Theory Of Vibrational Circular Dichroism Research Articles

Theory of Vibrational Circular Dichroism and Infrared Absorption: Extension to Molecules with Low-Lying Excited Electronic States

A vibronic theory of unpolarized infrared absorption and vibrational circular dichroism (VCD) is presented that is valid in the limit of vibrational resonance with low-lying electronic states (LLESs). The theory is developed within the complete adiabatic vibronic coupling formalism that describes both the correlation of electron density to nuclear positions and the correlation of electron current density to nuclear velocities. It is found that additional terms contribute to the electric-dipole and magnetic-dipole transition moments that become zero in the limit where all excited electronic states in the molecule are much higher in energy relative to fundamental vibrational transitions. Two correction terms appear that are extensions of the lowest-order non-Born−Oppenheimer expansion term when vibronic detail is included in the energy denominators. One term is a resonance term with respect to the energy difference between the electronic and vibrational transitions, and the other is a nonresonance term. Und...

A modified sum rule equation for the atomic tensors occurring in the theory of vibrational circular dichroism (VCD). Application to the atomic tensors recently calculated for ammonia

A modified sum rule equation is derived, relating the atomic polar tensors (APTs) and atomic axial tensors (AATs) occurring in the theory of vibrational circular dichroism (VCD), and it is applied to the atomic tensors of ammonia recently calculated by P.J. Stephens, K.J. Jalkanen, R.D. Amos, P. Lazzeretti and R. Zanasi, J. Phys. Chem., 94 (1990) 1811. It is shown that this modified sum rule equation is as useful for checking the quality of atomic tensors calculated with various methods, operators and basis sets as is the sum rule equation suggested by Stephens. In addition, the modified sum rule equation of this work has certain advantages. It is simpler, concerns only electronic parts of the atomic tensors, and has a higher degree of origin independence. It is therefore a convenient alternative, or complement, to the sum rule equation suggested by Stephens.

Velocity-gauge formalism in the theory of vibrational circular dichroism and infrared absorption

The first use of velocity-gauge factors in the theory of vibrational circular dichroism (VCD) and infrared absorption intensities is described. The approach involves the exact incorporation of all or part of the dependence of the electronic wave function on an electron-velocity perturbation, such as the vector potential or the velocities of the nuclei, into the atomic orbital basis functions as a gauge transformation. Any remaining dependence of the wave function on these perturbations is carried by the basis-function coefficient derivatives which are determined to first order by coupled Hartree–Fock perturbation theory. The magnetic field perturbation formulations of VCD in the common origin and distributed origin gauges are identified within the new formalism, providing a new direct derivation of the distributed origin gauge theory. The formalism also yields new a priori VCD intensity expressions, derived using nuclear velocity-gauge factors, in the complete adiabatic approximation. Several distinct a priori computational approaches to VCD intensities can now be identified—the vibronic coupling theory implemented with a direct sum over states (VC/SOS), the field adiabatic theory implemented with magnetic field perturbation (FA/MFP), and the complete adiabatic theory implemented with nuclear velocity perturbation (CA/NVP). In addition, basic expressions are presented for an energy gradient theory of VCD that employs both magnetic-field and nuclear-velocity perturbations (EG/MFNVP). It is shown that the CA/NVP theory of VCD possesses a higher Born–Oppenheimer content than the VC/SOS or FA/MFP theories and provides an improved basis for reducing a priori VCD theory to various models of VCD intensity.

Valence optical theory of vibrational circular dichroism and Raman optical activity

The valence-optical approach is used to develop a consistent bond dipole theory of vibrational circular dichroism and bond polarizability theory of vibrational Raman optical activity with results that are independent of both the local bond origins and the molecular origin. Two distinct versions of the results are presented: one is convenient for the development of simple models based on vibrations of idealized chiral structural elements, the other for detailed computations based on a full normal coordinate analysis for molecules composed entirely of axially-symmetric bonds. Explicit computational expressions are developed, and the outline given of a development for computational expressions when one or more bonds lack axial symmetry.

Bond polarizability and vibronic coupling theories of Raman optical activity: The electric-dipole magnetic-dipole optical activity tensor

A new formulation of the bond polarizability and vibronic coupling theories of Raman optical activity (ROA) is presented in which terms dependent upon the nuclear momentum are introduced for the first time. The new terms appear in the magnetic-dipole electric-dipole optical activity tensor and are directly analogous to the non-Born–Oppenheimer, momentum-dependent terms required in the formulation of the theory of vibrational circular dichroism. Through the use of simplifying approximations in the ROA vibronic coupling theory, a term-for-term correspondence with the bond polarizability theory is established. It is shown that the new terms are smaller than the original terms by the ratio of the vibrational transition frequency to the frequency of the incident radiation. The new terms also contribute oppositely to Stokes and anti-Stokes ROA which provides a basis for their experimental isolation.

Velocity-dependent property surfaces and the theory of vibrational circular dichroism

The familiar idea of a molecular property surface in which a property (such as the dipole moment) is expressed as a function of nuclear coordinates R I , is extended to cover properties odd under time-reversal by including the nuclear velocities ·R I as variables. One such property is the magnetic dipole moment m . This approach relates magnetic dipole vibrational transition moments to derivatives (∂ m / ∂ ·R I ) which may be calculated within the clamped-nucleus approximation, and used in the theory of vibrational circular dichroism. The same derivatives describe the electric field at a nucleus induced by an external dynamic magnetic field, leading to a physically transparent description of VCD. Sum rules relate these derivatives to the molecular paramagnetizability.

Vibrational circular dichroism theory: formulation defining magnetic dipole atomic polar tensors and vibrational nuclear magnetic shielding tensors

The theory of vibrational circular dichroism is formulated in terms of magnetic dipole atomic polar tensors, an extension of infrared atomic polar tensors to magnetic dipole transitions. Relations are provided to define a vibrational nuclear magnetic shielding tensor that describes electronic shielding of an external magnetic field for a nucleus.

A theory of vibrational circular dichroism in terms of vibronic interactions

A theory of vibrational circular dichroism is developed along the lines of the theory of intensity borrowing by forbidden electronic transitions. The vibrational transition exhibiting circular dichroism is a one-quantum jump in a mode capable of mixing different electronic states. The degree of mixing is different for the initial and final states of the vibrational transition; this is shown to be a source of circular dichroism. The theory is developed on the basis of the adiabatic and crude adiabatic approximations; expressions for rotatory strengths are given. Within the crude adiabatic picture, effects due to any change in the equilibrium configuration on electronic excitation are examined. Vibrational effects in electronic circular dichroism are also analysed.