equivalent structures where φ has equal magnitude but opposite sign. The equilibrium geometry has C(s) symmetry, however. The ab initio calculations confirm that the timescale of this inversion is at least an order of magnitude faster than that of rotation of the molecule in the lowest rotational energy levels. The molecular geometries are rationalized using simple rules that invoke the electrostatic interactions within the complexes. Centrifugal distortion constants, Δ(J) and Δ(JK), nuclear quadrupole coupling constants, χ(aa)(Cu), χ(aa)(Cl), (χ(bb) - χ(cc))(Cu), and (χ(bb) - χ(cc))(Cl), and the nuclear spin-rotation constant of the copper atom, C(bb)(Cu)+C(cc)(Cu), are also presented.     

AB initio studies on hydrogen bonded chains. II. Equilibrium geometry and vibrational spectra of the bent chain of hydrogen fluoride molecules

The ab initio crystal orbital method including electrostatic long range corrections has been applied to determine the equilibrium structure of the infinite bent chain of hydrogen fluoride molecules using extended gaussian basis sets ranging from double zeta to a near Hartree-Fock limit quality. Electronic band structure, hydrogen bond energy and dipole moment are reported as well. A sufficiently large number of points has been computed with the double zeta basis to determine an almost complete force field. With the larger basis sets the most important force constants have been reevaluated. From these force constants the optically active vibrational frequencies, phonon dispersion curves, phonon density of states and zero point energy have been derived within the framework of the harmonic approximation.