Self-consistent Field Results Research Articles

Frank-Kasper Phases of Diblock Copolymer Melts: Self-Consistent Field Results of Two Commonly Used Models.

We constructed phase diagrams of conformationally asymmetric diblock copolymer A-B melts using the polymer self-consistent field (SCF) calculations of both the dissipative particle dynamics chain (DPDC) model (i.e., compressible melts of discrete Gaussian chains with the DPD non-bonded potential) and the "standard" model (i.e., incompressible melts of continuous Gaussian chains with the Dirac δ-function non-bonded potential) in the χN-ε plane, where χN and ε characterize, respectively, the repulsion and conformational asymmetry between the A and B blocks, at the A-block volume fraction f = 0.2 and 0.3. Consistent with previous SCF calculations of the "standard" model, σ and A15 are the only stable Frank-Kasper (FK) phases among the five FK (i.e., σ, A15, C14, C15 and Z) phases considered. The stability of σ and A15 is due to their delicate balance between the energetic and entropic contributions to the Helmholtz free energy per chain of the system, which, within our parameter range, increases in the order of σ/A15, Z, and C14/C15. While in general the SCF phase diagrams of these two models are qualitatively consistent, A15 is not stable for the DPDC model at the copolymer chain length N = 10 and f = 0.3; any differences in the SCF phase diagrams are solely due to the differences between these two models.

Frank–Kasper Phases of Diblock Copolymer Melts Studied with the DPD Model: SCF Results

For conformationally asymmetric diblock copolymer (DBC) melts, we proposed a model system that can be readily used in dissipative particle dynamics (DPD) simulations and performed the corresponding self-consistent field (SCF) calculations to study the stability of Frank–Kasper (FK) phases. This provides the mean-field results needed for direct comparison with the DPD simulations, without any parameter fitting, to unambiguously quantify the fluctuation/correlation effects inherently neglected by the SCF theory but important in the low-molecular-weight DBC melts forming FK phases in experiments. Our SCF calculations of the DPD model are faster and use less memory, both by at least one order of magnitude, than those of the “standard” model and give accurate results. Among the five FK (i.e., A15, C14, C15, Z, and σ) phases considered here, C14 is found to be the only stable one; its stability is due to the conformational asymmetry and, in particular, it is stabilized over other FK phases by entropy. This is the first time C14 is predicted to be stable in SCF calculations of neat DBC melts. Our SCF phase diagrams for the DPD model of conformationally asymmetric DBCs are qualitatively different from those for the “standard” model reported in the literature, which may be due to the model differences and numerical accuracy.

Self-Consistent Field Analysis of Molecular Bottle-Brushes with Primary and Secondary Side Chains: Induced Persistence Length and Lateral Thickness

Macromolecules may feature liquid crystalline behavior when the chain aspect ratio, that is the ratio between the chain persistence length and the cross-sectional thickness of its segments, is large. Scaling theory suggests that for molecular bottle-brushes under good solvent condition the induced persistence length does not depend on the chain architecture but only on the amount of segments in the side chains per unit length of the backbone. Numerical self-consistent field results are presented for macromolecular bottle-brushes with side chains of variable architecture attached at regular intervals along the backbone chain. We consider side chains (flexible “flagstaffs”), which feature one branch-point onto which secondary side chains (the “flag”) emanate. We varied the distance of this branch-point from the main chain as our tuning parameter, resembling the “raising of the flag.” For a given height of the flags, that is when the mass-distribution along a side chain is architecturally fixed, the induced persistence length is a function of the branching parameter (ratio between the length of the longest path and the total number of segments in the graft). We found that the induced persistence length and hence the chain aspect ratio, vary non-monotonically with the height of the flags. The lowest aspect ratio is found when the flag is raised to about a quarter of the full height of the flagstaff. The induced persistence length is independent of this height when upon bending the translocation of the side chains from compressed to expanded regions is artificially suppressed, which leads us to speculate that the non-monotonic behavior of aspect ratio is related to the efficiency of side chains to partly translocate themselves upon bending.

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: Formulation, proof of concept, and a pilot implementation.

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.

Single-Molecule Magnet Properties of Transition-Metal Ions Encapsulated in Lacunary Polyoxometalates: A Theoretical Study.

