The numerical calculation of ESR spectra of randomly oriented quartet radicals

The ESR spectra of randomly oriented quartet radicals were calculated with the aid of an analytical formula. A line broadening through Lorentz lines was explicity taken into consideration. The experimental spectrum of an alternant hydrocarbon radical was simulated with sufficiently good agreement.     

Random-phase-approximation calculations on triplet spectra of conjugated molecules

Random-phase approximations (RPA) have been applied to the calculation of the triplet π-π* transition spectra of 18 conjugated molecules in the framework of Pariser-Parr-Pople approximations. It is found that the normal RPA (n-RPA) shows the triplet instability for most molecules in the Nishimoto-Mataga approximation of electron-repulsion integrals. However, it is shown that this instability can be circumvented by the use of the renormalized RPA (r-RPA) in which the correlated ground states are calculated by the second-order perturbation theory. It is also shown that even in the n-RPA the suitable parametrization of electron-repulsion integrals removes this instability. It is ascertained that such an increasing order of energies as ω(n-RPA)<ω(Tamm-Dancoff approximation)<ω(r-RPA) holds for most of energy levels.     

Incomplete averaging effects in the ESR spectra of randomly oriented paramagnetic particles

Experimental studies on a Fe³⁺-natrolite model system were performed to investigate formatiom of noiselike magnetic resonance spectra previously found in polycrystalline zeolite samples and some other finely divided systems. The results of these studies show that the observed noiselike spectra are nonaveraged sets of lines from randomly oriented microcrystals. Physical conditions of formation of noiselike spectra are formulated, and methods to extract previously inaccessible information are proposed.     

The polarization dependence of two-photon absorption rates for randomly oriented molecules

The method and results are presented for the analysis of the two-photon absorption experiment for randomly oriented molecules (in a single-beam regime) that can be easily extended to higher-order processes without any assumption regarding the nature of the initial state. Some known results were recovered and some new ones presented. The ratio of the averaged transition rate for circularly polarized light to the one for linearly polarized light, Ω, can be obtained from the following rules: (a) for any transition involving two states of the same symmetry (on any point group), Ω < 1: (b) exceptions to rule (a) are found in T, T_h, T_d, O and O_h groups for which A ? A transitions give Ω = 0 and E ? E gives Ω = $\text{24}\text{31}$: and (c) for any transition involving two states of different symmetry, Ω = $\text{3}\text{2}$. The results of these predictions are in excellent agreement with the available experimental data.     

Deceptive simplicity in NMR spectra of oriented molecules

The theory for deceptive simplicity in the NMR spectra of oriented molecules is discussed in terms of degeneracy of subspectra. The conditions for the degeneracy of AB, AB₂ and AA′BB′ spectra leading to deceptive simplicity in the spectra of the type ABX, AB₂X, AA′BB′X and AA′XX′ are reported. It is shown that the conditions for deceptive simplicity are easily fulfilled for ABX, AA′BB′X and AA′XX′ cases. It is further demonstrated that deceptive simplicity is not so common in AB₂X spectra. The proton spectra of partially oriented 2,4,5-trichloronitrobenzene (AB) and 2,6-dibromo-pyridine (AB₂) are use to illustrate degeneracy and those of p-chloro- and p-bromo-fluorobenzenes are reported to demonstrate deceptive simplicity.     

Application of Lie algebraic method to the calculation of rotational spectra for linear triatomic molecules

The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4) U2(4). After rovibrational interactions being considered, the eigenvalue expression of the Hamiltonian has the form of term value equation commonly used in spectrum analysis. The molecular rotational constants can be obtained by using the expression and fitting it to the observed lines. As an example, the rotational levels of v2 band for transition (02°0-0110) of molecules N2O and HCN have been fitted and the fitting root-mean-square errors (RMS) are 0.00001 and 0.0014 cm-1, respectively.     

