Volume 47, Issue 7, 01 October 1967

Phosphorescence of the Charge‐Transfer Triplet States of Some Molecular Complexes
View Description Hide DescriptionThe phosphorescencespectra of some charge‐transfer complexes were studied in glassy solution at 77°K. Long‐lived emission spectra which were different from the phosphorescencespectra of the constituent molecules were observed for the 1,2,4,5‐tetracyanobenzene complexes with mesitylene, durene, and hexamethylbenzene. The maxima of the long‐lived emission spectra were found to shift to lower frequencies as the ionization potential of the donor was decreased; for example, maxima appear at 19.8, 19.5, and 18.3 (× 10^{3} cm^{−1}) in the complexes with mesitylene, durene, and hexamethylbenzene, respectively. This shift is parallel to that observed for charge‐transfer fluorescence spectra which exhibit a mirror‐image relationship with the corresponding absorption spectra. Similar long‐lived emission spectra were also observed for complexes containing pyromellitic dianhydride, tetrachlorophthalic anhydride, and phthalic anhydride as electron acceptors. A combination of theory and experiment indicates that the long‐lived emission is attributable to a transition from a triplet state of charge‐transfer character. This is the first observation of a ``charge‐transfer triplet state.'' The lifetime of the phosphorescence due to the charge‐transfer triplet state was measured. The results indicate that the observed lifetime decreases with increasing donor ability for a series of complexes with a fixed electron acceptor. The mechanism of singlet—triplet mixing in the charge‐transfer complexes is discussed.

Triplet State of DNA
View Description Hide DescriptionAdditional proof has been obtained for the fact that the triplet state in DNA and poly dAT resides at the thymine residue by comparing the intensities of the triplet ESR and phosphorescence signals from DNA's from various sources having different (A+T)/(G+C) ratios. The TMP triplet which is not populated from the exited singlet state in dilute neutral solutions can be populated by having the TMP present in high concentrations or through energy transfer from the triplet state of acetone or acetophenone. The triplet state produced in this manner has been characterized by its Δm=2 ESR line, its phosphorescence spectrum, its decay time, and the effect of deuterium substitution on the latter. In all these respects the DNA and poly dAT triplet resembles the neutral TMP triplet (T) more closely than it resembles the ionized (pH 12) TMP triplet (T^{−}). A determination of the acidity constants of the excited states of A and T gives strong evidence against single‐proton transfer from the excited singlet or triplet state of T to A. While this cannot be considered final proof that the DNA triplet is that of neutral thymine, this is accepted as the most likely hypothesis.

Evaluation of Orbit—Orbit Interaction in Many‐Electron Atoms
View Description Hide DescriptionOrbit—orbit interaction has been evaluated for all the neutral atoms (in their ground states) up to radon (Z=86) using the numerical Hartree—Fock wavefunctions of Froese. Agreement between the previous calculations and that reported here is excellent wherever earlier results are available.

Infrared Spectra of Foreign Molecules in Beryl
View Description Hide DescriptionThirty infrared absorption lines in beryl between 1500 and 11 000 cm^{−1} are assigned to vibrations of two types of water and to CO_{2} all in the axial voids of the structure. The spectrum of Type‐I water arises from molecules which are capable of libration and are located between the silicate rings which make up the crystal. The spectrum of Type‐II water arises from molecules in the same sites, but with alkali ions nearby. These molecules are also capable of libration, but at a higher frequency. The Type‐I molecules have their C _{2} symmetry axes perpendicular to the crystal C _{6} axis, while the Type‐II molecules have their symmetry axes aligned parallel to the crystal C _{6} axis. The CO_{2} molecules are oriented with their long axes prependicular to the crystal C _{6} axis. Modification of the spectra by heat and hydrothermal treatments was not feasible and the identity of the alkali ions apparently does not influence Type‐II spectrum.

Perimetric Coordinates
View Description Hide DescriptionPekeris introduced perimetric coordinates to treat the helium atom, a three‐particle system. Recently several attempts have been made to obtain perimetric coordinates for four‐particle systems. The purpose of this paper is to point out that such coordinates do not exist for systems containing four or more particles.

Further Applications of the Domain Theory of Liquid Water: I. Surface Tension of Light and Heavy Water; II. Dielectric Constant of Lower Aliphatic Alcohols
View Description Hide DescriptionRecently, Jhon, Grosh, Ree, and Eyring used the significant‐structure theory to explain all the thermodynamic and transport properties of water, assuming that it contains domains of about 46 molecules which change their structure as a unit from an ``ice I‐like'' to an ``ice III‐like'' state. Following this, Hobbs, Jhon, and Eyring explained the dielectric constant of liquidwater. According to their theory, an applied field will make those domains grow which are favorably oriented with respect to the field at the expense of the less favorably oriented until a steady state is achieved. This domain theory of liquidwater has been applied to several cases. Surface tension of liquidwater has been successfully calculated in good agreement with experiment applying the generalized method of Change et al. Assumptions were made that the molecules in the top layers are in an asymmetric field and tend to orient in the direction of the field. This leads to continuous changes in the density for the various layers. The calculation of the dielectric constant of various alcohols was carried out by a similar scheme to that used for liquidwater, and the effect of the G factor in the formula has been discussed.

