The Jahn-Teller effect in CH 3 Cl +(X̃E2): A combined high-resolution experimental measurement and ab initio theoretical study

Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibrational modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E₃^″⊗e₁^' Jahn-Teller interaction is used to demonstrate the correctness of the formalism. A Python program is developed to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems and interface the expansions to the MCTDH quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn-Teller and pseudo-Jahn-Teller problems. Also it is the only one.

Vibronic interaction in CO3− photo-detachment: Jahn–Teller effects beyond structural distortion and general formalisms for vibronic Hamiltonians in trigonal symmetries

Expansion formalisms for trigonal Jahn–Teller and pseudo-Jahn–Teller vibronic Hamiltonians are developed and used to study and correctly interpret the photoelectron spectrum of CO₃⁻.

General formalism for vibronic Hamiltonians in tetragonal symmetry and beyond

We derive general expansion formulas in vibrational coordinates for all bimodal Jahn–Teller and pseudo-Jahn–Teller Hamiltonians in tetragonal symmetry.

Rotationally resolved vibrational spectra of AsH3 (+)X̃(2)A2 (″): Tunneling splittings studied by zero-kinetic-energy photoelectron spectroscopy

The rotationally resolved vibrational spectra of AsH3 (+)X̃(2)A2 (″) have been measured for the first time with vibrational energies up to 6000 cm(-1) above the ground state using the zero-kinetic-energy photoelectron method. The symmetric inversion vibrational energy levels (v2 (+)) and the corresponding rotational constants for v2 (+)=0-15 have been determined. The tunneling splittings of the inversion vibration energy levels have been observed and are 0.8 and 37.7 (±0.5) cm(-1) for the ground and the first excited vibrational states, respectively. The first adiabatic ionization energy for AsH3 was determined as 79 243.3 ± 1 cm(-1). The geometric parameters of AsH3 (+)X̃(2)A2 (″) as a function of inversion vibrational numbers have been determined, indicating that the geometric structure of the cation changes from near-planar to pyramidal with increasing inversion vibrational excitation. In addition to the experimental measurements, a two-dimensional theoretical calculation considering the two symmetric vibrational modes was performed to determine the energy levels of the symmetric inversion, which are in good agreement with the experimental results. The inversion vibrational energy levels of SbH3 (+)X̃(2)A2 (″) have also been calculated and are found to have much smaller energy splittings than those of AsH3 (+)X̃(2)A2 (″).

Combined theoretical and experimental study of the valence, Rydberg and ionic states of fluorobenzene

New photoelectron spectra (PES) and ultra violet (UV) and vacuum UV (VUV) absorption spectra of fluorobenzene recorded at higher resolution than previously, have been combined with mass-resolved (2 + 1) and (3 + 1) resonance enhanced multiphoton ionization (REMPI) spectra; this has led to the identification of numerous Rydberg states. The PES have been compared with earlier mass-analyzed threshold ionization and photoinduced Rydberg ionization (PIRI) spectra to give an overall picture of the ionic state sequence. The analysis of these spectra using both equations of motion with coupled cluster singles and doubles (EOM-CCSD) configuration interaction and time dependent density functional theory (TDDFT) calculations have been combined with vibrational analysis of both the hot and cold bands of the spectra, in considerable detail. The results extend several earlier studies on the vibronic coupling leading to conical intersections between the X(2)B1 and A(2)A2 states, and a further trio (B, C, and D) of states. The conical intersection of the X and A states has been explicitly identified, and its structure and energetics evaluated. The energy sequence of the last group is only acceptable to the present study if given as B(2)B2<C(2)B1<D(2)A1, a conclusion which is in agreement with most previous EOM-CCSD and other calculations. However, this symmetry ordering of the B and C states forces reconsideration of the nature of the PIRI spectrum. The coupling between these two states is induced by the a2 modes, ν12 and ν14 and we propose that the 14(1) band is observed in the B(2)B2 band in the PES for the first time, because of the improved resolution. This same assignment is given to the lowest energy band in the PIRI spectrum which was previously assigned as the origin band and further conclude that the entire PIRI spectrum is induced by ν12 and ν14. The relative intensities of the various Rydberg state peaks in the VUV absorption and REMPI spectra of fluorobenzene are very similar to those observed in the equivalent spectra of benzene.

Combined theoretical and experimental study of the valence, Rydberg, and ionic states of chlorobenzene