Collisional activation spectra of field ionised molecules

The collision of field ionised molecular ions of high kinetic energy (8 keV) with neutral target atoms (helium) gives rise to a large variety of fragments. In general the types of fragments, as well as their abundance ratios, closely resemble those formed under 70 eV electron-impact. The differences observed between the collisional activation spectra of several field ionised[C₇H₈]+. ions, as well as the differences observed between several [C₈H₈]+. ions can be rationalised assuming different degrees of isomerisation. The usefulness of collisional fragmentation spectra for structure determination of organic compounds has been demonstrated for a variety of compounds and some mixtures.     

Quantum optimal control for the full ensemble of randomly oriented molecules having different field-free Hamiltonians

We have presented the optimal control theory formulation to calculate optimal fields that can control the full ensemble of randomly oriented molecules having different field-free Hamiltonians. The theory is applied to the fifty-fifty mixture of randomly oriented (133)CsI and (135)CsI isotopomers and an optimal field is sought to achieve isotope-selective vibrational excitations with high efficiency. Rotational motion is frozen and two total times (T's) of electric field duration, 460,000 and 920,000 a.u. (11.1 and 22.2 ps), are chosen in the present calculation. As a result, the final yields for T = 460,000 and 920,000 a.u. are calculated to be 0.706 and 0.815, respectively. The relatively high final yield obtained for T = 920,000 a.u. strongly suggests that a single laser pulse can control the full ensemble of randomly oriented non-identical molecules. The result is quite encouraging in terms of the application to isotope-separation processes.     

Variational method for the calculation of the vibrational structure of the electronic spectra of polyatomic molecules. II

A variational method has been developed to solve the vibrational problem in the excited electronic state and to calculate the vibrational structure of the electronic spectrum of polyatomic molecules. The properties and structural characteristics of the variational matrix have been analyzed and an effective algorithm has been proposed for its approximate diagonalization. The effectiveness of the method and the corresponding suite of programs for the personal computer have been analyzed via the results of model calculations for a number of molecular structures. The method has high precision (errors of about 5% for frequencies and 15% for relative intensities), is an order of magnitude faster than previously used methods, and provides the possibility for the effective solution of the electrono-vibrational problem for polyatomic molecules, including the reverse problem.K. A. Timiryazev Agricultural Academy. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 1, pp. 149–156, January–February, 1993.     

Theoretical calculation of the vibrational spectra of some XHn type molecules

The potential function of some molecules of type XH_n has been obtained by a priori calculations of the total energy, within the Born Oppenheimer approximation, for several geometrical configurations. These functions have been used to calculate the simply excited vibrational levels. The calculated values of the electric dipole moment for the different geometrical configurations has enabled the computation of its derivative with respect to the nuclear coordinates. The results reported are critically discussed and some explanations are presented to justify the discrepancies found with the experimental data.

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Zusammenfassung Mittels einer apriorischen Berechnung der Gesamtenergie nach der Born-Oppenheimer-Methode ist die Potentialfunktion für einige Moleküle der Art XH_n in verschiedenen Konfigurationen erhalten worden. Diese Funktionen sind für die Berechnung der monoerregten SchwingungszustÄnde gebraucht worden. Die berechneten Werte des elektrischen Dipolmoments für verschiedene Geometrien haben die Berechnung der Ableitungen des Dipolmoments nach den Kernkoordinaten erlaubt. Die erhaltenen Resultate werden diskutiert und einige ErklÄrungen vorgeführt, um die gefundenen Unterschiede von den experimentellen Ergebnissen zu klÄren.

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Résumé La fonction potentiel de quelques molécules XH_n a été obtenue par le calcul a priori de l'énergie moléculaire, dans l'approximation de Born et Oppenheimer, pour plusieures configurations géométriques. Ces fonctions ont été utilisées pour calculer les vibrations monoexcitées. Les valeurs calculées du moment de dipole électrique pour différentes configurations donnent la possibilité de calculer ses dérivées par rapport aux coordonées nucléaires. On donne des justifications a l'accord peu satisfaisant entre les résultats et l'expérience.

