Renner-Teller Research Articles

Far-Infrared Laser Magnetic Resonance Spectroscopic Study of the ν2 Bending Fundamental of the CCN Radical in Its X̃2Πr State

Bending vibration–rotation transitions between the (010) μ2Σ− and (000) 2Πr vibronic states of the CCN radical in its ground electronic state have been observed using far-infrared laser magnetic resonance (FIR LMR) spectroscopy. Thirteen FIR laser lines were used to record 769 resonances. The LMR data, combined with previous data, were used to determine vibrational, Renner–Teller, fine-structure, rotational, hyperfine, and molecular g-factor parameters using a least-squares fitting routine. The model used was an N2 effective Hamiltonian modified to include the Renner–Teller effect explicitly in a 2Π electronic state. The band origin for the (010) μ2Σ− ← (000) X̃2Πr transition was determined to be 179.598176 ± 0.000067 cm−1. The spin–orbit splitting in the ground state was refined and the complete set of 14N-hyperfine parameters determined for the first time.

The silaketenylidene (SiCO) molecule: Characterization of the X̃ 3Σ− and à 3Π states

The ground (X̃ 3Σ−) and first excited triplet (à 3Π) electronic states of carbonylsilene or silaketenylidene, SiCO, have been investigated systematically using ab initio electronic structure theory. The total energies and physical properties including equilibrium geometries, dipole moments, harmonic vibrational frequencies, and associated infrared (IR) intensities were predicted using self-consistent-field (SCF), configuration interaction with single and double excitations (CISD), coupled cluster with single and double excitations (CCSD), equation-of-motion (EOM) CCSD, CCSD with perturbative triple excitations [CCSD(T)] methods with a wide range of basis sets. The linear X̃ 3Σ− ground state of SiCO has a real degenerate bending vibrational frequency, whereas the à 3Π state of SiCO is subject to the Renner–Teller effect and presents two distinct real vibrational frequencies along the bending coordinate. The bending vibrational frequency of the à 3Π state was evaluated via the EOM-CCSD technique. At the highest level of theory with the largest basis set, cc-pVQZ CCSD(T), the adiabatic X̃–à splitting without the zero-point vibrational energy (ZPVE) correction (Te value) was determined to be 68.5 kcal/mol (2.97 eV, 23 900 cm−1) and the adiabatic splitting with the ZPVE energy correction (T0 value) to be 69.0 kcal/mol (2.99 eV, 24 100 cm−1), which are in excellent agreement with the experimental T0 value of 68.78 kcal/mol (2.983 eV, 24 056 cm−1). The theoretical ground state harmonic Si–C stretching frequency ω3=564 cm−1 is much less than the experimental estimate of 800 cm−1.

Theoretical investigation of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules. 2. Perturbative calculation of the vibronic spectrum in the 11Δg state of B2H2 from the linear molecule standpoint

Second-order perturbative formulae for handling the Renner-Teller effect in Δ electronic states of symmetric tetra-atomic molecules with linear equilibrium geometry are derived. They are applied to calculate vibronic energy levels of the 11Δg state of B2H2. Perturbative parameters are derived by fitting the ab initio computed potential energy surfaces. The results of the calculations are compared with those obtained by means of a variational approach.

Theoretical investigation of the Renner-Teller effect in Delta electronic states of tetra-atomic molecules. 2. Perturbative calculation of the vibronic spectrum in the 1 1 Delta g state of B 2 H 2 from the linear molecule standpoint

Theoretical investigation of the Renner-Teller effect in Delta electronic states of tetra-atomic molecules. 2. Perturbative calculation of the vibronic spectrum in the 1 1 Delta g state of B 2 H 2 from the linear molecule standpoint

Theoretical investigation of the Renner-Teller effect in Delta electronic states of tetra-atomic molecules. 1. Variational calculation of vibronic structure in the 1 1 Delta g state of B 2 H 2

Theoretical investigation of the Renner-Teller effect in Delta electronic states of tetra-atomic molecules. 1. Variational calculation of vibronic structure in the 1 1 Delta g state of B 2 H 2

Theoretical investigation of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules. 1. Variational calculation of vibronic structure in the 11Δg state of B2H2