New photoelectron (PE) and ultra violet (UV) and vacuum UV (VUV) spectra have been obtained for chlorobenzene by synchrotron study with higher sensitivity and resolution than previous work and are subjected to detailed analysis. In addition, we report on the mass-resolved (2 + 1) resonance enhanced multiphoton ionization (REMPI) spectra of a jet-cooled sample. Both the VUV and REMPI spectra have enabled identification of a considerable number of Rydberg states for the first time. The use of ab initio calculations, which include both multi-reference multi-root doubles and singles configuration interaction (MRD-CI) and time dependent density functional theoretical (TDDFT) methods, has led to major advances in interpretation of the vibrational structure of the ionic and electronically excited states. Franck-Condon (FC) analyses of the PE spectra, including both hot and cold bands, indicate much more complex envelopes than previously thought. The sequence of ionic states can be best interpreted by our multi-configuration self-consistent field computations and also by comparison of the calculated vibrational structure of the B and C ionic states with experiment; these conclusions suggest that the leading sequence is the same as that of iodobenzene and bromobenzene, namely: X(2)B1(3b1 (-1)) < A(2)A2(1a2 (-1)) < B(2)B2(6b2 (-1)) < C(2)B1(2b1 (-1)). The absorption onset near 4.6 eV has been investigated using MRD-CI and TDDFT calculations; the principal component of this band is (1)B2 and an interpretation based on the superposition of FC and Herzberg-Teller contributions has been performed. The other low-lying absorption band near 5.8 eV is dominated by a (1)A1 state, but an underlying weak (1)B1 state (πσ(∗)) is also found. The strongest band in the VUV spectrum near 6.7 eV is poorly resolved and is analyzed in terms of two ππ(∗) states of (1)A1 (higher oscillator strength) and (1)B2 (lower oscillator strength) symmetries, respectively. The calculated vertical excitation energies of these two states are critically dependent upon the presence of Rydberg functions in the basis set, since both manifolds are strongly perturbed by the Rydberg states in this energy range. A number of equilibrium structures of the ionic and singlet excited states show that the molecular structure is less subject to variation than corresponding studies for iodobenzene and bromobenzene.

The Renner-Teller effect in HCCCN(+)(X̃(2)Π) studied by zero-kinetic energy photoelectron spectroscopy and theoretical calculations

The spin-vibronic energy levels of the cyanoacetylene cation have been measured using the one-photon zero-kinetic energy (ZEKE) photoelectron spectroscopic method. All three degenerate vibrational modes showing vibronic coupling, i.e., Renner-Teller (RT) effect, have been observed. All the splitting spin-vibronic energy levels of the fundamental H-C≡C bending vibration (v5) have been determined. The spin-vibronic energy levels of the degenerate vibrational modes have also been calculated using a diabatic model in which the harmonic terms as well as all the second-order vibronic coupling terms are used. The theoretical predictions are in good agreement with the experimental data and are used to assign the ZEKE spectrum. It is found that the RT effects for the H-(CC)-CN bending (v7) and the C-C≡N bending (v6) vibrations are weak, whereas they are strong for the H-C≡C bending (v5) vibration. The cross-mode RT couplings between any of the two degenerate vibrations are strong. The spin-orbit resolved fundamental vibrational energy levels of the C≡N stretching (v2) and C-H stretching (v1) vibrations have also been observed. The spin-orbit energy splitting of the ground state has been determined for the first time as 43 ± 2 cm(-1), and the ionization energy of HCCCN is found to be 93 903.5 ± 2 cm(-1).

The Renner-Teller effect in HCCCl(+)(X̃(2)Π) studied by zero-kinetic energy photoelectron spectroscopy and ab initio calculations

The spin-vibronic energy levels of the chloroacetylene cation up to 4000 cm(-1) above the ground state have been measured using the one-photon zero-kinetic energy photoelectron spectroscopic method. The spin-vibronic energy levels have also been calculated using a diabatic model, in which the potential energy surfaces are expressed by expansions of internal coordinates, and the Hamiltonian matrix equation is solved using a variational method with harmonic basis functions. The calculated spin-vibronic energy levels are in good agreement with the experimental data. The Renner-Teller (RT) parameters describing the vibronic coupling for the H-C≡C bending mode (ε4), Cl-C≡C bending mode (ε5), the cross-mode vibronic coupling (ε45) of the two bending vibrations, and their vibrational frequencies (ω4 and ω5) have also been determined using an effective Hamiltonian matrix treatment. In comparison with the spin-orbit interaction, the RT effect in the H-C≡C bending (ε4) mode is strong, while the RT effect in the Cl-C≡C bending mode is weak. There is a strong cross-mode vibronic coupling of the two bending vibrations, which may be due to a vibronic resonance between the two bending vibrations. The spin-orbit energy splitting of the ground state has been determined for the first time and is found to be 209 ± 2 cm(-1).

Torsional energy levels of CH₃OH⁺/CH₃OD⁺/CD₃OD⁺ studied by zero-kinetic energy photoelectron spectroscopy and theoretical calculations

The torsional energy levels of CH3OH(+), CH3OD(+), and CD3OD(+) have been determined for the first time using one-photon zero kinetic energy photoelectron spectroscopy. The adiabatic ionization energies for CH3OH, CH3OD, and CD3OD are determined as 10.8396, 10.8455, and 10.8732 eV with uncertainties of 0.0005 eV, respectively. Theoretical calculations have also been performed to obtain the torsional energy levels for the three isotopologues using a one-dimensional model with approximate zero-point energy corrections of the torsional potential energy curves. The calculated values are in good agreement with the experimental data. The barrier height of the torsional potential energy without zero-point energy correction was calculated as 157 cm(-1), which is about half of that of the neutral (340 cm(-1)). The calculations showed that the cation has eclipsed conformation at the energy minimum and staggered one at the saddle point, which is the opposite of what is observed in the neutral molecule. The fundamental C-O stretch vibrational energy level for CD3OD(+) has also been determined. The energy levels for the combinational excitation of the torsional vibration and the fundamental C-O stretch vibration indicate a strong torsion-vibration coupling.

Valence and Rydberg states of CH3Cl: a MR-CISD study

In this work ten singlet and nine triplet states are studied through multi-reference configuration interactions with singles and doubles (MR-CISD), including Davidson extensivity correction (MR-CISD+Q).