Comparing the accuracy of perturbative and variational calculations for predicting fundamental vibrational frequencies of dihalomethanes.

Three dihalogenated methane derivatives (CH2F2, CH2FCl, and CH2Cl2) were used as model systems to compare and assess the accuracy of two different approaches for predicting observed fundamental frequencies: canonical operator Van Vleck vibrational perturbation theory (CVPT) and vibrational configuration interaction (VCI). For convenience and consistency, both methods employ the Watson Hamiltonian in rectilinear normal coordinates, expanding the potential energy surface (PES) as a Taylor series about equilibrium and constructing the wavefunction from a harmonic oscillator product basis. At the highest levels of theory considered here, fourth-order CVPT and VCI in a harmonic oscillator basis with up to 10 quanta of vibrational excitation in conjunction with a 4-mode representation sextic force field (SFF-4MR) computed at MP2/cc-pVTZ with replacement CCSD(T)/aug-cc-pVQZ harmonic force constants, the agreement between computed fundamentals is closer to 0.3 cm-1 on average, with a maximum difference of 1.7 cm-1. The major remaining accuracy-limiting factors are the accuracy of the underlying electronic structure model, followed by the incompleteness of the PES expansion. Nonetheless, computed and experimental fundamentals agree to within 5 cm-1, with an average difference of 2 cm-1, confirming the utility and accuracy of both theoretical models. One exception to this rule is the formally IR-inactive but weakly allowed through Coriolis-coupling H-C-H out-of-plane twisting mode of dichloromethane, whose spectrum we therefore revisit and reassign. We also investigate convergence with respect to order of CVPT, VCI excitation level, and order of PES expansion, concluding that premature truncation substantially decreases accuracy, although VCI(6)/SFF-4MR results are still of acceptable accuracy, and some error cancellation is observed with CVPT2 using a quartic force field.

Anharmonic vibrational analysis of s-trans and s-cis conformers of acryloyl fluoride using numerical-analytic Van Vleck operator perturbation theory.

A new gas-phase infrared (IR) spectrum of acryloyl fluoride (ACRF, CH2CHCFO) with a resolution of 0.1cm-1 in the range 4000-450cm-1 was measured. Theoretical ab initio molecular structures, full quartic potential energy surfaces (PES), and cubic surfaces of dipole moments and polarizability tensor components (electro-optical properties, EOP) of the s-trans and s-cis conformers of the ACRF were calculated by the second-order Møller-Plesset electronic perturbation theory with a correlation consistent Dunning triple-ζ basis set. The numerical-analytic implementation of the second-order operator canonical Van Vleck perturbation theory was employed for predicting anharmonic IR and Raman scattering (RS) spectra of ACRF. To improve the anharmonic predictions, harmonic frequencies were replaced by their counterparts evaluated with the higher-level CCSD(T)/cc-pVTZ model, to form a "hybrid" PES. The original operator representation of the Hamiltonian is analytically reduced to a quasi-diagonal form, integrated in the harmonic oscillator basis and diagonalized to account for strong resonance couplings. Double canonical transformations of EOP expansions enabled prediction of integral intensities of both fundamental and multi-quanta transitions in IR/RS spectra. Enhanced band shape analysis reinforced the assignments. A thorough interpretation of the new IR experimental spectra and existing matrix-isolation literature data for the mixture of two conformers of ACRF was accomplished, and a number of assignments clarified.

Anharmonic vibrational effects in linear and two-dimensional electronic spectra.

For the description of vibrational effects in electronic spectra, harmonic vibrations are a convenient and widespread model. However, spectra of larger organic molecules in solution usually exhibit signs of vibrational anharmonicity, as revealed by deviation from the mirror image symmetry between linear absorption and emission spectra of the harmonic case. For perylene and terylene, two molecules with rigid Pi-electron systems and strong vibrational-electronic coupling, we employ a simple but effective theoretical model, which introduces cubic anharmonicity in the potentials of electronic surfaces. Vibrational anharmonicity is then readily quantified based on the experimentally measured peak ratio of the first vibronic progression peaks in linear absorption and emission. This method is straightforward but not applicable if emission from the initially excited state is short lived. For such a case, we employ two-dimensional electronic spectroscopy in the visible as a comprehensive time-resolved technique for the experimental determination of the vibrational anharmonicity of pinacyanol iodide, a solvated dye molecule exhibiting ultrafast excited state isomerization. We show that the ratio between certain cross peak amplitudes in two-dimensional electronic spectra is a direct measure of vibrational anharmonicity.