A variational approach for the ab initio handling of the Renner-Teller effect in Δ electronic states of tetra-atomic molecules is presented. The model Hamiltonian involves four nuclear degrees of freedom which correlate for a linear nuclear arrangement with two doubly degenerate bending modes. The bond lengths are assumed to be kept fixed at their equilibrium values and the effect of end-over-end rotations is neglected. The kinetic energy operator and the general form of the potential surfaces employed allow in principle for a treatment of large amplitude bending vibrations. However, because of restrictions implied, such as neglect of coupling between bending and stretching vibrations and interactions with other electronic states, the approach is aimed primarily at molecules bending with relatively small amplitudes around their linear equilibrium geometries. Two algorithms are developed, one for symmetric acetylene-like (A-B-B-A) molecules, the other for asymmetric (A-B-C-D) species. The approach is applied to calculate the vibronic spectrum of the lowest lying excited state, 1Δg, of B2H2, employing ab initio computed potential energy surfaces.

Near-Infrared Diode–Laser Spectroscopy of the CCO Radical in theÃ(010)3Δ–X(010)3Π(b) Band

The Ã(010)3Δ–X(010)3Π(b) band spectrum of the CCO radical has been studied in the region from 11,808 to 11,919 cm−1by near-infrared diode–laser spectroscopy. A least-squares fit has been made using only part of the observed Ã(010)3Δ–X(010)3Π(b) band transitions to obtain molecular constants for the Ã(010)3Δ state, removing transitions with upper levels of irregular behavior. The spin–orbit parameter and the subband origin determined in the present analysis have been discussed in relation to higher order contributions to the Renner–Teller effect.

Ab initio investigation of the vibronic spectrum involving the two lowest-lying electronic states of HCCO

The results of ab initio calculations of the vibronic spectra involving both lowest-lying states X2A″ and A2A′ of the ketenyl radical HCCO are presented. Potential energy surfaces are computed by means of the coupled cluster method with perturbative triple corrections [CCSD(T)]. A recently developed ab initio approach for the treatment of the Renner–Teller effect in tetra-atomic asymmetric molecules is applied to calculate the vibronic energy levels.

Ab initio investigation of the Renner–Teller effect in the ground electronic state of HCCD+

Results of an ab initio treatment of the Renner–Teller effect in the ground electronic state of HCCD+ are presented. The model Hamiltonian employed involves four nuclear degrees of freedom correlating at linear geometry with two degenerate bending vibrations. Computations of vibronic energy levels and wave functions are carried out by means of a variational approach. The results of calculations are compared with those for symmetric isotopic species HCCH+ and DCCD+.

Perturbative and variational handling of the Renner–Teller effect in Δ electronic states of triatomic molecules

Second-order perturbative formulae for handling the Renner–Teller effect in Δ electronic states of triatomic molecules are derived. They are applied to calculate vibronic energy levels of the X 5 Δ g state of FeH 2. The ab initio computed bending potential energy curves are employed. The results of perturbative calculations are compared with those obtained by means of a variational approach.

Ab initio investigation of the vibronic structure and the spin–orbit coupling in the [formula omitted] state of C 2D 2+

Results of an ab initio study of the Renner–Teller effect in the X 2 Π u state of C 2D 2 + are presented. Potential curves for the trans- and cis-bending vibrations calculated by means of the internally contracted multireference configuration interaction method are employed. Vibronic energy levels and their splitting upon spin–orbit coupling are computed by means of a variational approach.

Erratum to “ Ab initio treatment of the Renner-Teller effect in tetra-atomic molecules undergoing large amplitude bending vibrations” : [Chem. Phys. 225 (1997) 63–76

Erratum to “ Ab initio treatment of the Renner-Teller effect in tetra-atomic molecules undergoing large amplitude bending vibrations” : [Chem. Phys. 225 (1997) 63–76

Ab initio treatment of the Renner-Teller effect in tetra-atomic molecules undergoing large amplitude bending vibrations

The ab initio approach for handling the Renner-Teller effect in tetra-atomic molecules we derived in previous work is generalized to asymmetric molecules undergoing large-amplitude bending vibrations. The results of test calculations on the X 2Π u state of B 2H 2 + are presented.

