Equilibrium structure in the presence of internal rotation: A case study of cis-methyl formate

The Born-Oppenheimer (BO) equilibrium molecular structure () of cis-methyl formate has been determined at the CCSD(T) level of electronic structure theory using Gaussian basis sets of at least quadruple-ζ 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-ζ quality. A semi-experimental equilibrium structure () 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 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 and 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(C_m-O) = 1.434 Å, r(O-C_c) = 1.335 Å, r(C_m-H_s) = 1.083 Å, r(C_m-H_a) = 1.087 Å, r(C_c-H) = 1.093 Å, r(CO) = 1.201 Å, ∠(COC) = 114.4°, ∠(CCH_s) = 105.6°, ∠(CCH_a) = 110.2°, ∠(OCH) = 109.6°, ∠(OCO) = 125.5°, and τ(H_aCOC) = 60.3°. The accuracy is believed to be about 0.001 Å for the bond lengths and 0.1° for the angles.     

Rotational spectrum and structure of asymmetric dinitrogen trioxide, N2O3

The rotational spectra of the ground vibrational state and the ν₉ = 1 torsional state have been reinvestigated and accurate spectroscopic constants have been determined. The torsional frequency, ν₉ = 70(15) cm⁻¹, has been determined by relative intensity measurements. The assignment of the infrared spectrum has been slightly revised and an accurate harmonic force field has been calculated. The equilibrium structure has been determined using different, complementary methods: experimental, semi-experimental and ab initio, leading to r(NN) = 1.870(2) Å, in particular.     

Rotational spectra of isotopic species of SO2F2: experimental and ab initio structures

The rotational spectra of ³⁴SO₂F₂ and S¹⁸O¹⁶OF₂ have been measured in their ground vibrational state between 9 and 110 GHz. Accurate rotational constants have been derived. Various experimental structures including the average structure have been determined. The ab initio structure has been calculated at the CCSD(T) level of theory. The different structures are compared and the best equilibrium structure is the ab initio structure: r_e(SO)=1.401 (3) Å, r_e(SF)=1.532 (3) Å, ∠_e(OSO)=124.91(20)°, ∠_e(FSF)=95.53 (20)°.     

Microwave spectra of HPO and DPO: molecular structure

Microwave spectra of the unstable phosphorus containing molecule, HPO, and its deuterated species were measured in the frequency range of 70-380 GHz. The molecule was produced by a DC-glow discharge of a gas mixture of PH₃, CO₂, and H₂(D₂). Rotational constants and centrifugal distortion constants for HPO and DPO were determined accurately. Harmonic force constants were evaluated from the centrifugal distortion constants determined in the present study, and with vibrational frequencies reported previously. The zero-point average structure for HPO was obtained by taking the isotopic difference of the PH bond length into consideration: r_z(PH)=1.473(7) Å, r_z(PO)=1.4843(9) Å, and θ_z=104.57(16)°. The errors were estimated from the residual inertial defect. Equilibrium bond lengths for the PH and PO bonds were derived as 1.455(7) and 1.4800(9) Å, respectively, by assuming anharmonic constants of the corresponding diatomic molecules.     

Anharmonic force field and equilibrium structure of nitric acid

The quadratic, cubic and semi-diagonal quartic force field of nitric acid has been calculated at the CCSD(T) level of theory employing a basis set of triple-ζ quality. A semi-experimental equilibrium structure has been derived from experimental ground state rotational constants and rovibrational interaction parameters calculated from the ab initio force field. It is found that the A and B semi-experimental equilibrium rotational constants of the ¹⁸O isotopologues (for which the rotation of principal axes is large) cannot be accurately reproduced. This problem is discussed and a remedy is proposed. Finally, the semi-experimental structure is in agreement with the ab initio structure calculated at the CCSD(T) level of theory using a basis set of at least quadruple-ζ quality and a core correlation correction, except for the long NO single bond for which the CCSD(T) value is too short due to inadequate treatment of electron correlation. The empirical structures are also determined and their accuracy is discussed. The best equilibrium structure is: r_e(NO_syn) = 1.209(1) Å, r_e(NO_anti) = 1.194(1) Å, r_e(NO) = 1.397(1) Å, r_e(OH) = 0.968(1) Å, ∠(ONO_syn) = 115.8(1)°, ∠(ONO_anti) = 114.2(1)° and ∠(NOH) = 102.2(1)°.     

