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The ground-state rotational spectrum of propene-3-d

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 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.

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.

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.

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.

Measurements result in effective, usually temperature-dependent structural parameters of molecules, and never directly in equilibrium structures, which are theoretical constructs. A recent high-accuracy semiglobal potential energy surface of the electronic ground state of the ammonia molecule, called NH3-Y2010 (J. Mol. Spectrosc. 2011, 268, 123), which exhibits mass-independent equilibrium NH bond length and a HNH bond angle of 1.0109 Å and 106.75°, respectively, is employed together with the variational nuclear motion code GENIUSH (J. Chem. Phys. 2009, 130, 134112; 2011, 134, 074105) to determine directly measurable, effective structural parameters of the (14)NH(3) and (14)ND(3) molecules. The effective r(g)- and r(a)-type NH(ND) distances determined at 300 K are 1.0307(1.0254) and 1.0256(1.0217) Å, respectively, with an estimated accuracy of 2 × 10(-4) Å. The effective θ(g) HNH and DND bond angles at 300 K are 106.91° and 106.85°, respectively. The root-mean-square amplitudes of vibration, l(g), for the NH(ND) distances at 300 K are 0.073(0.062) Å. These structural parameters confirm the less accurate results of a room-temperature gas-electron-diffraction study (J. Chem. Phys. 1968, 49, 2488, all data in Å): r(g)(NH) = 1.030(2), l(g)(NH) = 0.073(2), r(g)(ND) = 1.027(3), and l(g)(ND) = 0.061(2). The computed difference in the r(g,T)(NH) bond lengths of the two spin isomers (ortho and para forms) of (14)NH(3) is 3 × 10(-5) Å at 0 K, the difference diminishes at temperatures of about 30-50 K.

Extending our previous study on the equilibrium structures of the major isotopologues of the water molecule (Csaszar et al. J. Chem. Phys. 2005, 122, 214305), temperature-dependent averaged structural parameters (for example, r(g)- and r(a)-type distances, their related root-mean-square amplitudes, and moments corresponding to the probability distribution functions of interatomic distances), effective rotational constants, and low-order vibration-rotation interaction constants have been determined for two major symmetric isotopologues of water, H(2)(16)O and D(2)(16)O. The nuclear motion treatments employed full quantum mechanical variational procedures which utilized the accurate adiabatic semiglobal PESs of water isotopologues named CVRQD (Barletta et al. J. Chem. Phys. 2006, 125, 204307). The temperature-dependent molecular structural parameters are based on expectation value computations and Boltzmann averaging in the temperature range 0-1500 K. The precise computed average internuclear, inverse internuclear, rms amplitude, and anharmonicity parameters could support a future gas electron diffraction (GED) investigation, though water isotopologues are far from being ideal species for GED analyses. Using a clearly defined and general formalism applicable to molecules of any size, we have evaluated vibrationally averaged effective rotational constants as expectation values using inertia tensor formulas in the Eckart frame for vibrational states of H(2)(16)O and D(2)(16)O. While such variationally determined rotational constants do not correspond strictly to constants resulting from fits performed by spectroscopists, the expected good agreement is found for the A and B rotational constants for both isotopologues. Low-order vibration-rotation interaction constants, the so-called alpha- and gamma-constants, have also been determined from the computed rotational constants; the latter were derived for the first time.

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).

The influence of intermolecular interactions on the Mossbauer quadrupole splitting (Delta) of 119Sn was investigated in detail by density functional theory (DFT) calculations. Six organotin(IV) complexes [Me2Sn(acac)2 (1), Ph3SnCl (2), Me3Sn-succinimide (3), Me3Sn-phthalimide (4), Me3SnCl (5), and cHex3SnCl (6)] of known solid-state structures and quadrupole splittings were selected. Theoretical Delta values were calculated for both fully optimized geometries and experimental solid-state structures of different size, and the results were compared to the experimental Delta values. Compared to a synthetic procedure described in the literature for compound 4, a more convenient synthesis is reported here. The experimental Delta of this compound has also been redetermined at 80 K. For compounds with negligible intermolecular interactions in the solid state, calculated Delta values obtained did not vary significantly. In contrast, the calculated Delta values turned out to be very sensitive to the size of the supramolecular moiety considered in the crystal lattice. The crystal structure of compound 2 shows no significant intermolecular interactions; however, the calculated and the experimental Delta values remained very different, even when the supramolecular moiety considered was extended. Distortion of the coordination sphere of tin in the molecule of 2 toward a trigonal bipyramidal geometry was considered, and a possible weak intermolecular Sn...Cl interaction was included in the model. Steps of the distortion followed the new structure correlation function, which was found for the R3SnCl (R=alkyl, aryl) compounds. The experimental Delta value could be approached by this method. These results suggest that compound 2 is involved in some unexpected intermolecular interaction at 80 K.

Planarity of the XC(d)NHY linkage has been investigated in unprecedented detail in a number of relatively simple compounds, including formamide (X ) Y ) H), acetamide (X ) CH3 ,Y ) H), urea (X ) NH2 ,Y ) H), carbamic acid (X ) OH, Y ) H), and methyl carbamate (X ) OCH3 ,Y ) H). Reliable estimates of the equilibrium structures of formamide, cyanamide, acetamide, urea, carbamic acid, methylamine, dimethyl ether, and methyl carbamate are derived, mostly for the first time. It is shown that formamide, considered prototypical for the amide linkage, is not typical as it has a planar equilibrium amide linkage corresponding to a single-minimum inversion potential around N. In contrast, several molecules containing the CONH linkage seem to have a pyramidalized nitrogen at equilibrium and a double-minimum inversion potential with a very small inversion barrier allowing for an effectively planar ground-state structure. Observables of rotational spectroscopy, including ground-state inertial defects, quadrupole coupling and centrifugal distortion constants, and dipole moment components, as well as equilibrium CdO and C-N bond lengths are reviewed in their ability to indicate the planarity of the effective and possibly the equilibrium structures.