     

Variational method for the calculation of the vibrational structure of the electronic spectra of polyatomic molecules. I

A method is proposed to calculate the vibrational structures of the electronic spectra of polyatomic molecules based on the variational solution of the vibrational problem in the excited state with the vibrational wave functions of the ground state as basis set. The electrono-vibrational problem leads to an evaluated and diagonalized variational matrix. The elements of the variational matrix have a simple form which is easily evaluated, has a clear physical meaning and is directly interconnected with observed spectral effects. This allows preliminary estimation of spectral phenomena and correction of the molecular model to take account of experimental results. The use of contemporary methods of diagonalization of the variational matrix, which possesses a characteristic structure, facilitates a tenfold increase in the speed of the method in comparison with traditional methods.K. A. Timiryazev Agricultural Academy. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 1, pp. 141–148, January–February, 1993.     

Spin-labelled mechanically interlocked molecules as models for the interpretation of biradical EPR spectra

Biradical spin probes can provide detailed information about the distances between molecules/regions of molecules because the through-space coupling of radical centres, characterised by J, is strongly distance dependent. However, if the system can adopt multiple configurations, as is common in supramolecular complexes, the shape of the EPR spectrum is influenced not only by J but also the rate of exchange between different states. In practice, it is often hard to separate these variables and as a result, the effect of the latter is sometimes overlooked. To demonstrate this challenge unequivocally we synthesised rotaxane biradicals containing nitronyl nitroxide units at the termini of their axles. The rotaxanes exchange between the available biradical conformations more slowly than the corresponding non-interlocked axles but, despite this, in some cases, the EPR spectra of the axle and rotaxane remain remarkably similar. Detailed analysis allowed us to demonstrate that the similar EPR spectral shapes result from different combinations of J and rates of conformational interconversion, a phenomenon suggested theoretically more than 50 years ago. This work reinforces the idea that thorough analysis must be performed when interpreting the spectra of biradicals employed as spin probes in solution.

Using a rotaxane biradical, we unambiguously demonstrate the need consider both J and rate of conformational interconversion carefully when interpreting the spectra of such systems when they are employed as spin probes in solution.     

Triplet-state ESR spectra of aromatic molecules oriented in stretched polyethylene films

Triplet-state ESR spectra show that when the aromatic molecules anthracene, anthracene-d₁₀, terphenyl, and acridine are dissolved in stretched, low-density polyethylene films, a fraction of these solute molecules become oriented with their X axis along the stretch direction but with their XY planes oriented randomly to the stretch direction. The fraction of molecules involved in the orientation process is largest for terphenyl.     

Quantum chemical calculation of phosphorescence microwave double resonance spectra

Lifetimes of individual spin sublevels, vibronic intensities of phosphorescence, zero field splitting, hyperfine and nuclear quadruple tensors for the lowest triplet state, g factors, and dipole nature of microwave transitions have been calculated on the bases of CNDO and INDO methods taking into account spin–orbit, spin–spin, vibronic, and hyperfine interactions by perturbation theory. The results are in qualitative agreement with phosphorescence microwave double resonance data. Influence of intermolecular interaction on the zero field splitting are also investigated.     

A two-dimensional (magnetic field and concentration) electron paramagnetic resonance method for analysis of multispecies complex equilibrium systems. information content of EPR spectra

A two-dimensional simulation method has been developed for the interpretation of electron paramagnetic resonance (EPR) spectra consisting of a multitude of strongly overlapping signal components. The set of EPR spectra for complex equilibrium systems is analyzed simultaneously as a function of metal and ligand concentrations and pH. The formation constants of the various species are adjusted together with the magnetic parameters of the component EPR spectra. At most 10 EPR-active and 5 EPR-silent species can be involved to simulate a maximum of 36 experimental spectra, while the number of adjusted parameters is at most 100. Statistical parameters are suggested to give the confidence intervals for parameter estimation and to distinguish alternative speciation models. The efficiency of the program is demonstrated for the copper(II)--L-asparagine system, in which 10 species, including 3 pairs of isomers, are characterized with magnetic parameters and formation constants. On the basis of the magnetic parameters, a structural assignment is made for the detected species. The two-dimensional approach can also supply the formation constant of the EPR-silent species, as demonstrated for the copper(II)--glycyl-L-serine system.