Microwave spectrum and structure of methyl phosphonic difluoride

The rotational spectrum of methyl phosphonic difluoride has been reinvestigated using a pulsed-molecular-beam Fabry-Perot cavity microwave spectrometer. The enhanced resolution of the Fourier transform microwave (FTMW) spectrometer (compared to the original work done in a conventional Stark spectrometer) has allowed the measurement of small A-E splittings of many of the rotational transitions caused by the internal rotation of the methyl top. The barrier to internal rotation, V₃ = 676 (25) cm⁻¹, has been determined experimentally from the A-E splittings of the rotational transitions in the ground vibrational state. This barrier height is substantially lower than the previously determined value for the barrier, which was 1252 (14) cm⁻¹. High-level ab initio calculations at the MP2/aug-cc-pVTZ level predict a barrier to internal rotation of 638 cm⁻¹, in agreement with the experimentally determined value found here. The high sensitivity of the FTMW spectrometer has also permitted the measurement of the ¹³C and ¹⁸O isotopomers in natural abundance. The addition of these two isotopomers has allowed an improved structural determination.     

Ab initio anharmonic force field and equilibrium structure of carbonyl chlorofluoride

The quadratic, cubic, and semi-diagonal quartic force field of OCFCl has been calculated at the MP2 level of theory employing a basis set of triple-zeta quality. The spectroscopic constants derived from the force field are in excellent agreement with those from previous and new experiments. The equilibrium structure has been derived from experimental ground state rotational constants and ab initio rovibrational interaction parameters. This semi-experimental structure is in excellent agreement with the ab initio structure calculated at the CCSD(T) level of theory. This good agreement indicates that the derived structure is accurate. The equilibrium geometry is: r_e(CO)=1.173(1) Å; r_e(C-F)=1.323(1) Å; r_e(C-Cl)=1.721(1) Å; ∠_e(OCF)=124.0 (1)°; and ∠_e(OCCl)=126.4(1)°.     

Fourier transform microwave spectroscopy of isotopically substituted diacetylenes: rs-structure, quadrupole coupling, and anisotropic nuclear spin-spin interaction

Monodeuterated diacetylene (HCCCCD) and its ¹³C-substituted species H¹³CCCCD, HC¹³CCCD, HCC¹³CCD, and HCCC¹³CD were investigated by Fourier transform microwave spectroscopy. The D nuclear quadrupole splittings were almost completely resolved. For H¹³CCCCD hyperfine splittings caused by the anisotropic nuclear spin-spin interaction between the H and ¹³C nuclei were also observed. The analysis yielded rotational constants, centrifugal distortion constants, and the constants for the nuclear quadrupole coupling and anisotropic nuclear spin-spin interaction. The substitution structure of HCCCCD was calculated as follows: r_s(C-H) = 1.056054(39) Å, r_s(CC) = 1.208631(4) Å, r_s(C-C) = 1.374117(6) Å, r_s(CC) = 1.208116(4) Å, and r_s(C-D) = 1.056231(17) Å, in the order of the arrangement of the bonds. A rough estimate of the equilibrium structure is also presented. The eQq constant for the deuterium nucleus is 0.2061(4) MHz. The anisotropic ¹³C-H spin-spin interaction constant was experimentally determined for the first time as b = −29.2(15) kHz, which is defined as the coefficient of (3I_2zI_3z − I₂ · I₃), where I₂ and I₃ denote the H and ¹³C nuclear spins, respectively, and I_2z and I_3z their components along the molecular axis. The observed b constant is not accounted for by the direct magnetic dipole-dipole interaction only, suggesting a significant contribution from indirect anisotropic interaction.     

A theoretical study of BrCN in the Π electronic ground state: Large amplitude bending motion

We have calculated the three-dimensional potential energy surfaces for the 1 ²A′ and 1 ²A″ states of BrCN⁺ at the MR-SDCI_DK+Q/[QZP-ANO-RCC (Br, C, N)] level of theory, where MR-SDCI_DK means ‘multi-reference single and double excitation configuration interaction calculation with Douglas-Kroll Hamiltonian.’ These ab initio potential energy surfaces have a common minimum (corresponding to the state) at a linear equilibrium structure with r_e(Br-C) = 1.735 Å and r_e(C-N) = 1.199 Å. Variational RENNER calculations yield a zero-point averaged structure (with the structural parameters calculated as expectation values over rovibrational wavefunctions) with 〈r(Br-C)〉₀ = 1.739 Å, 〈r(C-N)〉₀ = 1.204 Å, and 〈∠(Br-C-N)〉₀ = 172(4)°. A severe Fermi resonance between 2ν₂ and ν₃ has been found theoretically for the ²A″ potential energy surface. Comparing the ab initio zero-point averaged structure with a recent, experimentally derived r₀ structure, it is concluded that the effects of large-amplitude bending motion should be taken into account explicitly in the process of deriving the r₀ structure from the experimental values of the rotational constants. The electronic structure of BrCN⁺ has also been discussed.     