Single-molecule magnet (SMM) properties of transition-metal complexes coordinated to lacunary polyoxometalates (POM) are studied by means of state of the art ab initio methodology. Three [M(γ-SiW10O36)2] (M = Mn(III), Fe(III), Co(II)) complexes synthesized by Sato et al. (Chem. Commun. 2015, 51, 4081-4084) are analyzed in detail. SMM properties for the Co(II) and Mn(III) systems can be rationalized due to the presence of low-energy excitations in the case of Co(II), which are much higher in energy in the case of Mn(III). The magnetic behavior of both cases is consistent with simple d-orbital splitting considerations. The case of the Fe(III) complex is special, as it presents a sizable demagnetization barrier for a high-spin d(5) configuration, which should be magnetically isotropic. We conclude that a plausible explanation for this behavior is related to the presence of low-lying quartet and doublet states from the iron(III) center. This scenario is supported by ab initio ligand field analysis based on complete active space self-consistent field results, which picture a d-orbital splitting that resembles more a square-planar geometry than an octahedral one, stabilizing lower multiplicity states. This coordination environment is sustained by the rigidity of the POM ligand, which imposes a longer axial bond distance to the inner oxygen atom in comparison to the more external, equatorial donor atoms.

Interfacial tension between benzene and water in the presence of caprolactam

We studied the physical properties and the concentration profile of benzene+water+caprolactam mixtures near the fluid–fluid interface using self-consistent field (SCF) theory. This yields the interfacial tension which plays an important role in describing the stability of transient liquid droplets of one phase in the other. The studies were performed at a fixed temperature of 313K. Flory–Huggins binary interaction parameters and the compound lattice segment numbers are input parameters for the applied SCF theory. These parameters were derived from activity coefficient relations, which are used to describe experimental liquid–liquid and vapor–liquid phase equilibrium measurements. Using first principles, the benzene–water interface was studied and the resulting interfacial tension was found to be in agreement with experimental values. This study illustrates that caprolactam accumulates at the benzene–water interface, acting as a weak surfactant. The interfacial tension is also demonstrated to be affected by the caprolactam concentration and the SCF results are in fair agreement with the experimental observations.

ChemInform Abstract: Ab initio Theoretical Study of Small GaAs Clusters

Theoretical calculations for the closed‐shell ground state of small GaxAsy clusters (x=y; x=2–4) are carried out at the self‐consistent field (SCF) Hartree–Fock level of theory, using analytic energy gradients for rapid geometry optimization. In addition, for Ga2As2, the SCF results are compared with theoretical predictions obtained at the coupled cluster level of theory including all single, double and perturbative triple excitations, CCSD(T). The equilibrium structures for Ga2As2, Ga3As3, and Ga4As4 are found to be of D2h, C1, and Ci symmetry, respectively. The cluster binding energies with respect to GaAs dimers (3Σ−) and Ga(2P)+As(4S) atoms are also obtained.

Experimental and Self-Consistent-Field Theoretical Study of Styrene Block Copolymer Self-Adhesive Materials

This work addresses thermodynamic and mechanical properties of styrene block copolymer (SBC) self-adhesive materials. Mixtures of polystyrene-block-polyisoprene-block-polystyrene (SIS triblock) copolymers with resin and their blends with polystyrene-block-polyisoprene (SI diblock) copolymers were investigated experimentally and theoretically. The experiments involved small-angle X-ray scattering, atomic force microscopy, and tensile measurements, while the theoretical analysis invoked a mesoscopic representation of SBC materials combined with a continuum, 3D real-space self-consistent-field (SCF) approach. The calculations predict that the SBC systems should become microphase separated, with PS-rich spherical domains forming a bcc lattice in SIS triblock/SI diblock blends and in SIS triblock/resin systems with low resin content (20 wt %), while at high (60 wt %) resin content a disordered structure of PS-rich domains is expected. Extensive comparisons of SCF predictions concerning the type and the geometric characteristics of the morphologies obtained, the composition profiles, and the effect of diblock and resin content on the long-range space ordering of the PS-rich domains are performed against the experimental data. SCF theory predicts that approximately 79% of SIS molecules are connecting different PS-rich domains (i.e., are forming bridges) in SIS/SI blends, almost independently of the SI diblock content. The SCF results are combined with a slip tube model of rubber elasticity to predict the elastic behavior of SBC materials. In particular, the bridging properties are used to estimate the PS-rich domain cross-linking contribution, Gc, to the total shear modulus. The entanglement contribution, Ge, is evaluated from experimental and theoretical results reported in the literature concerning the properties of entanglements. The predicted stress−strain curves are in good qualitative agreement with the tensile experimental data for small values of strain.