Fourier Transform Microwave Spectrum of Propene-3-d1 (CH2═CHCH2D), Quadrupole Coupling Constants of Deuterium, and a Semiexperimental Equilibrium Structure of Propene.

The ground-state rotational spectrum of propene-3-d1, CH2═CHCH2D, was measured by Fourier transform microwave spectroscopy. Transitions were assigned for the two conformers, one with the D atom in the symmetry plane (S) and the other with the D atom out of the plane (A). The energy difference between the two conformers was calculated to be 6.5 cm-1, the S conformer having lower energy. The quadrupole hyperfine structure due to deuterium was resolved and analyzed for both conformers. The experimental quadrupole coupling and the centrifugal distortion constants compared favorably to their ab initio counterparts. Ground-state rotational constants for the S conformer are 40582.157(9), 9067.024(1), and 7766.0165(12) MHz. Ground-state rotational constants for the A conformer are 43403.75(3), 8658.961(2), and 7718.247(2) MHz. For the A conformer, a small tunneling splitting (19 MHz) due to internal rotation was observed and analyzed. Using the new rotational constants of this work as well as those previously determined for the 13C species and for some deuterium-substituted species from the literature, a new semiexperimental equilibrium structure was determined and its high accuracy was confirmed. The difficulty in obtaining accurate coordinates for the out-of-plane hydrogen atom is discussed.

Anharmonic Vibrational Analysis of the Infrared and Raman Gas-Phase Spectra of s-trans- and s-gauche-1,3-Butadiene.

A quantum-mechanical (hybrid MP2/cc-pVTZ and CCSD(T)/cc-pVTZ) full quartic potential energy surface (PES) in rectilinear normal coordinates and the second-order operator canonical Van Vleck perturbation theory (CVPT2) are employed to predict the anharmonic vibrational spectra of s-trans- and s-gauche-butadiene (BDE). These predictions are used to interpret their infrared and Raman scattering spectra. New high-temperature Raman spectra in the gas phase are presented in support of assignments for the gauche conformer. The CVPT2 solution is based on a PES and electro-optical properties (EOP; dipole moment and polarizability) expanded in Taylor series. Higher terms than those routinely available from Gaussian09 software were calculated by numerical differentiation of quadratic force fields and EOP using the MP2/cc-pVTZ model. The integer coefficients of the polyad quantum numbers were derived for both conformers of BDE. Replacement of harmonic frequencies by their counterparts from the CCSD(T)/cc-pVTZ model significantly improved the agreement with experimental data for s-trans-BDE (root-mean-square deviation ≈ 5.5 cm(-1)). The accuracy in predicting the rather well-studied spectrum of fundamentals of s-trans-BDE assures good predictions of the spectrum of s-gauche-BDE. A nearly complete assignment of fundamentals was obtained for the gauche conformer. Many nonfundamental transitions of the BDE conformers were interpreted as well. The predictions of multiple Fermi resonances in the complex CH-stretching region correlate well with experiment. It is shown that solving a vibrational anharmonic problem through a numerical-analytic implementation of CVPT2 is a straightforward and computationally advantageous approach for medium-size molecules in comparison with the standard second-order vibrational perturbation theory (VPT2) based on analytic expressions.

Electron delocalization in polyenes: a semiexperimental equilibrium structure for (3E)-1,3,5-hexatriene and theoretical structures for (3Z,5Z)-, (3E,5E)-, and (3E,5Z)-1,3,5,7-octatetraene.

Electronic structure theory reveals that π-electron delocalization increases with the chain length in polyenes. To analyze quantitatively this effect a semiexperimental equilibrium structure has been determined for trans-hexatriene by the mixed estimation method. For this fit rotational constants for a number of carbon and hydrogen isotopologues as well as a high-level ab initio structure have been used. The accuracy is 0.001 Å for bond lengths and 0.1° for bond angles. For the three isomers of octatetraene, high-level ab initio calculations have given a comparably accurate structure. These structures have been used in comparison with the structure of s-trans-butadiene to show that "C═C" bonds increase in length and "C-C" bonds decrease in length as the polyene chain lengthens. These structural effects of π-electron delocalization increase toward the center of polyenes. Most likely, π-π conjugation in the molecules studied plays a large part in their planarity that, in turn, forces the hydrogen atoms of cis fragments in bay regions to be in a close contact. Their distance is indeed shorter than the sum of their van der Waals radii, and they seem to participate in a six-membered ring.

Accurate equilibrium structures for piperidine and cyclohexane.

