The Multipole Expansion in Quantum Theory

Fiutak, J.

doi:10.1139/p63-002

Cited by 124 publications

(28 citation statements)

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“…This is not the case, however, with optically active molecules. A system is defined as optically active if it responds differently to right and left circularly polarized light The Hamiltonian of a system of charged particles interacting with an electromagnetic field is a multipole expansion [24] in which the semiclassical Kramers-Heisenberg dispersion equation is demonstrated to be identical with the corresponding quantum mechanical description [25]. Such a Hamiltonian, which describes a molecule in a field, is [24,26,27]: -12-…”

Section: Discussionmentioning

confidence: 99%

Inverse Faraday Effect in Hemoglobin Detected by Raman Spectroscopy: An Example of Magnetic Resonance Raman Activity.

Barrett¹

1985

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Section: Discussionmentioning

confidence: 99%

Inverse Faraday Effect in Hemoglobin Detected by Raman Spectroscopy: An Example of Magnetic Resonance Raman Activity.

Barrett¹

1985

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“…The Hamiltonian of a system of charged particles interacting with an electromagnetic field is a multiple expansion (Fiutak, 1963) in which the semiclassical Kramers-Heisenberg dispersion equation is demonstrated to be identical with the corresponding quantum mechanical description 193]). …”

Section: (8)mentioning

confidence: 99%

“…Such a Hami}tonian, which describes a mo]ecuie in a field, is (Herzfeldt and GSppert-Mayer, 1936;Fiutak, ]963; Buckingham, 1967) : = the electric field and the field gradient at the origin due to external charges ;…”

Section: (8)mentioning

confidence: 99%

Magnetic resonance Raman activity: Inverse Faraday effect in hemoglobin

Barrett¹

1986

J Biol Phys

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ABSTRACT:A complete polarization study of human oxy-and carbonmonoxyhemoglobin (carbonylhemoglobin) A and S is reported for backscattered light in the resonance Raman light-scattering situation with excitations in the long-wavelength region, ~ = 5682 ~ and 5815 ~, and in the short-wavelength region, ~ = 4579~ and 4880 ~, as comparison.All four polarization components of the scattered light with respect to the two conditions of linear and circular polarization of the incident light were measured.These were:(1) parallel; (2) perpendicular; (3) corotating; and (4) contrarotating.This method has been used to characterize the three invariants of the nonsymmetric Raman tensor for randomly oriented molecules.These invariants are based on a model in which the scattered light is dependent on only an induced electric dipole. With no higher moments involved in the scattering process, the amplitude of any band measured under the four conditions should satisfy the relation:(I) + (2) -(3) + (4). The experiments reported here demonstrate that althoughothis relation is satisfied for short-wavelength (4579 A and 4880 A) excitation, it does not apply for long-wavelength (5682 A and 5815 A) excitation, for which (I) + (2) < (3) + (4) holds.There are large d-d metal-electron influences on the long, but not the short, wavelength absorption region of hemoproteins.A large metal-electron magnetic dipole moment can thus be induced with circularly po-]arized light of long wavelength, owing to the availability of a transition involving charge transfer interaction coupling between metal orbitals and the porphytin ~* orbitals.The increase in light scattering is due to an invezse Faraday effect, resulting in magnetic resonance Raman activity.Owing to large crystal field influences and Jahn-Teller instability, the critical zerofield spl itting energy is also large.The incident circularly polarized radiation at ~ = 5700A (w = 17,544 cm -l) is approximately the critical cubic splitting parameter, A c the calculated value for which is 18,500 cm -l . This incident light equalizes or mixes the energy levels of the IA 1 and 5T 2 states; i.e., it populates magnetic substates.An induced electric dipole--magnetic dipole transition, besides an induced electric dipole transition, is then permitted for circularly polarized light at the Larmor precession frequency, but not permitted for linearly polarized light, as the d-d metal transition is electric dipole disallowed.The hemoglobin S solution and gel scatter longwavelength light in a s~milar fashion; i.e., a large induced magnetic dipole moment is implicated for the circularly polarized conditions.In addition, there are bands at 750 and I050 cm -I for the hemoglobin S gel not present in dissolved hemoglobin S nor in hemoglobin A. The presence of these bands is attributed to changes in the Big mode of porphyrin ring vibrations.

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“…The multipole expression for P(~)(r) can be formally summed [9][10], and we have the polarization field operator expressed in terms of the electron coordinate q,…”

Section: H = H(a ) + H(b ) + Hra D -Y P (R) E • (R) D V-y M (R) B(r) D Vmentioning

confidence: 99%

On the interaction between charged linear harmonic oscillators

Power

1978

Z Physik A

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A systematic investigation, including the effect of retardation, is given for the interaction of two one-dimensional harmonic oscillators. The comment of Reinecke and Ruder [1], where a repulsive character for the force over a certain region of separation has been described, is shown to arise because of permanent moments implicit in the model. The calculation of the potential energy is made using quantum electrodynamics with all the intersystem interaction being mediated by photons: the method allows the calculation of the next term in inverse powers of R.In a recent paper Reinecke and Ruder [1] have commented upon the usual textbook derivation of the van der Waals force between two linear harmonic oscillators. The ratio between their predicted R-6 and R-5 potentials depends upon a factor I/R = c/(coR) and suggests a retardation correction. In this note their result is clarified by a precise division between different types of intermolecular forces. It is normal [2] to make the division, for the range outside any overlap of wave functions, into electrostatic, inductive and dispersive forces. Commonly, but not universally [3], the term van der Waals force is used to describe the dispersive type of intersystem force. It is well-known that the zeropoint energy can only decrease on coupling two systems and hence this force, when both systems are in their ground states, must be attractive. It is necessary then to find out what type of interaction is involved in the repulsive R-s potential of Reference [1]. We show that it is an effect of permanent quadrupole moments implicit in the linear oscillator model. In many calculations for real systems a linear model is used: a typical example is the interaction of two H 2 molecules [4]. It is known that there is a repulsive R -s energy in a collinear alignment of two H 2 molecules. Its strength is half the strength of the dispersive energy (~22 x 10-15erg) at 5.5% but is comparable (~l.2x 10-as erg) at 8.5a 0-9.0%. The results of Reinecke and Ruder are then not surprising. In fact in the early development of the theory of molecular forces these orientational forces played an important role. Debye This is the result of Reinecke and Ruder [1] since d =~ for a harmonic oscillator. Although for randomly orientated molecules the mean potential vanishes, above zero temperature the Boltzmann factor favours attractive states and the quadrupolequadrupole interaction accounts for part of the overall attraction between asymmetric molecules. Keesom predicted the value of Q for H 2 with remarkable accuracy assuming the main contribution to H 2 attraction was the Boltzmann averaged U(R).

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The Multipole Expansion in Quantum Theory

Cited by 124 publications

References 0 publications

Inverse Faraday Effect in Hemoglobin Detected by Raman Spectroscopy: An Example of Magnetic Resonance Raman Activity.

Inverse Faraday Effect in Hemoglobin Detected by Raman Spectroscopy: An Example of Magnetic Resonance Raman Activity.

Magnetic resonance Raman activity: Inverse Faraday effect in hemoglobin

On the interaction between charged linear harmonic oscillators

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