Self-consistent Field Approach Research Articles

A new approach to density matrix functional theory

Starting from a pair-excitation multiconfiguration self-consistent field approach considering pairwise excitations of two electrons of opposite spin from a single occupied molecular orbital to a single virtual molecular orbital, we present a natural orbital functional for the electronic energy containing the natural orbitals and the pair-excitation coefficients as variational parameters to be optimized. The occupation numbers of the natural orbitals can be determined from the pair-excitation coefficients in this implicit functional. Test calculations for the water molecule give occupation numbers of the natural orbitals in reasonable agreement with the results of full configuration interaction calculations.

Raman optical activity spectra: basis set and electron correlation effects

Raman and vibrational Raman optical activity (ROA) spectra have been calculated for three molecules: H2O2, CHDTF and CHDTOH. The effects of electron correlation on the ROA parameters of these relatively small systems have been investigated by means of the multiconfigurational self-consistent field (SCF) approach. A range of correlation-consistent basis sets has been used in the calculations. The basis set convergence of the calculated ROA parameters is fairly well achieved when sets of at least d-aug-cc-pVTZ quality are used. On the other hand, the aug-cc-pVDZ set seems to be sufficient for a qualitative analysis. Diffuse functions, possibly a double set, are essential to ensure a good quality of the calculated ROA spectrum. In most cases the sign and approximate magnitude of the ROA are correctly predicted at the SCF level, and the corresponding ROA spectra should be considered qualitatively accurate.

A high level theoretical investigation of the N2O4→2 NO2 dissociation reaction: Is there a transition state?

The N2O4→2 NO2 dissociation reaction was investigated at a high level of theory using the couple cluster with all single and double excitations and connected triples [CCSD(T)] and complete active space self-consistent field approaches, and the cc-pVDZ, aug-cc-pVDZ, and cc-pVTZ basis sets. Only at the coupled cluster level a first-order saddle point was found connecting reactant and products. Collectively, structural, vibrational, and thermodynamic data for the three stationary points represent the best theoretical description of this reaction system to date, and are in good agreement with available experimental results. Unimolecular transition state theory rate constants (k∞) were also evaluated at 250, 298.15, and 350 K. At the CCSD(T)/cc-pVTZ level of calculation these results are 0.62×101, 1.90×103, and 1.66×105 s−1, respectively. Known experimental results at 298 K vary from 1.7×105 to 1.0×106 s−1. Including an estimate for basis set superposition error, we predict ΔH2980 for the dissociation reaction to be 12.76 kcal/mol (Expt. 13.1–13.7 kcal/mol).

Many-body effects in the Coulomb drag between low density electron layers

Recent Coulomb drag experiments in low-density double-layer electron systems have the power of distinguishing various many-body formulations of the effective interactions. In this work we theoretically study the correlation effects on the drag resistivity in these systems within various models. The effective inter-layer interactions are best described by the generalization to the double-layer case of the Kukkonen–Overhauser approach which differs significantly from the self-consistent field approach of Singwi et al. [Phys. Rev. 176 (1968) 589]. Following the formulation of Vignale and Singwi [Phys. Rev. B 32 (1985) 2156] we derive an expression for the effective inter-layer interaction which embodies the many-body correlations through the local-field corrections. The drag resistivity is calculated within this approach together with the Hubbard approximation for the intra-layer local-field factor and a simple model for the inter-layer correlations. Comparison with the recent measurements of Kellogg et al. [Solid State Commun. 123 (2002) 515] yields very good agreement. Our results are also contrasted with the corresponding drag resistivities given by the Singwi et al. theory, the dynamic random-phase approximation and the Hubbard approximation. The significant differences found between these theories emphasize the strong sensitivity of the drag resistivity to the effective inter-layer interactions.

Fast NDDO Method for Molecular Structure Calculations Based on Strictly Localized Geminals

The problem of constructing fast computational schemes has been attacked by using the antisymmetrized product of strictly localized geminals (APSLG) form of the trial wave function instead of the Slater determinant. The procedure is implemented on the semiempirical neglect of diatomic differential overlap (NDDO) level with three well-known parametrizationssmodified neglect of diatomic overlap (MNDO), first-Austin method (AM1) and third-parametric method (PM3). Heats of formation and geometry structures calculated are compared for self-consistent field (SCF) and APSLG approaches. Specific APSLG electronic structure parameterss bond characteristics and hybridization matricessobtained on the ground of variational principle are proven to correspond to chemical intuition. The advantages and limitations of the scheme proposed are discussed.