Renner–Teller splitting in the C 1s→π* excited states of CS2, OCS, and CO2

Fragment ions energetically emitted following the perpendicular (ΔΛ=+1) transitions of C 1s→π* of CS2, OCS, and CO2 are observed not only in the perpendicular (90°) direction but also in the parallel (0°) to the linear polarization; that is, ions have a momentum orthogonal to the linear molecule. This arises in the Renner–Teller (RT) vibronic coupling of bending vibrations in the C 1s→ in-plane π* excited state with a bent equilibrium geometry, though the RT splitting between the C 1s→ out-of-plane π* state with a linear geometry and the C 1s→ in-plane π* state is not visible directly due to the lifetime broadening. The 0° ion yield is relatively small in CS2 but is comparable to the 90° yield in CO2; in the latter the peak maximum at 0° is 0.06 eV lower than at 90° and the anisotropy parameter β is heavily dependent on the photon energy. In CO2 a great number of unresolved bending vibrations are coupled. The half-width at half-maximum on the lower energy side of the π* peak is much more sensitive to the RT splitting; 0.08, 0.11, and 0.29 eV for CS2, OCS, and CO2, compared with the full-width at half-maximum, 0.17, 0.39, and 0.64 eV. In CS2 the π* peak and β value are sharp and symmetric, indicating that the zero-point vibrational levels are only involved. In OCS three fine structures observed with separations of 0.21 eV are assigned to the ν3 mode, which is comparable to the stretching mode in CO.

Laser-induced fluorescence spectroscopy of the C̃ 2Σ+−X̃ 2Π1/2 band system of jet-cooled CCN radical

Laser-induced-fluorescence spectra of the C̃ 2Σ+−X̃ 2Πr system of the CCN radical were observed under jet-cooled conditions. The radical was generated in a supersonic expansion by a pulsed electric discharge of methyl cyanide diluted in Ar. Sixteen C̃ 2Σ+(v1,v2l,v3)–X̃ 2Π1/2(0,00,0) vibronic bands with v1=0–3, v2=0–2 (l=0–2), and v3=0–2 were observed, including some very weak vibronically induced parallel-type transitions with v2=1 (l=1). Rotational analyses were performed to give the band origins and the rotational constants for vibrationally excited states of all the three normal modes and their combinations in the C̃ 2Σ+ state. From the determined band origins, the term value and the vibrational parameters in the C̃ 2Σ+ state have been determined: Te=24 627.1(20) cm−1, ω1=1903.1(11) cm−1, ω2=469.88(38) cm−1, ω3=1256.6(40) cm−1, and g22=0.86(11) cm−1. A combination of the present ω2 frequency in the C̃ state with the data on the hot bands reported so far in literature has yielded the vibronic structures in the X̃ 2Πr and à 2Δ states, which are subject to a prominent Renner–Teller effect.

Quantum structural approach to high-Tcssuperconductivity theory: Herzberg-Teller, Renner-Teller, Jahn-Teller effects and intervalent geminal charge transfer

We use quantum molecular structure and spectroscopic thoughts of various possible vibronic interactions for the position space of two-electron geminal orbitals with Bloch sums. Our geminals have different degeneracy from one-electron molecular orbitals and are different from the momentum space of BCS free electrons. Based on Herzberg-Teller expansions, our consideration of the aspect of the Renner-Teller effect for cyclic boundary crystals (instead of the usual linear molecules) involves first-order vibronic interaction with isotope effects different from the second-order electron-phonon energy of BCS theory, bipolaron theory, etc. Our consideration of the Jahn-Teller effect with equal-minimum double-well potential leads to the intervalent charge transfer between two degenerate vibrationally affected electronic structures. Our considerations of different style vibrations other than the antisymmetric vibration for the nearest neighbor (e.g., displaced oscillator, etc.) may possibly be related to the case of special chemical structures with special doping and special coherence length. Our simple structural illustrations of such different vibronic Renner-Teller, Jahn-Teller effects and intervalent charge transfer (of ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathrm{x}}$ ${\mathrm{Sr}}_{\mathrm{x}}$ ${\mathrm{CuO}}_{4}$ and ${\mathrm{YBa}}_{2}$ ${\mathrm{Cu}}_{3}$ ${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{x}}$ ) may promote some possible thoughts of quantum chemical structures compared and mixed with the physical treatments of special high-${\mathrm{T}}_{\mathrm{c}}$ superconductors.