Microwave spectrum, molecular structure, and theoretical calculation of cyclohexanone oxime (chair form)

The microwave spectra of cyclohexanone oxime and d₁ (=NOD) and d₄(2,2,6,6-d₄) derivatives were observed in the frequency range from 8 to 40 GHz in the ground and excited vibrational states. The rotational constants were determined to be A = 3799.844(48), B = 1513.7912(23), and C = 1189.6118(29) MHz for normal species, A = 3791.835(88), B = 1461.0324(47), and C = 1157.5653(53) MHz for d₁ species, and A = 3364.141(49), B = 1487.9551(34), and C = 1154.0965(44) MHz for d₄ species in the ground vibrational state. The planar moments, P_bb (P_bb = (I_c + I_a − I_b)/2) of normal, d₁, and d₄ species were determined to be 111.9885(26), 111.9817(46), and 124.2394(49) uŲ, respectively. The almost same values of P_bb of normal and d₁ species suggest that the hydroxyl hydrogen atom is very close to the a-c plane. From the r_s coordinates of the hydroxyl hydrogen atom, the OH bond was found to be at the trans position with respect to the CN double bond. The conformation of cyclohexanone oxime was determined to be chair form by comparing the observed and calculated rotational constants, ΔI, and planar moments, and taking account of the calculated the relative energy difference, ΔE. The structural parameters, the three bond lengths, three bond angles, and three dihedral angles, were adjusted to the nine rotational constants observed. The bond angle of ∠C₂C₁N is much wider than that of ∠C₆C₁N by about 10°. The dihedral angles of ∠C₁C₂C₃C₄, ∠C₂C₃C₄C₅, and ∠C₃C₄C₅C₆ were determined to be 53.3(5), −57.2(5), and 57.2(5)°. Two vibrational modes were assigned to the ring-bending and ring-twisting ones, which are almost harmonic up to v = 3.     

Rotational spectrum of trifluoroacetone

The rotational spectra of 5 isotopologues of 1,1,1-trifluoroacetone have been assigned using pulsed-jet Fourier-transform microwave spectroscopy. All rotational transitions appear as doublets, due to the internal rotation of the methyl group. Analysis of the tunneling splittings using both the principal axis method (PAM) and the combined axis method (CAM) methods allows to determine accurately the height of the threefold barrier to internal rotation of the methyl group, and its orientation, leading to V₃ = 3.28 and 3.10 kJ mol⁻¹, respectively. The r_s geometry of the molecular skeleton, a partial r₀ structure of the molecule and supporting ab initio calculations are also reported.     

Rotational spectra of isotopic species of silyl fluoride. Part II: Theoretical and semi-experimental equilibrium structure

The equilibrium structure of silyl fluoride, SiH₃F, has been reinvestigated using both theoretical and experimental data. With respect to the former, quantum-chemical calculations at the coupled-cluster level have been employed together with extrapolation to the basis set limit, consideration of higher excitations in the cluster operator, and inclusion of core correlation as well as relativistic corrections (r(Si-F) = 1.5911 Å, r(Si-H) = 1.4695 Å, and ∠FSiH = 108.30°). A semi-experimental equilibrium structure has been determined based on the available rotational constants for the various isotopic species of silyl fluoride (²⁸SiH₃F, ²⁸SiD₃F, ²⁹SiH₃F, ²⁹SiD₃F, ³⁰SiH₃F, ³⁰SiD₃F, ²⁸SiH₂DF, and ²⁸SiHD₂F) together with computed vibrational corrections to the rotational constants (r(Si-F) = 1.59048(6) Å, r(Si-H) = 1.46948(9) Å, and ∠FSiH = 108.304(9)°).     