Ab initio calculations of zero-field splitting parameters in linear polyacenes

Abstract The results of ab initio calculations of zero-field splitting (ZFS) parameters are presented for the linear polyacenes from benzene to pentacene. We show how the electron spin–spin (SS) parameters can be efficiently obtained from restricted high-spin open-shell wave functions (ROHF), and present calculations of these, comparing with the results of a recent multi-configurational self-consistent field approach. The SS parameters are obtained from electron SS coupling strengths evaluated as expectation values over the wave functions and from state-to-state spin–orbit (SO) interactions. The results for the two lowest triplet states of naphthalene demonstrate that excellent values can be obtained even using moderate basis sets in the wave function, indicating that this technique can be used to obtain reliable ZFS parameters of aromatic compounds. Electron correlation is, however, not negligible; by accounting for full π-electron correlation the ZFS parameters are in considerably better agreement with experiment than the ROHF results. The ROHF method still reproduced the qualitative trend in the polyacene series in which the ZFS parameters are reduced with increasing size of the π-conjugation. We confirm that the SS coupling contributions completely determine the D and E parameters for the lowest triplet state of the linear polyacenes and that the SO coupling contributions are small. Geometry optimization of the lowest triplet state was found to be fairly significant for the calculated D and E values; these were reduced by about 30% and 40%, respectively, when the geometry was changed from the ground-state singlet to the triplet-excited state optimized geometry, with the latter values being in better agreement with experiment. The present calculations predict that the second triplet state of naphthalene is very unusual, as it has a negative zero-field splitting, implying an altered ordering of the spin sublevels compared to what is common in aromatic systems.

Photodissociation of alkyl and aryl iodides and effect of fluorination: Analysis of proposed mechanisms and vertical excitations by spin–orbit ab initio study

An ab initio study of the vertical electronic excitations in CX3I, C6X5H, and C6X5I (X=H and F) is presented. All-electron basis sets are used and the relativistic effects are accounted for with the relativistic elimination of small components scheme. The structures are optimized with the complete active space self-consistent field approach and the excitation energies are computed with the spin–orbit multiconfiguration quasidegenerate perturbation theory. The n–σ* transitions of CX3I, low-lying π–π* transitions of C6X5H, and low-lying n–σ*, π–π*, and π–σ* transitions of C6X5I are elucidated. For CH3I, energy values of parallel and perpendicular transitions differ from experimental values by 455 and 1156 cm−1, respectively. Effects of fluorination are emphasized, it is found that fluorination increases the gap between Q30 and Q11 transitions and increase is substantially more in aryl iodides than in alkyl iodides. Electronic factors influencing increased I* quantum yield in the photodissociation on fluorination of alkyl iodides is attributed to increased gap between Q30 and Q11 transitions reducing curve crossing probability and for aryl iodides there is additional role by phenyl transitions. A correlation diagram illustrating transitions of aryl iodides is presented.

First-principles analysis of molecular conduction using quantum chemistry software

We present a rigorous and computationally efficient method to do a parameter-free analysis of molecular wires connected to contacts. The self-consistent field approach is coupled with Non-equilibrium Green's Function (NEGF) formalism to describe electronic transport under an applied bias. Standard quantum chemistry software is used to calculate the self-consistent field using density functional theory (DFT). Such close coupling to standard quantum chemistry software not only makes the procedure simple to implement but also makes the relation between the I–V characteristics and the chemistry of the molecule more obvious. We use our method to interpolate between two extreme examples of transport through a molecular wire connected to gold(1 1 1) contacts: band conduction in a metallic (gold) nanowire, and resonant conduction through broadened, quasidiscrete levels of a phenyl dithiol molecule. We obtain several quantities of interest like I–V characteristics, electron density and voltage drop along the molecule.

Dipole?reaction field interaction model for the solvent reorganization energy and its application to the benzoquinone?benzoquinone anion radical system

Based on the spherical cavity approximation and the Onsager model, a dipole–reaction field interaction model has been proposed to elucidate the solvent reorganization energy of electron transfer (ET). This treatment only needs the cavity radius and the solute dipole moment in the evaluation of the solvent reorganization energy, and fits spherelike systems well. As an application, the ET reaction between p-benzoquinone and its anion radical has been investigated. The inner reorganization energy has been calculated at the level of MP2/6–31+G, and the solvent reorganization energies of different conformations have been evaluated by using the self-consistent reaction field approach at the HF/6–31+G level. Discussions have been made on the cavity radii and the values are found to be reasonable when compared with the experimental ones of some analogous intramolecular ET reactions. The ET matrix element has been determined on the basis of the two-state model. The fact that the value of the ET matrix element is about 10 times larger than RT indicates that this ET reaction can be treated as an adiabatic one. By invoking the classical Marcus ET model, a value of 4.9 × 107M−1s−1 was obtained for the second-order rate constant, and it agrees quite well with the experimental one.

