Ying‐Nan Chiu

Quantum Theory of Interference and Polarization of Stark—Zeeman Lines in Molecules

With special emphasis on the application to transitions between the rovibronic states of molecules, general formulas for the polarization and for the intensity inclusive of interference of multipole emission between Stark—Zeeman levels are derived. The derivation makes use of angular momentum method for molecules and irreducible spherical tensor operators for the interaction of radiation and matter.Results are made applicable to linearly polarized radiation with any arbitrary orientation (specified by three Euler angles) of the polarization and propagation vectors with respect to the space‐fixed axes. These higher multipole interference effects in a resolved molecular Stark—Zeeman line serve as an extension of the pioneer works on atomic Zeeman transitions of Van Vleck and others. The formulas are tabulated in terms of their dependence on reduced rovibronic matrix elements and their rotational and angular dependence. For the latter dependence that involve products of Clebsch—Gordon coefficients and produc...

Temperature‐Dependent Optical Activity Due to Quantized Molecular Rotation and Optical Rotation by Oriented Molecules

Classical works on optical rotation have dealt with random systems for which all molecular orientations are equally probable. We have considered here optical rotation by quantum mechanically rotating molecules. The contributions to optical rotation from the individual rotational levels of a symmetric‐ and a spherical‐top molecule have been derived. These may be asymmetric molecules belonging to the C3, D3, or T point group. The contributions are weighed by the Boltzmann distribution over the rotational levels, thus giving rise to temperature dependence. Such dependence will be significant at low temperatures. It is shown that, the same as for classical random systems, the optical rotation by quantized rotors comes from the interference of an electric multipole of a given rank with a magnetic multipole of the same rank. However, because of the dependence on the rotational energy level K, for the rotation of infrared “light” which is close to the frequency of a rotational transition, the optical rotation ma...

Higher Asymmetry in Optical Rotation

This study shows that optical rotation could arise from higher‐order interference effects of two‐photon processes in quantum electrodynamics. In the lowest‐order limit, applicable to electric‐ or magnetic‐dipole allowed transitions in small molecules, the conventional expression of angle of rotation proportional to Im(0| R |b)·(b| M |0) is attributable to the interference of one photon being in an electric‐dipole (R) mode which has odd parity and the other photon being in a magnetic‐dipole (M) mode which has even parity. The asymmetry stems from the opposite parities of the transition operators R, M, both transforming as tensors of the first rank. For application to larger molecules and forbidden transitions, we dispense with the usual refractive index and medium polarization formalism and derive, using quantum electrodynamics, the higher‐asymmetry contribution to optical activity due to the interference of higher electric and magnetic multipoles of any order. It is shown that the perpendicularity of the ...

Vibronic symmetry correlation in molecular combination and dissociation

The principle of conservation of vibronic symmetry in molecular combination and dissociation is discussed. It leads to the aufbau of the vibronic (vs purely electronic) states of polyatomic molecules. Methods to construct composite vibrational (and vibronic) wavefunctions from those of molecular fragments (reactants or products or transition complexes) are described. These vibronic functions, constructed from local site symmetry, will have the overall symmetry of the point group that is preserved throughout the reaction and will possess the correct dissociation limit. The construction of a composite vibrational wavefunction is illustrated by using a symmetrically and collinearly dissociating X2Y2 molecule. The theory of vibronic correlation is applied to the recently observed production of excited formaldehyde (and its chemiluminescence) from the reaction of O2(1Δg) with olefins. This theory promises one a qualitative way to conceive the possible vibronic excitation of reactants and products in a chemical...

Theory of a Novel Odd‐Parity Raman Scattering Mechanism: Depolarization Ratios and Reversal Coefficients for Random Molecular Systems

Raman scattering is treated as a two‐photon process. A scattering mechanism that involves one‐photon in an electric dipole mode of radiation and one photon in a magnetic dipole mode (or an electric quadrupole mode) has been worked out. The scattering tensors are of odd parity and may be of higher than the second rank. Therefore, this mechanism may be used to study the “silent” modes forbidden in the ir and the conventional Raman effect which is of even parity. When the molecule has inversion or reflection symmetry, this mechanism gives rise to an odd‐parity electronic Raman effect between two (different) electronic states of opposite parities. This is in contrast to the recently discovered electronic Raman effect due to antisymmetric tensors which connect states of the same parity. When the molecule is optically active and has no inversion or reflection symmetry, this mechanism gives rise to novel vibrational and rotational Raman effects with symmetry and selection rules which are different from the conve...

