The calculation of Franck-Condon factors for the electronic transitions of the polyacenes

Progressional intensities have been calculated for the ¹ L _a band of the polyacenes which give good agreement with experiment. The Franck-Condon factors are calculated on the assumption that the frequencies and normal modes in the ground and excited states are identical. Our results, based on a simple force field, also show that the assumption (by McCoy and Ross) that the C-C stretching frequencies are degenerate is satisfactory as far as the calculation of the shape of the overall vibrational envelope is concerned.

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Zusammenfassung Wir berechneten die Intensitäten der ¹ L _a-Progressionen von Acenen, in guter Übereinstimmung mit dem Experiment. Die Franck-Condon-Faktoren werden unter der Annahme bestimmt, daß Frequenzen und Normalschwingungen im Grund- und angeregten Zustand gleich sind. Unsere mit einem einfachen Kraftansatz erhaltenen Ergebnisse zeigen weiter, daß die Annahme (von McCoy und Ross) entarteter C-C-Valenzschwingungen ausreicht, um die allgemeine Schwingungsstruktur der Bandenenveloppe zu berechnen.

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Résumé Nous avons calculé les intensités de progression de la bande ¹ L _a des acènes, en bon accord avec l'expérience. Les facteurs de Franck-Condon sont déterminés, en admettant des fréquences et vibrations normales identiques pour les états fondamental et excité. Nos résultats, sur base d'un champ de force simple, montrent de plus que l'hypothèse (de McCoy et Ross) des vibrations de valence C-C dégénérées est satisfaisant pour le calcul de la forme générale de l'enveloppe vibrationelle des bandes.

     

Franck-Condon simulation of the B-A bands of BO

Franck-Condon simulation of the emission B-A band system of boron monoxide are given. The computed band origin wavenumbers are found to be in good agreement with those derived from measured band head positions. In the absence of intensity measurements for the B-A bands, the simulated intensities were tested by calculation of the relative intensities of the well known A-X bands under the assumption that the electronic transition moment function is constant. The resulting good agreement between the simulated and experimentally obtained intensity patterns for A-X bands supports the reliability of our simulated B-A spectrum.     

More light on the low electronic transition energy bands of dithizone

The visible electronic spectral behaviour of different concentrations of dithizone in pure and mixed various organic solvents has been investigated. It is identified that in dilute basic solvents solutions, dithizone (H₂DZ) exists mainly in monovalent anionic form (HDZ⁻), where its extent of ionization is largely dependent on the solvent basicity effect. The visible absorption band belonging to absorption of HDZ⁻ form and the shorter visible one belonging to absorption of H₂DZ form are assigned to a transition involving the whole solute associated with intramolecular CT interaction. On the other hand, the longer wavelength visible band observed in the spectrum of the H₂DZ form is assigned to absorption of hydrogen bonding solvated molecular complex. This involves an electron transfer from the lone pair of electrons belonging to solvent molecule to the σ*-antibonding orbital of the acidic NH bond belongs to H₂DZ form.     

Simple molecular orbital calculations on the electronic structure of iron-porphyrin complexes

The simple Hückel method was first applied to the electronic structure of the iron-porphyrin complexes by Pullman et al. [12]. In this paper, their work is extended to include (a) the effect of a dipole or a point charge placed at the sixth coordination position, and (b) the effect of a nitrogen atom placed at the fifth coordination position. A set of new parameter values is used, whose estimation is made by directing special attention to their dependence on the charge distribution among the atoms.The resulting charge distribution for ferro-porphyrin seems to be reasonable. The fact that the position of the Soret peak is insensitive to the sixth ligand can be understood from the resulting orbital energy levels.The difficulty of finding a reasonable charge distribution for ferri-porphyrin is discussed.

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Zusammenfassung Die einfache Hückelsche Methode ist auf die Elektronenstruktur der Eisen-Porphyrin-Komplexe zuerst von Pullman et al. [12] angewandt worden. In der folgenden Arbeit wird ihr Verfahren auf (a) die Wirkung eines Dipols oder einer Punktladung an der sechsten Koordinationsstelle und (b) die eines Stickstoffatoms an der fünften erweitert. Ein Satz neuer Parameterwerte wird verwandt, bei deren Bestimmung besonders auf ihre Abhängigkeit von der Ladungsverteilung geachtet wird.Die erhaltene Ladungsverteilung für Ferroporphyrin erscheint vernünftig. Die Unempfindlichkeit der Lage der Soret-Bande gegen den sechsten Liganden ist aus den erhaltenen Energieniveaus zu verstehen.Die Schwierigkeit, eine vernünftige Ladungsverteilung für Ferriporphyrin zu finden, wird diskutiert.