Cation–π interactions between ammonium ion and aromatic rings: an energy decomposition study

The nature of the cation–π interaction between ammonium ion and a series of aromatic groups has been revisited through standard supermolecular energy decomposition schemes such as the Kitaura–Morokuma and the reduced variational space self-consistent field approaches. The emerged picture describes the ammonium–aromatics interaction as basically governed by electrostatics with significant contributions from the polarization, dispersion, and at a minor extent from, even from the aromatic–ammonium charge transfer. The role of molecular properties of the aromatic partners such as their mutipole moments, first and second order polarizability as well as the electronic properties of the frontier orbitals have been investigated in the light of the decomposed components. A final comment on the implications of our results on the reliability of the force fields currently employed for classical simulations and drug design investigations, has also been addressed.

Effects of disorder on the ground-state energy of a two-dimensional electron gas

We study the effects of disorder scattering on the ground-state energy of a two-dimensional electron system. Considering charged impurity scattering within the mode-coupling approximation to the memory function formalism, we calculate the correlation effects using a self-consistent field approach. In a different model, we also treat the disorder effects phenomenologically. The exchange, correlation, and ground-state energies and the compressibility are calculated for both models. In terms of the compressibility both models have similar predictions in the high-density region. The mode-coupling theory results at lower density are in better qualitative agreement with the experimental findings.

Induced magnetization and inhomogeneous superconductivity in presence of external magnetic field

Thermodynamic characteristics of the one-dimensional attractive Hubbard model are calculated by means of the generalized self-consistent field (GSCF) approach for a wide range of interaction strength U⩽0, in the presence of external magnetic field h⩾0, temperature T⩾0 and electron concentration 0⩽ n⩽1. The GSCF theory shows a sharp transition driven by h>0 and T from the uniform superconducting state into a spatially inhomogeneous state in which the order parameter Δ q (−) has wave vector ( 0<| q |⩽π ). The concentration of double occupied sites and the bound electron pairs with opposite spins n pair are calculated and we found a simple relationship between the order parameters Δ (−) q and average spin s, valid for the arbitrary U, all n and h.

Phase diagram and BCS–Bose condensation crossover in 1D and 2D Hubbard models

The ground-state energy, the concentration of double occupied sites and the density of bound electron pairs in low-dimensional attractive Hubbard model are calculated by means of the generalized self-consistent field (GSCF) approach. This approach gives an excellent agreement with the corresponding Bethe-ansatz solution and the quantum Monte-Carlo calculations in a wide range of interaction strength U<0 and electron concentration n. A simple relationship is found between the order parameter and the density of bound electron pairs, valid for any dimension and in entire parameter space U, n and magnetic field h. The electron pairing and the crossover from the itinerant BCS regime into the Bose condensation regime of local pairs are studied in dependence of both U and n. The GSCF theory correctly displays the separation of the energy gap from the BCS order parameter at n≠1 as | U| increases.

Systematic convergence in the dynamical hybrid approach for complex systems: A numerically exact methodology

An efficient method, the self-consistent hybrid method, is proposed for accurately simulating time-dependent quantum dynamics in complex systems. The method is based on an iterative convergence procedure for a dynamical hybrid approach. In this approach, the overall system is first partitioned into a “core” and a “reservoir” (an initial guess). The former is treated via an accurate quantum mechanical method, namely, the time-dependent multiconfiguration self-consistent field or multiconfiguration time-dependent Hartree approach, and the latter is treated via a more approximate method, e.g., classical mechanics, semiclassical initial value representations, quantum perturbation theories, etc. Next, the number of “core” degrees of freedom, as well as other variational parameters, is systematically increased to achieve numerical convergence for the overall quantum dynamics. The method is applied to two examples of quantum dissipative dynamics in the condensed phase: the spin-boson problem and the electronic resonance decay in the presence of a vibrational bath. It is demonstrated that the method provides a practical way of obtaining accurate quantum dynamical results for complex systems.

Vibrational self-consistent field approach to anharmonic spectroscopy of molecules in solids: Application to iodine in argon matrix

An extension of the vibrational self-consistent field (VSCF) method is developed for quantitative calculations of molecular vibrational spectroscopy in a crystalline solid environment. The approach is applicable to fields such as matrix-isolation spectroscopy and spectroscopy of molecular crystals. Advantages of the method are that extended solid vibrations and their coupling to intramolecular modes are incorporated, and that the treatment includes anharmonic effects, both due to the intrinsic property of individual modes and due to coupling between modes. Suitable boundary conditions are adopted in treating the solid environment. In applications, e.g., molecules in rare-gas crystals, hundreds of coupled molecular and matrix modes can be handled computationally. The method is applied to the vibrational matrix-shift of iodine in an argon matrix, and the calculated overtone frequencies are compared to experimental values obtained from both time-domain coherent Raman and frequency-domain Resonance Raman measurements. The physical origin of the shifts is interpreted in detail, and the properties of the iodine–argon interactions essential to obtain the correct sign and magnitude of the shift are elucidated. An I2–Ar potential, based on anisotropic atom–atom interactions and fitted to ab initio calculations, gives the best agreement with experiment. The results show that the VSCF solid-state approach is a powerful tool for matrix spectroscopy.