Individual Polymer Paths and End-Point Stretching in Polymer Brushes

Molecular dynamics simulations and self-consistent field calculations have been used to study average polymer paths of end-grafted, strongly overlapping polymers in a good solvent. Contrary to what is usually assumed, and in agreement with earlier classical and self-consistent field results, we find the end points of average polymer paths which end at a certain distance from the grafting surface to be stretched. The agreement between simulations and self-consistent calculations clearly demonstrates that end-point stretching effects, appearing for the experimentally relevant case of finite-length and finitely stretched polymers, are not suppressed by fluctuations.

SulfurKβx-ray emission from carbonyl sulfide: Variations with polarization and excitation energy at theSKthreshold

Sulfur K{beta} x-ray-emission spectra from carbonyl sulfide have been measured with resonant excitation at the sulfur K absorption threshold and compared with results of self-consistent field and singles-doubles configuration-interaction calculations. For excitation to the strong 4{pi} absorption resonance, a splitting of the main emission peak is interpreted in terms of influence of the 4{pi} electron on the final valence-hole states. The polarization selectivity of the emission spectrometer was used to distinguish emission polarized parallel versus perpendicular with respect to the polarization of the excitation radiation. The observed polarization dependence is consistent with the molecular symmetries of the calculated intermediate and final states. {copyright} {ital 1998} {ital The American Physical Society}

Density Functional Study of the Valence-Tautomeric Interconversion Low-Spin [CoIII(SQ)(Cat)(phen)] ⇌ High-Spin [CoII(SQ)2(phen)

The results of self-consistent field (SCF) nonlocal density functional molecular orbital calculations are presented for the various spin states and tautomeric forms of a cobalt complex with two o-quinone-derived ligands. In addition, new variable-temperature solution magnetic susceptibility, EPR, and electronic absorption data are presented to characterize the low-spin [CoIII(3,5-DTBSQ)(3,5-DTBCat)(phen)] to high-spin [CoII(3,5-DTBSQ)2(phen)] valence-tautomeric interconversion, where 3,5-DTBSQ- and 3,5-DTBCat2- are the semiquinonate and catecholate forms of 3,5-di-tert-butyl-o-benzoquinone, respectively, and phen is 1,10-phenanthroline. The solution magnetic susceptibility data were fitted to give ΔH = 2238 cm-1 and ΔS = 118.1 J mol-1 K-1 for the ls-CoIII ⇌ hs-CoII equilibrium. Appreciable changes are seen in the electronic absorption spectrum as the complex changes between the two tautomeric forms. Unrestricted SCF calculations gave J = −594 cm-1 for the parameter characterizing the antiferromagnetic exc...

On the electric properties of Br2

Electric multipole moments and polarizabilities for Br2 are obtained from finite field self consistent field (SCF), many-body perturbation theory and coupled cluster calculations with large gaussian-type basis sets. At the MP2 level of theory the bond length dependence of the mean and the anisotropy of the dipole polarizability (ααβ/e 2 a 0 2 E h -1) around the equilibrium bond length of Re = 2·28105 A is adequately described by , . A very large \\[18s15p12d6f] basis set consisting of 330 basis functions yields SCF values α = 44·10 and Δ α = 28·31 e 2 a 0 2 E h -1. Adding electron correlation corrections obtained at the CCSD(T) level of theory and vibrational corrections obtained at the MP2 level, the mean dipole polarizability at the ground vibrational state is estimated at α = 44·74 (to be compared with the experimental value of 45·0) and the anisotropy at Δ α = 25·39 e 2 a 0 2 E h -1. At the MP2 level the mean second dipole hyperpolarizability γ/ e 4 a 0 4 E h -1 varies around R e as . SCF, MP2 and CCSD(T) results are combined to give as final theroeticalprediction the estimate of γ = (10·2 ± 1·0) x 103 e 4 a 0 4 E h -3.