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Résumé La simple méthode de Hückel a été appliquée à la structure électronique des complexes fer-porphyrine pour la première fois par Pullman et al. [12]. Dans l'article suivant, leur travail est étendu afin d'inclure (a) l'effet d'un dipôle ou d'une charge ponctuelle sur la sixième position coordinative, et (b) l'effet d'un atome de nitrogène sur la cinquième position. Un jeu de nouvelles valeurs des paramètres est usé qu'on détermine en tenant compte spécialement de leur dépendance de la distribution des charges atomiques.La distribution de charge obtenue pour la ferroporphyrine semble être raisonnable. Le fait que la position de la bande Soret est insensitive contre le sixième ligand, peut être compris à l'aide des énergies des orbitales calculées.La difficulté de trouver une distribution de charge raisonnable pour la ferriporphyrine est discutée.

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The research reported in this paper was sponsored in part by the King Gustaf VI Adolf's 70-Years Fund for Swedish Culture, Knut and Alice Wallenberg's Foundation, the Swedish Natural Science Research Council, and in part by the Aeronautical Research Laboratory, OAR, through the European Office, Aerospace Research, United States Air Force.

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On leave from Department of Physics, Faculty of Science, University of Tokyo, Tokyo, Japan.     

Ab initio calculations on low-lying electronic states of SbO2- and Franck-Condon simulation of its photodetachment spectrum

Geometry optimization and harmonic vibrational frequency calculations have been carried out on the low-lying singlet and triplet electronic states of the antimony dioxide anion (SbO2-) employing a variety of ab initio methods. Both large-core and small-core relativistic effective core potentials were used for Sb in these calculations, together with valence basis sets of up to augmented correlation-consistent polarized-valence quintuple-zeta (aug-cc-pV5Z) quality. The ground electronic state of SbO2- is determined to be the X (1)A1 state, with the a (3)B1 state, calculated to be approximately 48 kcal mole(-1) (2.1 eV) higher in energy. Further calculations were performed on the X (2)A1, A (2)B2, and B (2)A2 states of SbO2 with the aim to simulating the photodetachment spectrum of SbO(2) (-). Potential energy functions (PEFs) of the X (1)A1 state of SbO2- and the X (2)A1, A (2)B2, and B (2)A2 states of SbO2 were computed at the complete-active-space self-consistent-field multireference internally contracted configuration interaction level with basis sets of augmented correlation-consistent polarized valence quadruple-zeta quality. Anharmonic vibrational wave functions obtained from these PEFs were used to compute Franck-Condon factors between the X (1)A1 state of SbO2- and the X (2)A1, A (2)B2, and B (2)A2 states of SbO2, which were then used to simulate the photodetachment spectrum of SbO2-, which is yet to be recorded experimentally.     

The vibrational progressions of the N-->V electronic transition of ethylene: a test case for the computation of Franck-Condon factors of highly flexible photoexcited molecules

The vibrational progressions of the N-->V electronic transition of ethylene--a test case for the computation of Franck-Condon factors between electronic states exhibiting very different equilibrium geometries--have been calculated by using both the Cartesian and the curvilinear internal coordinate representations of the normal modes of vibration. The comparison of the theoretical spectra with the experimental one shows that the Cartesian representation yields vibrational progressions which are not observed in the experimental spectrum, whereas the curvilinear one gives a very satisfying agreement, even in harmonic approximation.     

Computational convergence of electronic structure calculations of transition metal ligand complexes

Calculations of binding energies and optimum geometries of compounds of the series M(H₂O)⁺ with M = Sc to Zn have been carried out and compared with gas-phase experimental data and with the Rosi and Bauschlicher MCPF calculations. Hartree–Fock calculations and correlated calculations at MP2, MP4, and QCISD(T) levels were used to test the dependence of the results upon the level of correlation. A test of basis set dependence was also carried out, using parallel calculations on four basis sets ranging in size from a small DZ set to a TZ contraction. Correlation levels above MP2 and elaboration of the metal d-function basis set to (4d/3d) size or greater were both necessary for convergence with the most uniformly reliable results obtained from QCISD(T) calculations on a basis set with a (6d/4d) contraction for the d-function space. However, MP2 or higher-level calculations with a contracted four or five d function set [(5d/3d) or (4d/3d)] are capable of yielding results on binding energies and geometries close to the current gas-phase experimental uncertainty on electrostatically bound transition metal complexes. © 1993 John Wiley & Sons, Inc.     