Extended and improved microwave (MW) measurements are reported for the isotopologues of piperidine. New ground state (GS) rotational constants are fitted to MW transitions with quartic centrifugal distortion constants taken from ab initio calculations. Predicate values for the geometric parameters of piperidine and cyclohexane are found from a high level of ab initio theory including adjustments for basis set dependence and for correlation of the core electrons. Equilibrium rotational constants are obtained from GS rotational constants corrected for vibration-rotation interactions and electronic contributions. Equilibrium structures for piperidine and cyclohexane are fitted by the mixed estimation method. In this method, structural parameters are fitted concurrently to predicate parameters (with appropriate uncertainties) and moments of inertia (with uncertainties). The new structures are regarded as being accurate to 0.001 Å and 0.2°. Comparisons are made between bond parameters in equatorial piperidine and cyclohexane. Another interesting result of this study is that a structure determination is an effective way to check the accuracy of the ground state experimental rotational constants.

Weak acidity of vinyl CH bonds enhanced by halogen substitution.

As shown by the rates of proton-deuteron exchange in ethylenes with halogen substituents, the weak acidity of vinyl CH bonds is enhanced by halogen substitution. Relative rates of exchange in basic deuterium oxide reflect the relative acidities. Substitution in the α position has the strongest effect. Less electronegative halogens such as bromine increase the acidity more than does fluorine. The vinyl CH acid strengths correlate closely with the energies of deprotonation of isolated molecules into isolated anions, as computed with the MP2/cc-pVQZ model. The smaller deprotonation energies are associated with the stronger acids. Atomic charges from a natural bond order analysis done with the MP2/aug-cc-pVQZ model show that the negative charge becomes more dispersed in the anions of the stronger acids. Results are given for 13 haloethylenes and for 6 halogen-substituted butadienes, cyclopropenes, and a cyclobutene.

Semiexperimental equilibrium structures for cis,cis- and trans,trans-1,4-difluorobutadiene by the mixed estimation method and definitive relative energies of the isomers.

Equilibrium molecular structures accurate to 0.001 Å 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.

Anharmonic vibrational analysis of the gas-phase infrared spectrum of 1,1-difluoroethylene using the operator van Vleck canonical perturbation theory.

Anharmonic vibration frequencies of 1,1-difluoroethylene (11DFE) in the gas phase are predicted by means of the numerical-analytic operator version of the canonical van Vleck perturbation theory in the second and fourth orders (CVPT2 and CVPT4). The full quartic and "semi-diagonal" sextic rectilinear normal coordinate potential energy surfaces, needed for CVPT2 and CVPT4, respectively, were obtained with the MP2/cc-pVTZ quantum-mechanical model. CVPT2 is superior to the traditional second-order vibrational perturbation theory approach (VPT2) because of the uniform general treatment of the Fermi and second-order Darling-Dennison resonances. The fourth-order version, CVPT4, provides a more refined solution and proves convergence of the perturbative treatment. Labeling of the basis functions by polyad numbers breaks down the infinite Hamiltonian matrix into a block-diagonal form. The polyad expression for 11DFE has been determined as P = 14(ν1 + ν7) + 8ν2 + 6(ν3 + ν8) + 4(ν4 + ν9) + 3(ν6 + ν11 + ν12) + 2(ν5 + ν10), where the νi are quantum numbers. The theoretical prediction of anharmonic infrared absorption intensities corroborated an assignment of the majority of observed gas-phase bands up to 3500 cm(-1). The solution was refined by iteratively fitting harmonic frequencies, until predicted fundamental anharmonic frequencies matched the observed values. The average error for about 90 observed frequencies after fitting only fundamental frequencies is ∼1.05 cm(-1). The fitted "semi-experimental" harmonic frequencies agree very well the quantum-mechanical predictions based on the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ models.

Microwave spectra of the deuterium isotopologues of cis-hexatriene and a semiexperimental equilibrium structure.

Microwave transitions and ground state rotational constants are reported for five newly synthesized deuterium isotopologues of cis-1,3,5-hexatriene (cHTE). These rotational constants along with those of the parent and the three (13)C species are used with vibration-rotation constants calculated from an MP2/cc-pVTZ model to derive an equilibrium structure. That structure is improved by the mixed estimation method. In this method, internal coordinates from good-quality quantum chemical calculations (with appropriate uncertainties) are fit simultaneously with moments of inertia of the full set of isotopologues. The new structure of cHTE is confirmed to be planar and is stabilized by an interaction between the hydrogen atoms H2 and H5, which form a bond and participate in a six-membered ring. cHTE shows larger structural effects of π-electron delocalization than does butadiene with the effects being magnified in the center of the molecule. Thus, strong structural evidence now exists for an increase in π-electron delocalization as the polyene chain lengthens.