Inwardly curved polymer brushes: concave is not like convex

Inwardly curved polymer brushes are present in cylindrical and spherical micelles or in membranes tubes and vesicles decorated with anchored polymers, and influence their stability. We consider such polymer brushes in good solvent and show that previous works, based on a self-similar concentric structure of the brush, do not describe the most stable structure. We use scaling laws to derive very simply the leading term of the free energy in the high curvature limit, where the osmotic pressure is the relevant physical ingredient. We also derive the complete conformation at all curvatures using a self-consistent field approach. The free energy is computed therefrom using a local scaling description

Collective electronic oscillator/semiempirical calculations of static nonlinear polarizabilities in conjugated molecules

The collective electronic oscillator (CEO) approach based on the time-dependent Hartree–Fock approximation is combined with INDO/S, MNDO, AM1, and PM3 semiempirical Hamiltonians. This technique is applied to compute and analyze the static nonlinear polarizabilities of a series of donor/acceptor substituted oligomers. To mimic the experimental conditions, polarizabilities in substituted molecules are calculated for the isolated complex and in a dielectric medium, wherein the solvent contributions are incorporated using the self-consistent reaction field approach. The dielectric environment significantly increases second and third order static polarizabilities and considerably improves the agreement with experimental data. We find that calculated spectroscopic observables agree well with experimental values. We conclude that the CEO/semiempirical approach is an inexpensive and numerically efficient method of computing nonlinear molecular properties.

Polyelectrolytes tethered to a similarly charged surface

Conformations of weakly charged quenched polyelectrolyte chains tethered to a similarly charged planar surface are analyzed on the basis of a combination of scaling, analytical, and numerical self-consistent field (SCF) approaches. Scaling theory predicts universal power law dependences of the large-scale conformational properties (like the end-to-end distance) of grafted chains on the overall surface charge per unit area. The SCF approach allows analysis of the detailed conformational structure of grafted polyions as a function of the distribution of immobilized charges between the surface and grafted chains. The analytical solution is only available in the limiting cases of sparse grafting of polyions to the charged plane and sufficiently dense grafting of polyions to a neutral surface. In the intermediate case when both interchain interactions and interaction of grafted chains with the surface are important, only numerical solutions can be obtained. We consider various ways to distribute the charges between the surface and the brush chains while keeping the sum of the two contributions constant. Upon increasing the charge on the surface, by concomitant reduction of the grafting density of the tethered chains we found: (i) an increase in height of the polymer layer; (ii) the development of a depletion zone of end points near the surface; and (iii) a sharpening of the end-point distribution with the peak shifting away from the surface. In the appropriate limiting cases excellent agreement of analytical SCF predictions is obtained with the numerical results.

Ultrafast multidimensional dynamics of strong hydrogen bonds

The laser driven dynamics of the OH(D) stretching vibration in phthalic acid monomethylester is investigated. The combination of a 55-dimensional all-Cartesian reaction surface Hamiltonian and the time-dependent self-consistent field approach is shown to provide a microscopic picture of intramolecular vibrational energy redistribution taking place upon interaction with an external laser field. Choosing suitable zeroth-order vibrational states and combinations thereof a quasi-periodic in-phase and out-of-phase oscillatory behavior is observed manifesting energy flow on different time scales. The fingerprints of this behavior in transient absorption spectroscopy are also discussed.

Exocyclic push–pull conjugated compounds. Part 4: rotational barriers in poorly polarized push–pull ethylenes

The rotational barrier for substituted ethylenes was calculated with MO ab initio methods, both in the Hartree–Fock (HF) single determinant scheme and with multiconfigurational self-consistent field (MCSCF) approaches. The HF model affords reliable results only when applied to molecules substituted with strong electron donor groups, assigning a push–pull character to the molecule. The MCSCF approach was employed for calculating rotational barriers in poorly polarized ethylenes not directly amenable to the HF methods; however, this method was found hard to handle for low symmetry molecules with substituents interacting with the double bond. A method is proposed based on the interpolation of the energy of the perpendicular conformation from a Fourier truncated function constructed with HF molecular energies calculated for frozen conformations twisted up to 60°. The application of HF theory for studying internal rotation in substituted ethylenes with poorly polarized character is discussed and an upper limit of 35–40kcal/mol can be set up for having reliable barriers from the calculated energy of the rotational transition state at this level of theory.