A theoretical study of FeCN in the Δ electronic ground state

The three-dimensional potential energy and dipole moment surfaces for the electronic ground state ⁶Δ of FeCN have been computed at the MR-SDCI + Q + E_rel/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] level of theory, where MR-SDCI means ‘multi-reference single and double excitation configuration interaction’ and ANO means ‘atomic natural orbital’. Based on these potential energy and dipole moment surfaces, the spectroscopic parameters, rovibronic energies, structural parameters, vibrational transition moments, and the wavenumbers and intensities of selected rotation-vibration transitions have been calculated. The equilibrium structure is linear with r_e(Fe-C) = 2.048 Å and r_e(C-N) = 1.168 Å, and the zero-point averaged structure is bent with 〈r(Fe-C)〉₀ = 2.082 Å, 〈r(C-N)〉₀ = 1.172 Å, and 〈∠(Fe-C-N)〉₀ = 170(5)°. At all the MR-SDCI + Q and the size-extensive multi-reference averaged quadratic coupled-cluster (MR-AQCC) levels of theory, with and without relativistic correction E_rel, that were employed in the present work, ⁶Δ FeCN is predicted to be slightly more stable than ⁶Δ FeNC. For example, the energy difference between the two isomers is approximately 150 cm⁻¹ at the highest level of theory employed, MR-AQCC + E_rel/[Roos ANO (Fe), aug-cc-pVQZ (C, N)] with zero-point energy correction. The electronic structure of ⁶Δ FeCN has also been compared with that of ⁶Δ FeNC. At present, no experimental spectroscopic data are available for ⁶Δ FeCN. It is hoped that the present work will stimulate experimental investigations of this molecule.     

Large amplitude bending motion in CsOH, studied through ab initio-based three-dimensional potential energy functions

The large-amplitude bending motion in CsOH, a ‘classical’ molecule whose microwave spectrum was first recorded in 1967, has been studied ab initio. The three-dimensional potential energy surface has been calculated at the RCCSD(T)_DK3/[QZP + g ANO-RCC (Cs, O, H)] level of theory and employed in MORBID calculations of the rotation-vibration energies and intensities. The ground electronic state is ¹Σ⁺ with the equilibrium structure r_e(Cs-O) = 2.3930 Å, r_e(O-H) = 0.9587 Å, and ∠_e(Cs-O-H) = 180.0°. The O-H moiety is bound to Cs by an ionic bond and the molecule can be described as Cs^δ+(OH)^δ-. Hence, the bending potential is shallow and gives rise to large-amplitude bending motion. The ro-vibrationally averaged structural parameters, determined as expectation values over MORBID wavefunctions, are 〈r(Cs-O)〉₀ = 2.3987 Å, 〈r(O-H)〉₀ = 0.9754 Å, and 〈∠(Cs-O-H)〉₀ = 163°. Although the averaged structure in the vibrational ground state is far from being linear, the Yamada-Winnewissi-linearity parameter for CsOH is γ₀≈-1.0, the value characteristic for a linear molecule.     

Ground state parameters of BiH3 from infrared and millimeter-wave spectra: ground state and equilibrium structures

Unstable, short-lived BiH₃ has been synthesized and investigated by rotational spectroscopy in the range 158 (J=1-0) to 1280 GHz (J=8-7). Quadrupole and spin-rotation hyperfine structures (eQq=584.676(96) MHz), and the A₁A₂ splitting of the K=3 ground state level, have been resolved. By merging the pure rotational data with 1764 ground state combination differences obtained from the analysis of high resolution Fourier transform infrared spectra of the ν₁-ν₄ bands [J. Mol. Spectrosc. (2004) (in press)] spanning J and K values up to 16 and 14, respectively, with 0?ΔK?9, the ground state rotational and centrifugal distortion constants up to octic and sextic terms for reductions A and B, respectively, have been determined. Of the reductions of the ground state rovibrational Hamiltonian, reduction B including ε rather than h₃ as off-diagonal element is clearly favored. An experimental r₀ structure of the very-near spherical oblate symmetric top BiH₃, r(BiH)=178.82 pm and α(HBiH)=90.320°, has been deduced from the rotational constants B₀=2.64160172(18) and C₀=2.6010403(31) cm⁻¹. The derived experimental r_e structure, r_e(BiH)=177.834(50) pm and α_e(HBiH)=90.321(10)°, was determined. This is in excellent agreement with the most recent ab initio structure, r_e(BiH)=177.84 pm, and α_e(HBiH)=90.12°.     