Semiexperimental equilibrium structures for the equatorial conformers of N-methylpiperidone and tropinone by the mixed estimation method.

N-Methylpiperidone (MPIP) and tropinone, which contain a structural motif found in numerous alkaloids, are too large to determine an accurate equilibrium structure either by ab initio methods or by experiment. However, the ground state rotational constants of the parent species and of all isotopologues with a substituted heavy atom ((13)C, (15)N, (18)O) are known from microwave spectroscopy. These constants have been corrected for the rovibrational contribution calculated from an ab initio cubic force field. These semiexperimental equilibrium rotational constants have been supplemented by carefully chosen structural parameters from medium level ab initio calculations. The two sets of data have been used in a weighted least-squares fit to determine reliable equilibrium structures for both molecules. This work shows that it is possible to determine reliable equilibrium structures for large molecules (34 degrees of freedom in the case of tropinone) at a detailed level of accuracy, and the method could be applied without too much difficulty to still larger molecules.

Semiexperimental equilibrium structure of the lower energy conformer of glycidol by the mixed estimation method.

Rotational constants were determined for (18)O-substituted isotopologues of the lower energy conformer of glycidol, which has an intramolecular inner hydrogen bond from the hydroxyl group to the oxirane ring oxygen. Rotational constants were previously determined for the (13)C and the OD species. These rotational constants have been corrected with the rovibrational constants calculated from an ab initio cubic force field. The derived semiexperimental equilibrium rotational constants have been supplemented by carefully chosen structural parameters, including those for hydrogen atoms, from medium level ab initio calculations. The combined data have been used in a weighted least-squares fit to determine an equilibrium structure for the glycidol H-bond inner conformer. This work shows that the mixed estimation method allows us to determine a complete and reliable equilibrium structure for large molecules, even when the rotational constants of a number of isotopologues are unavailable.

Analysis of the rotational structure in the high-resolution infrared spectrum of trans-hexatriene-1-13C1: a semiexperimental equilibrium structure for the C6 backbone of trans-hexatriene.

trans-Hexatriene-1-(13)C(1) (tHTE-1-(13)C(1)) has been synthesized, and its high-resolution (0.0015 cm(-1)) infrared spectrum has been recorded. The rotational structure in the C-type bands for ν(26) at 1011 cm(-1) and ν(30) at 894 cm(-1) has been analyzed. To the 1458 ground state combination differences from these bands, ground state rotational constants were fitted to a Watson-type Hamiltonian to give A(0) = 0.8728202(9), B(0) = 0.0435868(4), and C(0) = 0.0415314(2) cm(-1). Upper state rotational constants for the ν(30) band were also fitted. Predictions of the ground state rotational constants for tHTE-1-(13)C(1) from a B3LYP/cc-pVTZ model with scale factors based on the normal species were in excellent agreement with observations. Similar good agreement was found between predicted and observed ground state rotational constants for the three (13)C(1) isotopologues of cis-hexatriene, as determined from microwave spectroscopy. Equilibrium rotational constants for tHTE and its three (13)C(1) isotopologues, of which two were predicted, were used to find a semiexperimental equilibrium structure for the C(6) backbone of tHTE. This structure shows increased structural effects of π-electron delocalization in comparison with butadiene and some differences from the cis isomer of HTE. Structures predicted with the MP2/cc-pVTZ model are also compared.

Gas-phase Raman spectra of s-trans- and s-gauche-1,3-butadiene and their deuterated isotopologues.

The gas-phase Raman spectra of 1,3-butadiene and its 2,3-d(2),1,1,4,4-d(4) and d(6) isotopologues have been recorded using intense (6 W) green laser excitation and sensitive CCD detection. Hundreds of bands have been observed and assigned for each isotopologue. These spectra provide the best data to date for the s-trans conformer and also provide the first direct observation of the gas-phase Raman bands of the s-gauche conformer. Spectra recorded at elevated temperatures up to 250 °C for the d(0) and d(6) species help confirm the assignment of bands for the gauche rotamer. DFT computations were utilized to complement the studies. For the most part, the observed gas-phase gauche bands are in good agreement with previous matrix isolation studies. A best set of frequencies are reported for the fundamentals of the gauche rotamer of the d(0) and d(6) species.

