Dipole Moment Operator and Spectral Parameters of Torsion Transitions

It is shown that a two-level quantum system possessing dipole moment operator with permanent non-equal diagonal matrix elements and driven by external semiclassical monochromatic high-frequency electromagnetic (EM) (laser) field can amplify EM radiation waves of much lower frequency.

Abstract The Bloch equations for the macroscopic polarization components Pr and Pi and the population difference ⊿N of a two-level system are derived with inclusion of diagonal elements of the electric dipole moment operator. The influence of such elements on the solutions is discussed. The effect of Stark-switching technique on the observed transient emission signal is considered.

The group-theoretical analysis was carried out to derive a spin-vibronic model Hamiltonian and a diabatic dipole moment operator for a cerium trihalide molecule, CeX3. The model comprises seven lowest-lying 4f1 electronic states coupled by six vibrational modes, (A2'' + E' + E'' + A1' + A2') × (a1' + a2'' + e' + e'), with an accounting for spin-orbit coupling. Multimode potential energy surfaces have been calculated for the CeF3 molecule at the multi-reference singles and doubles configuration interaction level of theory corrected for quadruple excitations, MRCISD+Q, and dipole moment surfaces at the MRCISD level. A hybrid approach employing a quasi-diabatization technique was utilized to determine the relevant model parameters up to forth order in power series of the Q1(a1'), Q3(e'), Q4(e') normal coordinates, and eighth order of the Q2(a2'') out-of-plane bending normal coordinate. Spin-orbit coupling was taken into account through zero-order, with the respective constants obtained from matrix elements of the Breit–Pauli operator in the basis of states generated at the MRCISD level. The spin-vibronic Hamiltonian and dipole moment operator obtained in this way has been utilized in the variational calculations to simulate the infrared absorption spectrum of CeF3. The resulting spectrum features a complex structure owing to an intricate interplay of the vibronic (Jahn–Teller and pseudo-Jahn–Teller) and spin-orbit coupling effects, and hence cannot be explained within the conventional Born–Oppenheimer (BO) approximation. The strongest absorption appearing in the simulated spectrum at about 500 cm–1, mostly associated with the Q3(e') stretching mode, is split into two bands by about 3 cm–1. This finding is in full agreement with the CeF3 matrix isolation infrared spectroscopy data. On the whole, the results of the calculations clearly indicate the vibronic rather than vibrational origin of the spectral bands, including the bands in the low-frequency region of the spectrum, and thus show the fallacy of the generally accepted assignment of the bands observed in the experiment to the fundamental vibrational transitions of the molecule made on the assumption of the admissibility of describing this within the Born–Oppenheimer approximation. The new assignment of the experimental IR spectrum of CeF3 is proposed.Forcitation:Vasilyev O.A., Solomonik V.G. First-principles simulation of the cerium trifluoride infrared spectrum beyond the Born–Oppenheimer approximation. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2018. V. 61. N 3. P. 31-44