Fourier transform microwave spectroscopy of N,N-dimethylacetamide

The jet-cooled Fourier-transform microwave spectrum of N,N-dimethylacetamide was recorded in the region of 12-24 GHz, and was analyzed to determine rotational constants and nuclear quadrupole coupling constants. Coriolis-like coupling parameters characterizing interaction between internal rotation of methyl groups and the overall rotation were also determined from internal-rotation tunneling splittings of the rotational transitions. The Coriolis-like coupling parameters permitted determination of the barrier heights to internal rotation of the three methyl groups, which were found to be 677, 237, and 183 cm⁻¹ for the C-methyl top, the trans-N-methyl top and the cis-N-methyl top, respectively.     

Fourier-transform microwave spectroscopy of N-methylaniline

The jet-cooled Fourier-transform microwave spectrum of N-methylaniline (C₆H₅-NHCH₃) was recorded in the region of 10-26 GHz, and was analyzed to determine rotational constants and nuclear quadrupole coupling constants. Furthermore, a Coriolis-like coupling parameter characterizing an interaction between an internal rotation of a methyl group and an overall rotation was also determined from A-E splittings observed in pure rotational transitions with high K_a values. The Coriolis-like coupling parameter permitted the determination of the barrier to internal rotation of the methyl group which was found to be 975 cm⁻¹.     

Analysis of rotational structure in the high-resolution infrared spectrum and assignment of vibrational fundamentals of butadiene-2,3-C2

The 2,3-¹³C₂ isotopomer of butadiene was synthesized, and its fundamental vibrational fundamentals were assigned from a study of its infrared and Raman spectra aided with quantum chemical predictions of frequencies, intensities, and Raman depolarization ratios. For two C-type bands in the high-resolution (0.002 cm⁻¹) infrared spectrum, the rotational structure was analyzed. These bands are for ν₁₁ (a_u) at 907.17 cm⁻¹ and for ν₁₂ (a_u) at 523.37 cm⁻¹. Ground state and upper state rotational constants were fitted to Watson-type Hamiltonians with a full quartic set of centrifugal distortion constants and two sextic ones. For the ground state, A₀ = 1.3545088(7) cm⁻¹, B₀ = 0.1469404(1) cm⁻¹, and C₀ = 0.1325838(2)  cm⁻¹. The small inertial defects of butadiene and two ¹³C₂ isotopomers, as well as for five deuterium isotopomers as previously reported, confirm the planarity of the s-trans rotamer of butadiene.     

The Ground State Spectroscopic Parameters and Equilibrium Structure of PD3

Infrared spectra of PD₃ have been measured in the 20-320 cm⁻¹ range and in the region of the ν₂/ν₄ and ν₁/ν₃ fundamental bands near 750 and 1690 cm⁻¹, respectively, with a resolution of ca. 0.0025 cm⁻¹. Furthermore, submillimeter-wave spectra covering the J=4-3, 13-12, and 14-13 clusters in the vibrational ground state were recorded. The observed ΔJ=+1 rotational lines were augmented by about 5500 ground state combination differences formed from transitions belonging to the fundamental bands. Of these, 1300 involved perturbation-allowed lines with ΔK≠0. These data and observations taken from the literature were appropriately weighted and fitted to 14 ground state molecular constants. The A and B reductions of the rotational Hamiltonian were found to be equivalent. Improved effective ground state and equilibrium structures were determined for both PH₃ and PD₃; the equilibrium structures, r_e (PH)=141.1607(83) pm and α_e (HPH)=93.4184(95)° and r_e (PD)=141.1785(57) pm and α_e (DPD)=93.4252(68)°, are in good agreement.     

Millimeter-wave spectroscopy of rare isotopomers of HC5N and DC5N: determination of a mixed experimental-theoretical equilibrium structure for cyanobutadiyne

Cyanobutadiyne has been produced by gas phase copyrolysis of pyridine and phosphorus trichloride in a flow reactor. The yield of the reaction is sufficiently good to allow the detection of rotational transitions of the ¹³C and ¹⁵N containing species in natural abundance. Normal pyridine and its fully deuterated variant have been used as precursors, making it possible to study the ground-state rotational spectra of 14 isotopomers in the millimeter wave region. Very accurate values of the rotational and quartic centrifugal distortion constants have been obtained for all the isotopic species investigated, and in addition the sextic distortion constant has been precisely determined for the most abundant variants H¹²C₅¹⁴N and D¹²C₅¹⁴N, for which the measurements have been extended up to 460 GHz. A mixed experimental-theoretical equilibrium structure has been evaluated for cyanobutadiyne combining experimental ground-state rotational constants with theoretically computed zero-point contributions. The r_e geometry is compared with operationally defined purely experimental structures, namely r₀, r_s, and r_m⁽¹⁾ molecular structures.