Gas-phase Raman spectra and the potential energy function for the internal rotation of 1,3-butadiene and its isotopologues.

The gas-phase Raman spectra of 1,3-butadiene and its 2,3-d(2), 1,1,4,4-d(4), and -d(6) isotopologues have been recorded with high sensitivity in the region below 350 cm(-1) in order to investigate the internal rotation (torsional) vibration. Based on more accurate structural information, the internal rotor constants F(n) were calculated as a function of rotation angle (ϕ). The data for all the isotopologues were then fit using a one-dimensional potential energy function of the form V = (1)/(2)∑V(n)(1 - cos ϕ). Initial V(n) values were based on those generated from theoretical calculations. The agreement between observed and calculated frequencies is very good, although bands not taken into account were present in the spectra. The energy difference between the trans and gauche forms was determined to be about 1030 cm(-1) (2.94 kcal/mol), and the barrier between the two equivalent gauche forms was determined to be about 180 cm(-1) (0.51 kcal/mol), which agrees well with high-level ab initio calculations. An alternative set of assignments also fits the data quite well for all of the isotopologues. For this model, the energy difference between the trans and gauche forms is about 1080 cm(-1) (3.09 kcal/mol), and the barrier between gauche forms is about 405 cm(-1) (1.16 kcal/mol).

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.

Ab initio coupled cluster determination of the equilibrium structures of cis- and trans-1,2-difluoroethylene and 1,1-difluoroethylene.

The equilibrium structures of cis- and trans-1,2-difluoroethylene and 1,1-difluoroethylene, C(2)H(2)F(2), have been determined with high-level coupled cluster techniques combined with large basis sets, explicit consideration of core/valence, and scalar relativistic and higher order correlation effects. Excellent agreement was found with new semiexperimental structures, increasing the level of confidence in both approaches. Differences in bond lengths among ethylene and the fluoroethylenes are discussed.

Infrared spectra of CF(2)=CHD and CF(2)=CD(2): scaled quantum-chemical force fields and an equilibrium structure for 1,1-difluoroethylene.

Infrared (IR) spectra in the gas phase are reported for CF(2)=CHD and CF(2)=CD(2) in the region 350-4000 cm(-1). Ab initio calculations of an harmonic force-field and anharmonicity constants have been made with an MP2/aug-cc-pVTZ model. These enable a number of Fermi resonances in each species to be analyzed and a complete set of "observed" harmonic frequencies to be derived. The latter are combined with similar data for CF(2)=CH(2) in a scaling of the model harmonic force field to both anharmonic and harmonic frequencies. Inspection of the scale factors reveals minor defects of the model, evident in the out-of-plane wagging modes and in the CF stretch/CF stretch interaction force constant. Fermi resonance treatments involved in all isotopomers studied are compatible with the overall force-field refinement results. The treatment leaves a small anomaly in the (13)C shift on nu(1). Improved microwave spectra are reported for five isotopic species, and a semiexperimental equilibrium structure for F(2)C=CH(2) is determined and compared favorably with the structure obtained from new high-level ab initio calculations. Centrifugal distortion constants are predicted for the five isotopic species, and those for F(2)C=CH(2) are compared with values fit to microwave spectra.

Infrared spectra of (12)CF(2)=(12)CH(2) and (12)CF(2)=(13)CH(2), quantum-chemical calculations of anharmonicity, and analyses of resonances.

Infrared spectra obtained in gas and liquid argon phases are reported for (12)CF(2) horizontal line(12)CH(2) and (12)CF(2) horizontal line(13)CH(2). These spectra firmly establish the positions of nu(3)(A(1)) and nu(6)(A(2)) for both isotopomers. Using anharmonicity constants from MP2 calculations, Fermi resonances affecting nu(1)(A(1)), nu(2)(A(1)), nu(3), and nu(8)(B(1)) are analyzed. Deperturbed fundamental frequencies from these analyses are used in conjunction with unaffected fundamentals and ab initio anharmonicity data to predict all 12 "observed" harmonic frequencies. A Darling-Dennison type resonance between 2nu(6) and nu(11) + nu(12) is diagnosed, the calculation of which from ab initio data requires modification of the existing second-order treatment of such constants, where Fermi resonance type terms are also present. Predictions are made of many overtone and combination band frequencies, aiding assignment of observed spectra. From the isolated CH stretching frequency obtained here of 3125.4 cm(-1), the C-H equilibrium bond length is predicted to be 1.0762(11) A.