The First Excited Ca–C–C Bending Vibration Levels in theÃ2Π andX2Σ+States of the CaCCH Radical: The Renner–Teller Effect andK-type Resonance

The 510and 511bands of the CaCCHÃ2Π–X2Σ+transition, corresponding to the Ca–C–C bending mode, have been rotationally analyzed through cw dye laser excitation and dispersed fluorescence with a CCD array detector. The upper state is subject to Renner–Teller and spin–orbit couplings, and strongK-type resonance interactions were observed between the nearby2Δ and2Σ vibronic components. A model that invokes a full matrix treatment of these interactions was employed in a least-squares fit of a total of 708 rotational lines of the two bands, recorded with high precision. The fundamental bending frequencies have been determined as ν5= 101.394(1) and 102.940(1) cm−1for theÃ2Π andX2Σ+electronic states, respectively. The Renner–Teller parameter has been determined as ϵ5ω5= 3.528(14) cm−1. The nonadiabatic parameter for the ν5mode,gK= 0.6542(10) cm−1, is in accord with the observation that the2Δ5/2vibronic component liesabovethe normally highest κ2Σ component.

Calculations on ground and excited state potential energy surfaces of floppy free radicals: HC 4H 2, HC 3NH, and HC 3O

Ab initio calculations using the 6-311G(d, p) basis set at the QCISD and CCSD(T) levels were undertaken on the ground and lowest excited electronic states of the isoelectronic carbon-chain free radicals, HC 4H 2, HC 3NH and HC 3O. The equilibrium geometry for each molecule is a C s structure with four electrons in a″ orbitals, and the lowest excited states are characterized by configurations with three, five, and six a″ electrons. The effective vibrational potential energy surfaces of these states along the two lowest frequency in-plane bending coordinates were investigated in order to assess the trend in large-amplitude motions and isomerization across different electronic configurations in a series of isoelectronic molecules. The (4- a″) ground state potential surfaces of HC 3NH and HC 3O are subject to the Renner-Teller effect, and intersect the (5- a″) excited state surfaces at linear 2π states of at 2300 cm −1 and 8400 cm −1, respectively, above the energy of the equilibrium geometries. The (3- a″) states of HC 3O and HC 3NH lie 27 000 cm −1 and 24 000 cm −1 above the (4- a″) equilibrium states, respectively, and form Renner-Teller pairs with the (6- a″) tates. Although two minima are found for HC 3O and HC 3NH on the (3- a″) surface, none of these minima is stable with respect to planarity. The (5- a″) surface of HC 4H 2 has a single minimum at a C 2v structure, which is unstable with respect to the ground state. The (3- a″) surface has two minima, both of which are stable. Equilibrium structures, excitation energies, and potential surface properties for these structures are reported.

On a theoretical model for the Renner–Teller effect in tetra-atomic molecules

A model for the ab initio treatment of the Renner–Teller effect in tetra-atomic molecules is elaborated. It is based on the approach developed by Petelin and Kiselev [Int. J. Quantum Chem. 6, 701 (1972)]. Particular attention is paid to Π electronic states. Perturbative formulas are derived for several coupling cases. The model is checked by means of ab initio calculations at various levels of sophistication. Results of computations of various quantities related to the model are presented for the X 2Πu states of B2H+2 and C2H+2. The reliability of the basis assumptions is demonstrated by comparing the results obtained in the framework of the model considered with those of independent ab initio calculations.

Microwave spectroscopy of the HCCS and DCCS radicals (X̃ 2Πi) in excited vibronic states: A study of the Renner–Teller effect

The microwave spectra of the HCCS and DCCS radicals are studied in the frequency range of 160–400 GHz and the rotational transition series are assigned to several low-lying vibronic states in the CCS or H(D)CC bending vibration. Analysis is carried out to obtain effective constants for respective vibronic states. The γeff constants for the vibronic μ/κ2Σ states are found to be anomalous, in that the variation of the γeff constants in the same bending mode is large up to 3 GHz and the γeff value can reach to nearly twice the rotational constants Bv. This behavior cannot be understood by the current Renner–Teller theory. We have developed a theory to include cross vibronic interaction between two vibronic 2Σ(vt=1) states in different bending modes. Since the difference of the vibrational quantum numbers for these states is Δ(v4+v5)=0, the interaction has a much larger effect than the one considered by Petelin and Kiselev [Int. J. Quantum Chem. 6, 701 (1972)] for the vibronic states with Δ(v4+v5)=±2. Calculation with the newly derived expressions for γeff reproduces the anomaly in HCCS when the Renner parameters are fixed at ε4=−0.37 and ε5=+0.10 from the ab initio calculation, and the parameter |ε45| for the cross vibronic interaction is varied to be 0.4, a value which is obtained for the first time. The relative sign of the above ε4 and ε5 values is explicitly judged to be correct. In addition, the Beff and the P-doubling constants in the 2Πi and 2Δi states are found to be effected by a higher-order perturbation of the cross vibronic interaction.