UV photoelectron and ab initio quantum mechanical characterization of nucleotides: The valence electronic structure of anionic 2?-deoxyadenosine-5?-phosphate

He(I) ultraviolet (UV) photoelectron spectroscopy and ab initio, self-consistent field (SCF) calculations with the 6-31G basis set have been employed to characterize the valence electronic structures of anionic 2′-deoxyadenosine-5′-phosphate (5′-dAMP−). Theoretical ionization potentials (IPs) of 5'-dAMP-, of the neutral model compounds 9-methyladenine (9-MeA) and 3-hydroxytetrahydrofuran (3-OH-THF), and of the model anion CH3HPO4− have been obtained by applying Koopmans' theorem to ab initio SCF results. The ionization potentials predicted from the SCF calculations have been compared to He(I) photoelectron spectra of 9-MeA and 3-OH-THF. The SCF calculations predict a value (8.45 eV), for the highest occupied π orbital in 9-MeA which agrees well with the experimental vertical IP (8.39 eV). However, IPs for the highest occupied lone-pair orbitals in 3-OH-THF are predicted to be more than 1.52 eV higher than the experimental IPs. Results from recently reported [H. S. Kim and P. R. LeBreton, Proc. Natl. Sci. USA 91, 3725–3729 (1994), and N. S. Kim and P. R. LeBreton, J. Am. Chem. Soc., 118, 3694 (1996)] second-order Moller-Plesset perturbation (MP2) calculations and configuration interaction calculations using the configuration interaction singles (CIS) method indicate that configuration interaction effects strongly influence the energies of the first five ionization events arising from removal of electrons from the closed-shell model anion CH3HPO4−. Results from the 6-31G SCF calculations of 5′-dAMP−, 9-MeA, 3-OH-THF, and CH3HPO4− indicates that valence orbital electron distributions in the nucleotide and in the model compounds and anion are similar. The correspondence between the orbital structure of the nucleotide, and the model compounds and anion makes it possible, employing experimental photoelectron data and MP2/CIS computational results for the model compounds and anion, to individually correct IPs calculated for the nucleotide at the 6-31G SCF level. Here, this approach has provided values for the 13 lowest IPs of 5′-dAMP− and indicates that the first IPs of the base, sugar, and phosphate groups are 6.1, 7.8, and 5.5 eV, respectively. © 1996 John Wiley & Sons, Inc.

Adsorption of Neutral Polymers: Interpretation of the Numerical Self-Consistent Field Results

We use results on polymer absorption obtained from a recent mean-field theory with two order parameters to interpret numerical results of the Scheutjens and Fleer approach. An extension of the analytical theory accounting for the local swelling of the polymer is also presented and discussed.

Calculations of magnetic properties. IV. Electron-correlated magnetizabilities and rotational g factors for nine small molecules

Calculations of the magnetizabilities and the rotational g factors at the self-consistent-field (SCF) and second-order Mo/ller–Plesset perturbation theory (MP2) levels of theory are reported for H2, N2, F2, HF, CO, HCN, HNC, H2O, and NH3. The sums rules, that verify the reliability of the calculations, are shown to be well satisfied. The second-order correlation corrections to the magnetizabilities are found to be small, thus substantiating the generally observed good agreement between the experimental and SCF results. Vibrational corrections to the properties of the diatomic molecules are given. Very good agreement is found between the experimental and vibrationally corrected MP2 rotational g factors for the diatomic molecules.

A study of solvent effects on hyperpolarizabilities: The reaction field model applied to acetonitrile

The reaction field method has been applied in the calculation of the nonlinear optical properties of acetonitrile (CH3CN) in the liquid phase. Both self-consistent field (SCF) and second order perturbation theory (MP2) methods are used to calculate the dipole moment, polarizability, first and second static hyperpolarizabilities. Based on previous gas-phase studies which stress the importance of electron correlation in the calculation of hyperpolarizabilities, the MP2 results should be more reliable than the corresponding SCF results. The choice of a cavity radius is of considerable importance. For the two choices made, one based on the liquid density and the other on van der Waals’ parameters, the total second hyperpolarizability changed by as much as a factor of 3 and these calculated values bracket the two differing experimental results. The form of the reaction field factor suggests that the radius dependence should be less for acetonitrile in a solvent of reduced dielectric constant. Although this is true, as demonstrated by calculations involving acetonitrile dissolved in chloroform, significant dependence is still observed. The effect of using an ellipsoidal cavity as opposed to a spherical one is also examined. In this case the hyperpolarizability is less sensitive to the change in cavity parameters from those corresponding to the liquid density to those based on van der Waals’ radii. The hyperpolarizability determined is intermediate between the two values obtained with the spherical cavity and closer to one of the experimental values. Further work using more sophisticated solvation models is required in order to establish whether the reaction field model, with an appropriate choice of cavity parameters, can be used to investigate the hyperpolarizabilities of molecules in solution reliably.

