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Density Matrix (density + matrix)
Selected AbstractsSimulation of Real-Valued Discrete-Time Periodically Correlated Gaussian Processes with Prescribed Spectral Density MatricesJOURNAL OF TIME SERIES ANALYSIS, Issue 2 2007A. R. Soltani Abstract., In this article, we provide a spectral characterization for a real-valued discrete-time periodically correlated process, and then proceed on to establish a simulation procedure to simulate such a Gaussian process for a given spectral density. We also prove that the simulated process, at each time index, converges to the actual process in the mean square. [source] Estimating the Rank of the Spectral Density MatrixJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2005Gonzalo Camba-Mendez Abstract., The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive definite matrix estimate that has a normal asymptotic distribution with a covariance matrix the rank of which is known. [source] Temperature-dependent pseudopotential between two pointlike electrical chargesCONTRIBUTIONS TO PLASMA PHYSICS, Issue 5-6 2003M.-M. Gombert Abstract The pair distribution functions for particles electrically charged, at a temperature T, expressed in terms of density matrices and the corresponding pseudopotentials are studied. For an electron pair, the symmetry of the wave functions is taken into account. Exact expansions with respect to the separation distance and to a quantum parameter (, T,½) are carried out. The known results are recovered. For high temperature, accurate approximations are derived. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Electron invariants and excited state structural analysis for electronic transitions within CIS, RPA, and TDDFT modelsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2010A. V. Luzanov Abstract We revisit the interpretative scheme (Luzanov et al., Theor Exp Chem 1974, 10, 354) of singly excited configuration interaction (CIS) model given earlier at semiempirical level. Detailed computations and spectral (natural orbital) treatment of the CIS density matrices of various types are presented. The corresponding hole-particle densities and related excitation localization indices are described. All the quantities are extended to the excited states calculated in the random phase approximation and closely related time-dependent density functional theory (TDDFT). The localization indices and charge transfer numbers which are invoked to describe interfragment interactions provide a basis for our scheme which is referred to as the excited state structural analysis for electronic transitions. The proposed analysis is exemplified by various moderate and large-size conjugated molecules treated within ab initio TDDFT and the Parizer,Parr,Pople approximation. Finally, we propose a possible generalization to the electronic transitions between CIS-like states followed by applications to singlet organic biradicals treated within the ,-electron spin-flip CIS. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Nonlinear wave function expansions: A progress reportINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2007Ron Shepard Abstract Some recent progress is reported for a novel nonlinear expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions using the Graphical Unitary Group Approach and the wave function is expanded in a basis of product functions, allowing application to closed and open shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational expansion that depends on a relatively small number of nonlinear parameters called arc factors. Efficient recursive procedures for the computation of reduced one- and two-particle density matrices, overlap matrix elements, and Hamiltonian matrix elements result in a very efficient computational procedure that is applicable to very large configuration state function (CSF) expansions. A new energy-based optimization approach is presented based on product function splitting and variational recombination. Convergence of both valence correlation energy and dynamical correlation energy with respect to the product function basis dimension is examined. A wave function analysis approach suitable for very large CSF expansions is presented based on Shavitt graph node density and arc density. Some new closed-form expressions for various Shavitt Graph and Auxiliary Pair Graph statistics are presented. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] One-particle density matrix functional for correlation in molecular systemsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2003Mario Piris Abstract Based on the analysis of the general properties for the one- and two-particle reduced density matrices, a new natural orbital functional is obtained. It is shown that by partitioning the two-particle reduced density matrix in an antisymmeterized product of one-particle reduced density matrices and a correction ,c we can derive a corrected Hartree,Fock theory. The spin structure of the correction term from the improved Bardeen,Cooper,Schrieffer theory is considered to take into account the correlation between pairs of electrons with antiparallel spins. The analysis affords a nonidempotent condition for the one-particle reduced density matrix. Test calculations of the correlation energy and the dipole moment of several molecules in the ground state demonstrate the reliability of the formalism. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 317,323, 2003 [source] Reduced density matrices,Then and now,INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2001A. John Coleman Abstract The history and results of over forty years of research on the theory of reduced density matrices is discussed, and several key unsolved research problems announced. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001 [source] Imposing bounds on the high-order reduced density matrices elementsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2001C. Valdemoro Abstract A family of N -representability conditions are imposed on the third- and fourth-order reduced density matrix elements in order to ascertain that they are within bounds. These bounds are needed in the construction of high-order reduced density matrices as well as in the correction of the matrices which result from the iterative solution of the standard and of the modified contracted Schrödinger equations. The results obtained for the fourth-order reduced density matrix are strikingly good in two nontrivial cases. A new and more economical method for constructing the fourth-order reduced density matrix in terms of the lower order ones is also reported here. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001 [source] Determination of a one-electron reduced density matrix using a coupled pseudo-atom model and a set of complementary scattering dataACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2007Jean-Michel Gillet A possible model of one-electron reduced density matrices is presented, adapted from the Hansen,Coppens pseudo-atomic description of electron density [Hansen & Coppens (1978). Acta Cryst. A34, 909,913]. Potential benefits from a joint refinement of the model from X-ray diffraction and deep inelastic scattering data are illustrated. [source] The 2-matrix of the spin-polarized electron gas: contraction sum rules and spectral resolutionsANNALEN DER PHYSIK, Issue 3 2004P. Ziesche Abstract The spin-polarized homogeneous electron gas with densities ,, and ,, for electrons with spin ,up' (,) and spin ,down' (,), respectively, is systematically analyzed with respect to its lowest-order reduced densities and density matrices and their mutual relations. The three 2-body reduced density matrices ,,,, ,,,, ,a are 4-point functions for electron pairs with spins ,,, ,,, and antiparallel, respectively. From them, three functions G,,(x,y), G,,(x,y), Ga(x,y), depending on only two variables, are derived. These functions contain not only the pair densities according to g,,(r) = G,uarr;(0,r), g,,(r) = G,,(0,r), ga(r) = Ga(0,r) with r = |r1 - r2|, but also the 1-body reduced density matrices ,, and ,, being 2-point functions according to ,s = ,sfs and fs(r) = Gss(r, ,) with s = ,,, and r = |r1 - r,1|. The contraction properties of the 2-body reduced density matrices lead to three sum rules to be obeyed by the three key functions Gss, Ga. These contraction sum rules contain corresponding normalization sum rules as special cases. The momentum distributions n,(k) and n,(k), following from f,(r) and f,(r) by Fourier transform, are correctly normalized through fs(0) = 1. In addition to the non-negativity conditions ns(k),gss(r),ga(r) , 0 [these quantities are probabilities], it holds ns(k) , 1 and gss(0) = 0 due to the Pauli principle and ga(0) , 1 due to the Coulomb repulsion. Recent parametrizations of the pair densities of the spin-unpolarized homogeneous electron gas in terms of 2-body wave functions (geminals) and corresponding occupancies are generalized (i) to the spin-polarized case and (ii) to the 2-body reduced density matrix giving thus its spectral resolutions. [source] Semiclassical limit for the Schrödinger-Poisson equation in a crystalCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2001Philippe Bechouche We give a mathematically rigorous theory for the limit from a weakly nonlinear Schrödinger equation with both periodic and nonperiodic potential to the semiclassical version of the Vlasov equation. To this end we perform simultaneously a classical limit (vanishing Planck constant) and a homogenization limit of the periodic structure (vanishing lattice length taken proportional to the Planck constant). We introduce a new variant of Wigner transforms, namely the "Wigner Bloch series" as an adaption of the Wigner series for density matrices related to two different "energy bands." Another essential tool are estimates on the commutators of the projectors into the Floquet subspaces ("band subspaces") and the multiplicative potential operator that destroy the invariance of these band subspaces under the periodic Hamiltonian. We assume the initial data to be concentrated in isolated bands but allow for band crossing of the other bands which is the generic situation in more than one space dimension. The nonperiodic potential is obtained from a coupling to the Poisson equation, i.e., we take into account the self-consistent Coulomb interaction. Our results hold also for the easier linear case where this potential is given. We hence give the first rigorous derivation of the (nonlinear) "semiclassical equations" of solid state physics widely used to describe the dynamics of electrons in semiconductors. © 2001 John Wiley & Sons, Inc. [source] Quantum phenomena via complex measure: Holomorphic extensionFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7 2006Article first published online: 11 MAY 200, S.K. Srinivasan The complex measure theoretic approach proposed earlier is reviewed and a general version of density matrix as well as conditional density matrix is introduced. The holomorphic extension of the complex measure density (CMD) is identified to be the Wigner distribution function of the conventional quantum mechanical theory. A variety of situations in quantum optical phenomena are discussed within such a holomorphic complex measure theoretic framework. A model of a quantum oscillator in interaction with a bath is analyzed and explicit solution for the CMD of the coordinate as well as the Wigner distribution function is obtained. A brief discussion on the assignment of probability to path history of the test oscillator is provided. [source] Chemical reactions in the gas phase and in condensed matter: From wavefunctions to density operatorsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 