Resonance Quenching as a Diffusion‐Type Process. I. Theory
View Description Hide DescriptionMigration and trapping of excitons by quenching centers is described as a diffusion‐type process. The corresponding initial‐value problem is solved in one, two, and three dimensions, giving expressions for the fluorescence lifetime and yield. The efficiency of resonance quenching depends on the lifetime of the quenching centers, being maximum when they are permanent. The decay of excitation is faster than exponential, and its rate increases with the number of dimensions of the system. Theories of the iterated‐transfer type are compared and discussed.

Triplet States of Naphthalene Derivatives. I. 1,4‐Dibromonaphthalene
View Description Hide DescriptionA doublet structure is observed in the T _{1}←S _{0}, T _{2}←S _{0}, and S _{1}←S _{0} spectra of single crystals of 1,4‐dibromonaphthalene. The crystal structure is known to contain asymmetric units, and the spectral band doubling is attributed to the difference in dispersion interactions at the two sites. The observed asymmetric site splittings are 52 cm^{−1}(T _{1}), 103 cm^{−1}(T _{2}), and 85 cm^{−1}(S _{1}). Each of these values is in reasonable accord with expectations for certain diagonal Coulomb terms in the exciton matrix. The vibrational analyses of the T _{1}, T _{2}, and S _{1} states are presented. These states are located at 20 197 cm^{−1}(T _{1}), 29 783 cm^{−1}(T _{2}), and 30 357 cm^{−1}(S _{1}). The triplet spectra are briefly discussed with reference to the polarization of the vibronic bands.

Hard‐Sphere Model of Binary Liquid Mixtures
View Description Hide DescriptionAn equation of state [Eq. (2) of the text] which has been successfully applied to pure liquids composed of small, nonpolar molecules was generalized to the case of binary mixtures. The generalized equation was used to calculate excess thermodynamic functions for 10 equimolar mixtures, and agreement with experiment was found to be generally good. The partial molar heat of solution of gaseous neon in liquid argon was also calculated, but good agreement with experiment was not obtained in this calculation.

Dipole Moments of KF and KBr Measured by the Molecular‐Beam Electric‐Resonance Method
View Description Hide DescriptionThe molecular‐beam electric‐resonance method has been used to obtain the dipole moments for different vibrational levels of ^{39}K^{19}F (v=0, 1, 2, 3, 4, 5), ^{41}K^{19}F (v=0), ^{39}K^{79}Br (v=0, 1, 2), and ^{39}K^{81}Br (v=0, 1, 2). The absolute errors in the determined dipole moments are systematical errors of one part in 10^{4}, while the relative errors are about five parts in 10^{6} for the dipole moments of KF and 10 parts in 10^{6} for the dipole moments of KBr.

Electron Spin Resonance in Single Crystals of Anhydrous Copper Sulfate
View Description Hide DescriptionThe magnetic resonance of synthetic anhydrous copper sulfate has been investigated at 23.3 GHz at temperatures between 77°K and 4.1°K. In the paramagnetic region, the observed resonance consists of two lines. One of these is relatively narrow and remains essentially fixed even down to 4.1°K. The second line is unusually broad and its behavior indicates that it is due to the copper ions in the anhydrous crystal. The g values and corresponding linewidths have been measured for the broad line at 77°K. As the temperature drops to the Néel point, this broad line increases in width, then shifts, and disappears rather rapidly, indicating that it is associated with the antiferromagnetic phase.

Nuclear Quadrupole Resonance Zeeman Study of 2,4‐Dichlorophenoxyacetic Acid
View Description Hide DescriptionThe major field gradient directions and field gradient asymmetry parameters for Cl in 2,4‐dichlorophenoxyacetic acid are determined. Partial double‐bond characters of 0.026 and 0.044 for the para and ortho chlorine atoms are found. There is apparently some molecular distortion as the angle between the (Cl–C) para and the (Cl–C) ortho vectors is less than 120°.

Study of Collision‐Induced Phenomena with a Dempster Mass Spectrometer. I. Theoretical
View Description Hide DescriptionUtilizing the natural focusing characteristics of the Dempster mass spectrometer, equations are derived for the measurement of cross sections for collision‐induced reactions and for total collision cross sections.