How accurate are molecular mechanics predictions for fullerenes? A benchmark comparison with Hartree-Fock self-consistent field results

As research into the growing family of fullerene compounds continues to expand, theoreticians making predictions about these large carbon clusters are interested in reliable approaches to reduce the computational expense of calculations. Here we show that an empirical method, molecular mechanics (MM3), can be effectively used to optimize the geometries of fullerenes and consequently reduce the time required for more elaborate quantum mechanical calculations. Equilibrium structures and heats of formation were predicted for 22 fullerences ranging from C[sub 28] to C[sub 120] using MM3. The MM3 geometries are found to be in good agreement with those obtained by the minimum basis Hartree-Fock self-consistent field (SCF) method. However, the heats of formation obtained with MM3 and SCF are quite different. At the MM3 optimized geometry, an SCF energy point was calculated for each structure and found to be very close to the fully optimized SCF energy. This procedure yields accurate energy differences between isomers at a fraction of the computational cost. We propose other ways of using MM3 to speed ab initio calculations as well. 40 refs., 7 figs., 4 tabs.

Optimization techniques in energy calculations involving the Hartree-Fock density matrix

Three optimization procedures are examined for their utilization in determining the optimum density matrix for a single determinant wave function. The total energy of a molecular system is written as a function of the density matrix and then optimized subject to the constraints of idempotency and total electron population. This direct calculation of the density matrix (DCDM) method was studied in an attempt to have a formalism which would avoid convergence problems associated with the self-consistent field (SCF) cycle, and which would be applicable to large molecular systems. The optimization procedures studied were the Powell algorithm, Gauss-Jordan reduction, and dynamic programming. Computational factors studied include convergence criteria, stepsize, and weight factors for constraint equation penalty functions. The application considered is for HF. An ab-initio SCF method was used to obtain initial values for the density matrix, and its SCF results were compared to corresponding DCDM predictions. Approximations of the quadratic two-electron energy contributions will be necessary to apply dynamic programming, but this appears to be the method most applicable to large molecular systems if an acceptable approximation can be found. Gauss-Jordan reduction is an applicable technique, but probably not for large molecular systems. BOTM appears to be the method most applicable without introducing approximations, but weight factors for the penalty functions will have to be more efficiently determined as Lagrange multipliers, and this addition would result in a technique probably not applicable to large molecular systems.

Structure of a bidisperse polymer brush: Monte Carlo simulation and self-consistent field results

Using the bond-fluctuation model, Monte Carlo simulations are performed for polymer brushes composed of chains of two different chain lengths under good solvent condition. Profiles of monomer density and free end density, chain linear dimensions, and average monomer position along a chain are studied. Quantities measured in the simulations are derived from the analytic self-consistent field (SCF) theory and compared with the simulation data. The structural properties can be quite accurately described by the theory only when both the long and short chains are stretched

A b i n i t i o theoretical study of arsine and trimethylgallium: The formation of GaAs by a stable adduct

Theoretical calculations for the closed-shell ground state of arsine (AsH3), trimethylgallium (TMG) [Ga(CH3)3], and the arsine–TMG adduct [H3As⋅Ga(CH3)3] are carried out at the self-consistent field (SCF) Hartree–Fock level of theory. In addition, the SCF results are compared with theoretical predictions obtained at the coupled cluster level of theory including all single and double excitations (CCSD). The equilibrium structure of arsine is found to be of C3v symmetry, while TMG and the adduct are found to be of C3 symmetry. Ab initio calculations are also performed on D3h gallane (GaH3) and the gallane–arsine adduct (H3Ga⋅AsH3) of C3v symmetry. The adduct binding energies and vibrational frequencies (SCF) are also obtained resulting in two stable bonded adduct species—arsine⋅TMG and arsine⋅gallane. Finally, our theoretical predictions support a slightly exothermic gas-phase reaction yielding GaAs through a TMG⋅AsH3 adduct which is formed without an activation barrier.