13 2009David A. Micha Abstract This contribution generalizes the treatment of chemical reactions in the gas phase based on the reaction channel decomposition of the wavefunction, by introducing a similar channel decomposition of the statistical density operator valid also for condensed phases such as liquid solutions and solid surfaces. Coupled equations for the channel components of the density operator are derived and a brief presentation is given of their partial Wigner transform, which leads to a general treatment for coupling quantum and classical variables. This provides a general approach for reactions involving electronically excited states in many-atom systems. It is pointed out that reactions involving coupled quantal and classical variables can be correctly described provided (a) initial conditions for trajectories are generated from quantal distributions and (b) the bundle of trajectories for the whole initial classical phase space is propagated coupled to the quantal elements of the density matrix and used in the calculation of reaction flux averages. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Inequivalent electron densities derived from an approximate correlated ground-state wave function using the Hiller,Sucher,Feinberg identity: Comparisons with quantum Monte Carlo densities for He and Ne atomsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2009Claudio Amovilli Abstract The Hiller,Sucher,Feinberg (HSF) identity is combined with the three-parameter correlated wave function of Chandrasekhar in order to generate an alternative electron density ,(r) for the He atom. This and the conventional "local" operator form of ,(r) are then compared with a diffusion quantum Monte Carlo density. An exact limiting relation is also presented, via HSF identity, between the one-particle density matrix and the pair density in a many-electron atom, which transcends its Hartree,Fock counterpart and has no N -representability difficulties. For the Ne atom, the accuracy of the semiempirical correlated electron density recently obtained by Cordero et al. (Phys. Rev. A 2007, 75, 052502) using fine-tuning of Hartree,Fock theory was assessed by appealing to the ground-state density from diffusion quantum Monte Carlo. The high accuracy of the Cordero et al. density was thereby confirmed. A HSF calculation on neon, with a correlated many-body wave function as starting point, is a worthwhile future aim. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] Necessary conditions for the N -representability of pair distribution functionsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2006Paul W. Ayers Abstract A necessary condition for the N -representability of the electron pair density proposed by one of the authors (E. R. D.) is generalized. This shows a link between this necessary condition and other, more widely known, N -representability conditions for the second-order density matrix. The extension to spin-resolved electron pair densities is considered, as is the extension to higher-order distribution functions. Although quantum mechanical systems are our primary focus, the results are also applicable to classical systems, where they reduce to an inequality originally derived by Garrod and Percus. As a simple application, bounds to the average angle between an electron pair are derived. It is shown that computational methods based on variational minimization of the energy with respect to the electron pair density can give extremely poor results unless robust N -representability constraints are considered. For reference, constraints for the N -representability of the pair density are summarized. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source] One-particle density matrix functional for correlation in molecular systemsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2003Mario Piris Abstract Based on the analysis of the general properties for the one- and two-particle reduced density matrices, a new natural orbital functional is obtained. It is shown that by partitioning the two-particle reduced density matrix in an antisymmeterized product of one-particle reduced density matrices and a correction ,c we can derive a corrected Hartree,Fock theory. The spin structure of the correction term from the improved Bardeen,Cooper,Schrieffer theory is considered to take into account the correlation between pairs of electrons with antiparallel spins. The analysis affords a nonidempotent condition for the one-particle reduced density matrix. Test calculations of the correlation energy and the dipole moment of several molecules in the ground state demonstrate the reliability of the formalism. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 317,323, 2003 [source] Relaxation of quantum hydrodynamic modesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4 2002Eric R. Bittner Abstract In this article, we develop a series of hierarchical mode-coupling equations for the momentum cumulants and moments of the density matrix for a mixed quantum system. Working in the Lagrange representation, we show how these can be used to compute quantum trajectories for dissipative and nondissipative systems. This approach is complementary to the de Broglie,Bohm approach in that the moments evolve along hydrodynamic/Lagrangian paths. In the limit of no dissipation, the paths are the Bohmian paths. However, the "quantum force" in our case is represented in terms of momentum fluctuations and an osmotic pressure. Representative calculations for the relaxation of a harmonic system are presented to illustrate the rapid convergence of the cumulant expansion in the presence of a dissipative environment. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] Analysis of difference two-electron density matrix between two states of magnetic moleculesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2001D. Yamaki Abstract Previously, a method based on the two-electron density matrix (2-DM) has been used to obtain chemical interpretations with electron correlations. In the method, a 2-DM is expanded by its natural geminals. These natural geminals are visualized to obtain their chemical interpretations. An electronic state is understood as the set of geminals that have various correlations of two electrons. In this work, a extension of previous 2-DM-based method is described to compare two states of a system. In this method, the difference 2-DM between the two states is used instead of 2-DM itself. The applications of the method to trans-butadiene and trimethylene methane are shown. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001 [source] Imposing bounds on the high-order reduced density matrices elementsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2001C. Valdemoro Abstract A family of N -representability conditions are imposed on the third- and fourth-order reduced density matrix elements in order to ascertain that they are within bounds. These bounds are needed in the construction of high-order reduced density matrices as well as in the correction of the matrices which result from the iterative solution of the standard and of the modified contracted Schrödinger equations. The results obtained for the fourth-order reduced density matrix are strikingly good in two nontrivial cases. A new and more economical method for constructing the fourth-order reduced density matrix in terms of the lower order ones is also reported here. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001 [source] The correlation between blood oxygenation level-dependent signal strength and latencyJOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 4 2005Karsten Müller PhD Abstract Purpose To investigate the relationship between signal strength and latency of the blood oxygenation level-dependent (BOLD) signal. Materials and Methods Several correlation analyses were performed on data obtained in a functional magnetic resonance imaging (fMRI) experiment, where subjects were presented with a simple visual stimulus. The BOLD signal strength was correlated with both the phase shift of the spectral density matrix and time-to-peak calculated from trial-averaged time courses. Correlation coefficients were calculated for visual stimuli of 2, 6, and 15 seconds in duration. Results Analyzing all functional runs for the same subject separately, i.e., including for each run all significantly activated voxels, we observed that correlations between phase shift and signal strength, as well as between time-to-peak and signal strength, decreased with increasing stimulus length. However, when analyses were restricted to voxels found activated in all functional runs, we observed similar correlations between BOLD signal strength and latency in all runs, independent of the length of stimulation. This result was again obtained for both latency measures: the spectral density phase shift and time-to-peak. Conclusion For both latency measures, phase shift and time-to-peak, a high correlation between BOLD signal strength and latency was observed. We have shown that this correlation is independent of the length of visual stimulation. Thus, the correlation between BOLD signal strength and latency seems to be an inherent property of the BOLD response that is independent of the length of stimulation and can be observed using different methods for determining signal latency. J. Magn. Reson. Imaging 2005;21:489,494. © 2005 Wiley-Liss, Inc. [source] Investigating the stimulus-dependent temporal dynamics of the BOLD signal using spectral methodsJOURNAL OF MAGNETIC RESONANCE IMAGING, Issue 3 2003Karsten Müller PhD Abstract Purpose To compare several spectral parameters using different durations of visual hemifield stimulation in order to explore the different temporal behavior of the blood oxygenation-level dependent (BOLD) signal in various brain regions. Materials and Methods Spectral methods were applied to three different groups of subjects with visual stimulation lasting 6, 12, and 30 seconds. Furthermore, diffusion weighting was applied in an interleaved way. The core of the data processing was the computation of the spectral density matrix using the multidimensional weighted covariance estimate. Spectral parameters of coherence and phase shift were computed. Results The correlation between signal changes and phase shifts was dependent on the duration of the visual stimulation. The shorter the duration of visual stimulation, the stronger the correlation between percentage signal change and phase shift. Conclusion The experiments with short and long stimuli differed mainly in the distribution of the activated voxels in the plane of percentage signal change and phase shift. It was revealed that the height of the signal change depends on the phase shift, whereas the diffusion weighting has no influence. J. Magn. Reson. Imaging 2003;17:375,382. © 2003 Wiley-Liss, Inc. [source] Estimating the Rank of the Spectral Density MatrixJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2005Gonzalo Camba-Mendez Abstract., The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive definite matrix estimate that has a normal asymptotic distribution with a covariance matrix the rank of which is known. [source] Computer modeling of frequency-modulation spectra of coherent dark resonancesLASER PHYSICS LETTERS, Issue 9 2006J. Vladimirova Abstract Dynamics of a three-level quantum system in , -configuration driven by a resonant laser field with and without frequency modulation (FM) is studied for the first time in detail using two simulation techniques , the density matrix and quantum trajectories analysis. This analysis was applied to the Fmspectroscopy of coherent dark resonances in Cs atoms and computer simulation results