Study of Collision‐Induced Phenomena with a Dempster Mass Spectrometer. II. Experimental
View Description Hide DescriptionA method for the study of collision‐induced phenomena in a Dempster mass spectrometer is demonstrated. Experimental studies are made of the following reactions, and their reaction cross sections are determined at 1000 V ion‐accelerating potential:The value of 1.0×10^{−17}cm^{2} for the reactionwas used for calibration. In addition, the total collision cross sections for the following systems were determined:

Improvement of Uncoupled Hartree‐Fock Expectation Values for Physical Properties. II
View Description Hide DescriptionA comparison is made between approximate polarizabilities calculated in the coupled Hartree‐Fock approximation with those obtained from the uncoupled Hartree‐Fock approximation with first‐order corrections.

Thermal Electron Escape in Irradiated Dipolar Systems
View Description Hide DescriptionThe possibility of thermal electron escape from the neighborhood of positive ions is studied from the point of view of the change of free energy. On the basis of a generalized spur (track) model a sufficient condition is formulated for the decrease of free energy in electron escape. This condition is fulfilled in every system if the electron‐electron repulsion is high, or in polar systems if the diffusing electrons are not too fast. Short dielectric relaxation time and large difference between static and infrared dielectric constants increase the escape probability.

Radiation Chemistry of Ice. I. Nature and pH Dependence of the Reducing Species
View Description Hide DescriptionThe decisive role of dielectric relaxation time in the electron‐escape process indicated by earlier theoretical studies of the author has been investigated by scavenger experiments in normal and supercooled water and crystalline ice. In these substances of similar dielectric constants but of different relaxation times, the importance of the latter is confirmed in that no free electrons could be detected in irradiatedice samples. A semiempirical law concerning the pH dependence of H‐atom yield in irradiatedice is also inferred from the experimental results.

Reformulation of the Representation of Transport Coefficients Using the Autocorrelation‐Function Formalism and the Linear‐Trajectory Approximation
View Description Hide DescriptionThe linear‐transport coefficients are exactly described in terms of the ``generalized force'' autocorrelation function. For weakly coupled systems these formal expressions take simple forms equivalent to the results obtained from other approaches. In addition, the linear‐trajectory method is described for the case of strongly interacting systems, and an elementary analysis of the transport coefficients at finite frequency is given (see Appendix B).

Theory of Excitons in Liquids. III. Nonresonant Broadening of Impurity Spectra in Simple Liquids
View Description Hide DescriptionRecent studies of the molecular theory of spectralline shapes and shifts have been confined to the gaseous state. In this paper we extend a formalism, originally introduced by Fano, to the description of simple liquids. Applying ideas borrowed from the molecular theory of transport processes in simple liquids, we are able to describe the influence of the host liquid on the spectral lines of an impurity molecule in the absence of overlap between the radiating molecule and the surrounding liquid. Two effects have been found to be important: the influence of the static molecular field arising from the long‐range part of the intermolecular interaction, and the influence of quasibinary hard‐core encounters. The structure of the liquid has been taken into account in the local equilibrium approximation. The assumptions adopted in our presentation are discussed in detail, and the possibility of the extension of our treatment to the case of resonance broadening and the case of significant overlap between the radiating molecule and liquid surroundings is pointed out.

Reduced Density Matrices of Atoms and Molecules. II. On the N‐Representability Problem
View Description Hide DescriptionFor the 2‐matrix of the ``double occupancy configuration interaction'' (DOCI) wavefunction described in a previous paper, the N‐representability problem is stated in terms of algebraic equations relating the density‐matrix elements λ_{ i }, Λ_{ ij }, λ_{ ij } to the wavefunction coefficients C_{K} . An operator formalism is developed and used to derive a number of necessary N‐representability conditions for both diagonal and off‐diagonal elements of the DOCI 2‐matrix. These conditions consist principally of certain linear inequalities for the diagonal elements and nonnegativity requirements for the eigenvalues of certain synthetic matrices built from both diagonal and off‐diagonal 2‐matrix elements. A hole‐particle duality is noted and used to expedite the derivations. Four special cases for which all the N‐representability conditions can be explicitly given are used to show that the conditions obtained are not yet sufficient for DOCI N representability.
It is then proved that the DOCI diagonal N‐representability conditions apply with equal necessity to the diagonal elements of any N‐representable 2‐matrix. These new necessary conditions for the general N‐representability problem are given a simple and satisfying probability interpretation in terms of the Pauli exclusion principle for fermion pair distributions. Off‐diagonal conditions are generated by requiring that the diagonal conditions be maintained under all possible unitary transformations of the orbital basis set. This latter procedure is illustrated by an application to the DOCI 2‐matrix which accounts for all off‐diagonal conditions previously obtained.