Cooperative Optical Transitions in the Oxygen Dimer: Excimer States, Selection Rules, and Oscillator Strengths

An alternative and approximate method is used to compute the dipole intensity of the cooperative optical transition in an oxygen molecular dimer, O4. This approximation attributes the interaction of the two oxygen molecules to the overlap of their valence electrons and constructs the composite molecular states of the dimer by permuting all four πg valence electrons (two from each molecule) in a Slater determinant. The overall symmetry of the possible composite, dimeric and exciton states is determined for different collision geometry belonging to D∞h, C2vx, C2hy, C2vz, D2h, C3yz, C2, C3xz, and S4 point groups. The polarization of the transition is determined from these overall symmetries of the dimer. The transition matrix elements of the dimer are weighted by overlap integrals and are expressed in terms of the angles between the two molecules. This is in contrast to the conventional method which gives transition matrix elements weighted by electrostatic matrix element divided by an energy factor. The lat...

Reformulation and extension of Wigner‐Witmer and Mulliken's correlation rules for the spin and orbital states of diatomic molecules upon dissociation

Projection operator technique and angular momentum coupling methods are used to construct the eigenfunctions of diatomic molecular states in terms of the eigenfunctions of separate atomic states. The resulting eigenfunctions of the molecular term manifolds contain correct and compatible permutation symmetry and continuous group as well as point group symmetry pertinent to the molecule. These eigenfunctions will, in contrast to molecular orbital description, give the correct states of the atomic dissociation products required in chemical reactions and collisional energy transfer. In the above construction, we elucidate the correlation principle that dictates the nonexistence of two incompatible symmetries for certain states and allows for certain symmetries of the molecular term manifold to arise from given atomic multiplet states. The qualitative aspects of the newly derived correlation rules in simple methematical language are shown to agree with the early works of Wigner‐Witmer and Mulliken. These rules...

Relativistic Effect and Nonconservative Spin–Orbital Forces in the Radiative Transition of Molecules

A treatment is given of a one‐electron orbital model for a many‐electron molecule, in which each electron is allowed to interact with the over‐all orbital and spin magnetic fields, as well as the (Coulomb) electric field of the rest of the electrons and nuclei. It is shown that when redundancy is properly taken care of, by introducing a factor of 12 for the mutual‐magnetic vector potential Aij between the electrons, the subsequent reduction of Diracs equation reproduces all of Darwins orbit–orbit, spin–own‐orbit, spin–other‐orbit, and spin–spin interactions, etc., given by the Breit–Pauli approximation. The above treatment is extended to a system of Dirac electrons interacting with the (time‐dependent) electromagnetic field of radiation, in which field–field interaction in the form of Aij·Aj (radiation), is also included. After integration over the photon space, effective transition operators for the large‐component spinors are obtained. When the non‐Hermitian part of the “Dirac Hamiltonian” for the lar...

Rotational Structure of a Novel Raman Effect in Quantized Symmetric‐ and Spherical‐Top Molecules

By angular momentum techniques, the theoretical line intensities of a higher‐order odd‐parity Raman effect have been derived. This effect may be used as an alternative mechanism to study the silent modes forbidden in the infrared spectra, and in the conventional lower‐order Raman effect which is of even parity. It can be compared with the recently discovered (three‐photon) hyper‐Radman effect which is also of odd parity and contrasted with the recently studied electronic Raman effect using the antisymmetric scattering tensor which is of even parity: It has different selection rules (Secs. IV, V) and angular characteristics (Sec. III and Appendix B). It is Raman scattering in which one photon is in an electric dipole mode, whereas the other photon is in a magnetic dipole (or electric quadrupole) mode. The scattering tensor is of odd parity. The intensities along the perpendicular direction of observation of the scattering by symmetric‐top molecules in their transition from the state | J′K′〉 to | JK〉 and by...

Rotation–vibration symmetry correlation in bimolecular reactions: Building‐up principle from molecular fragments

A rotational–vibrational symmetry correlation scheme between an intermediate reaction complex and the corresponding reactant or product fragments is proposed. The emphasis is on the symmetry of the eigenfunctions at both limits: the fragments at infinite separation and the complex as a molecule. Because of the introduction of rotation, the permutation‐inversion group rather than the usual point group is taken as the symmetry group of the rotating and vibrating fragments and its symmetry species are correlated to the point group species of the complex. Correlations are presented for the systems AB–AB, A2–A2, B2–A2, A–A2, and B–A2 at various symmetric configurations without any consideration given to the energetics of the reactions. This general approach makes the scheme useable for a variety of reactions. It also provides the building‐up principle for the rotation–vibration states of polyatomic molecules. Application to the O2–O2 dimer formation is discussed.