Ab initio calculations on low-lying electronic states of SnCl(2)- and Franck-Condon simulation of its photodetachment spectrum

Geometry optimization and harmonic vibrational frequency calculations have been carried out on low-lying doublet and quartet electronic states of stannous (tin(II)) dichloride anion (SnCl(2)(-)) employing the CASSCF and RCCSD(T) methods. The small-core fully-relativistic effective core potential, ECP28MDF, was used for Sn in these calculations, together with valence basis sets of up to augmented correlation-consistent polarized-valence quintuple-zeta (aug-cc-pV5Z) quality. The ground electronic state of SnCl(2)(-) is determined to be the X(2)B(1) state, with the A(2)B(2) and ?(4)Sigma state, calculated to be ca. 1.50 and 2.72 eV higher in energy respectively. The electron affinities of the X(1)A(1) and ?(3)B(1) states of SnCl(2) have been computed to be 1.568+/-0.007 and 4.458+/-0.002 eV respectively, including contributions of core correlation and extrapolation to the complete basis set limit. The SnCl(2) (X(1)A(1)) + e <-- SnCl(2)(-) (X(2)B(1)) and SnCl(2) (?(3)B(1)) + e <-- SnCl(2)(-) (X(2)B(1)) photodetachment bands have been simulated with computed Franck-Condon factors, which include an allowance for anharmonicity and Duschinsky rotation.     

Simple models for large-molecule calculations

In spite of tremendous advances in computational quantum chemistry during recent years, there remains the problem of how to deal with molecules so large that calculations of electronic structure and properties require the use of simplified models. This review contains (i) an appraisal of some currently available theoretical models together with proposals for further development, and (ii) a discussion of the use of such models (via variation-perturbation theory) in the interpretation and prediction of electronic properties. The great majority of electronic properties can be discussed in terms of three distribution functions: the electron density, the spin density, and the current density. The electron density is “observed” in x-ray scattering and the spin density in (spin-polarized) neutron scattering, while the current density (present whenever a magnetic field is applied) gives rise to effects observed typically in ESR and NMR experiments. The aim of model calculations should be to obtain a realistic picture of the distribution functions, sufficient for semiquantitative property calculations. For this purpose, as history suggests, it may not always be essential to proceed to the limits of computational feasibility.     

A different approach for calculating Franck-Condon factors including anharmonicity

An efficient new procedure for calculating Franck-Condon factors, based on the direct solution of an appropriate set of simultaneous equations, is presented. Both Duschinsky rotations and anharmonicity are included, the latter by means of second-order perturbation theory. The critical truncation of basis set is accomplished by a build-up procedure that simultaneously removes negligible vibrational states. A successful test is carried out on ClO2 for which there are experimental data and other theoretical calculations.     

Wavelets for electronic structure calculations

Molecular electronic structure calculations have a multi‐scale character through the presence of a set of singularities corresponding to atomic nuclei, and thus there exists a potential to improve the efficiency of these calculations using fast wavelet transform techniques. We report on the development of a one dimensional prototype benchmark problem of sufficient complexity to capture the features of 3‐D problems that are being solved today in quantum electronics calculations. Theoretical estimates of decay across scales and spatial distribution of wavelet coefficients for the solutions of the 1‐D and 3‐D problems are derived and verified experimentally. Equivalence in a multi‐resolution context of the solutions of the 1‐D prototype and the 3‐D problem is established. This revised version was published online in July 2006 with corrections to the Cover Date.     

Efficient evaluation of harmonic polyatomic Franck-Condon factors

An efficient computational method for obtaining large numbers of Franck-Condon factors between polyatomic harmonic oscillator vibrational states is presented.     

Basis set error estimation for DFT calculations of electronic g‐tensors for transition metal complexes

We present a detailed study of the basis set dependence of electronic g‐tensors for transition metal complexes calculated using Kohn–Sham density functional theory. Focus is on the use of locally dense basis set schemes where the metal is treated using either the same or a more flexible basis set than used for the ligand sphere. The performance of all basis set schemes is compared to the extrapolated complete basis set limit results. Furthermore, we test the performance of the aug‐cc‐pVTZ‐J basis set developed for calculations of NMR spin‐spin and electron paramagnetic resonance hyperfine coupling constants. Our results show that reasonable results can be obtain when using small basis sets for the ligand sphere, and very accurate results are obtained when an aug‐cc‐pVTZ basis set or similar is used for all atoms in the complex. © 2014 Wiley Periodicals, Inc.     