for the absorption spectra are in qualitative agreement with those taken in an experiment. (© 2006 by Astro, Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA) [source] On the polarization properties of the micromaser pumped by the atoms with degenerate levelsLASER PHYSICS LETTERS, Issue 3 2004V. A. Reshetov Abstract The polarization properties of the micromaser field pumped by the atoms with the resonant levels, which are degenerate in the projections of the total angular momentum on the quantization axis, are studied numerically. The standard micromaser operation, when the atoms enter the cavity excited to the upper resonant level, and the micromaser operation under the coherent pump, when the atoms enter the cavity in a superposition of resonant atomic levels, are considered. The treatment is based on the master equation for the density matrix of the micromaser field, which takes into account the degeneracy of atomic levels. (© 2004 by HMS Consultants. Inc. Published exclusively by WILEY-VCH Verlag GmbH & Co.KGaA) [source] Entangled photon pairs from radiative cascades in semiconductor quantum dotsPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 15 2006N. Akopian Abstract Entangled photon pairs are emitted from a biexciton decay cascade of single quantum dots when spectral filtering is applied. We show this by experimentally measuring the density matrix of the polarization state of the photon pair emitted from a continuously pumped quantum dot. The matrix clearly satisfies the Peres criterion for entanglement. By applying in addition a temporal window, the quantum dot becomes an entangled light source. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Electron-electron relaxation in disordered interacting systemsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 3 2008Peter Bozsoki Abstract We study the relaxation of a non-equilibrium carrier distribution under the influence of the electron-electron interaction in the presence of disorder. Based on the Anderson model, our Hamiltonian is composed from a single particle part including the disorder and a two-particle part accounting for the Coulomb interaction. We apply the equation-of-motion approach for the density matrix, which provides a fully microscopic description of the relaxation. Our results show that the nonequilibrium distribution in this closed and internally interacting system relaxes exponentially fast during the initial dynamics. This fast relaxation can be described by a phenomenological damping rate. The total single particle energy decreases in the redistribution process, keeping the total energy of the system fixed. It turns out that the relaxation rate decreases with increasing disorder. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A theory of nonlinear susceptibility in polaritonic band-gap materials doped with multi-level atomsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 8 2005D. Mukherji Abstract We have studied the nonlinear susceptibility in dispersive polaritonic band-gap (DPBG) materials in the presence of five-level impurity atoms. Initially, the atom is prepared in a coherent superposition of two levels |b, and |c,. The levels |b, and |c, are coupled to the upper level |a, with a coherent laser field. The nonlinear susceptibility has been calculated corresponding to transitions |a, , |c, and |a, , |b, using the equation of motion for the density matrix. The atomic system is interacting with the polariton reservoir. The effect of atom-polariton reservoir coupling on the imaginary part of the nonlinear susceptibility has been studied when the resonance energy lies in lower band of the polariton spectrum. It is found that by shifting the resonance energy away from the band edge, the system goes to the probe gain state. It is also found that by changing the intensity of the coherent laser field, the system switches from gain to loss state and vice-versa. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Determination of a one-electron reduced density matrix using a coupled pseudo-atom model and a set of complementary scattering dataACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2007Jean-Michel Gillet A possible model of one-electron reduced density matrices is presented, adapted from the Hansen,Coppens pseudo-atomic description of electron density [Hansen & Coppens (1978). Acta Cryst. A34, 909,913]. Potential benefits from a joint refinement of the model from X-ray diffraction and deep inelastic scattering data are illustrated. [source] Resonance Structures of the Amide Bond: The Advantages of PlanarityCHEMISTRY - A EUROPEAN JOURNAL, Issue 27 2006Jon I. Mujika Abstract Delocalization indexes based on magnitudes derived from electron-pair densities are demonstrated to be useful indicators of electron resonance in amides. These indexes, based on the integration of the two-electron density matrix over the atomic basins defined through the zero-flux condition, have been calculated for a series of amides at the B3LYP/6-31+G* level of theory. These quantities, which can be viewed as a measure of the sharing of electrons between atoms, behave in concordance with the traditional resonance model, even though they are integrated in Bader atomic basins. Thus, the use of these quantities overcomes contradictory results from analyses of atomic charges, yet keeps the theoretical appeal of using nonarbitrary atomic partitions and unambiguously defined functions such as densities and pair densities. Moreover, for a large data set consisting of 24 amides plus their corresponding rotational transition states, a linear relation was found between the rotational barrier for the amide and the delocalization index between the nitrogen and oxygen atoms, indicating that this parameter can be used as an ideal physical-chemical indicator of the electron resonance in amides. [source] | ||||||||||||||||