Density functional calculations on electronic circular dichroism spectra of chiral transition metal complexes

Time-dependent density functional theory (TD-DFT) has for the first time been applied to the computation of circular dichroism (CD) spectra of transition metal complexes, and a detailed comparison with experimental spectra has been made. Absorption spectra are also reported. Various Co(III) complexes as well as [Rh(en)(3)](3+) are studied in this work. The resulting simulated CD spectra are generally in good agreement with experimental spectra after corrections for systematic errors in a few of the lowest excitation energies are applied. This allows for an interpretation and assignment of the spectra for the whole experimentally accessible energy range (UV/vis). Solvent effects on the excitations are estimated via inclusion of a continuum solvent model. This significantly improves the computed excitation energies for charge-transfer bands for complexes of charge +3, but has only a small effect on those for neutral or singly charged complexes. The energies of the weak d-to-d transitions of the Co complexes are systematically overestimated due to deficiencies of the density functionals. These errors are much smaller for the 4d metal complex. Taking these systematic errors and the effect of a solvent into consideration, TD-DFT computations are demonstrated to be a reliable tool in order to assist with the assignment and interpretation of CD spectra of chiral transition metal complexes.     

Spectral-product methods for electronic structure calculations

Progress is reported in development, implementation, and application of a spectral method for ab initio studies of the electronic structure of matter. In this approach, antisymmetry restrictions are enforced subsequent to construction of the many-electron Hamiltonian matrix in a complete orthonormal spectral-product basis. Transformation to a permutation-symmetry representation obtained from the eigenstates of the aggregate electron antisymmetrizer is seen to enforce the requirements of the Pauli principle ex post facto, and to eliminate the unphysical (non-Pauli) states spanned by the product representation. Results identical with conventional use of prior antisymmetrization of configurational state functions are obtained in applications to many-electron atoms. The development provides certain advantages over conventional methods for polyatomic molecules, and, in particular, facilitates incorporation of fragment information in the form of Hermitian matrix representatives of atomic and diatomic operators which include the non-local effects of overall electron antisymmetry. An exact atomic-pair expression is obtained in this way for polyatomic Hamiltonian matrices which avoids the ambiguities of previously described semi-empirical fragment-based methods for electronic structure calculations. Illustrative applications to the well-known low-lying doublet states of the H₃ molecule in a minimal-basis-set demonstrate that the eigensurfaces of the antisymmetrizer can anticipate the structures of the more familiar energy surfaces, including the seams of intersection common in high-symmetry molecular geometries. The calculated H₃ energy surfaces are found to be in good agreement with corresponding valence-bond results which include all three-center terms, and are in general accord with accurate values obtained employing conventional high-level computational-chemistry procedures. By avoiding the repeated evaluations of the many-centered one- and two-electron integrals required in construction of polyatomic Hamiltonian matrices in the antisymmetric basis states commonly employed in conventional calculations, and by performing the required atomic and atomic-pair calculations once and for all, the spectral-product approach may provide an alternative potentially efficient ab initio formalism suitable for computational studies of adiabatic potential energy surfaces more generally. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

An efficient treatment of kinematic factors in pseudo-relativistic calculations of electronic structure

Relativistic two-electron operators obtained by the Douglas-Kroll transformation contain p-dependent kinematic prefactors which are not present in the corresponding Breit-Pauli operators. These factors are usually calculated using a resolution of the identity approach, which requires integral transformations. In the present article we describe an alternative approach, based on a local approximation, where the effect of the prefactors can be absorbed in the atomic contraction coefficients. The effect of the local approximation is investigated in detail. The suggested approach is simple to implement in integral codes that allow the use of a general contraction scheme. Received: 27 June 1997 / Accepted: 1 October 1997     

Shape adjustment of diffuse electronic bands

Certain expressions have been deduced from hypotesis concerning the nature of transitions which fit to molecular electronic spectra. Furthermore, these are fitted with the use of only a few parameters. Important quantities of the molecules are obtained through this technique.     

Estimation of reliability of quantum-chemical calculations of electronic transitions in aqua complexes of transition metals

The correlation comparison of energy levels of aqua complexes of row IV transition metals was calculated using different methods on the basis of the WinGAMESS program with standard potentials of these systems and experimental values of the rate constants. The calculation showed that the use of DFT (density functional theory) considerably increases the reliability of calculations.     

Three-dimensional numerical integration for electronic structure calculations

Two three-dimensional numerical schemes are presented for molecular integrands such as matrix alements of one-electron operators occuring in the Fock operator and expectation values of one-electron operators describing molecular properties. The schemes are based on a judicious partitioning of space so that product-Gauss integration rules can be used in each region. Convergence with the number of integration points is such that very high accuracy (8–10 digits) may be obtained with obtained with a modest number of points. The use of point group symmetry to reduce the required number of points is discussed. Examples are given for overlap, nuclear potential, and electric field gradient integrals.