Configurational entropy of polyethylene and other linear polymers

The configurational entropy of the polyethylene chain at the melting points calculated in two ways. In both calculations, tetrahedral angles and discrete trans and gauche arrangements of all bonds are assumed, and trans bonds are assumed more stable than gauche by energy U₁. First, calculations are made on chains of up to N = 18 bonds, disallowing all configurations having overlapping atoms, and the result is extrapolated to large N. Second, a calculation is made directly for long chains, with overlaps excluded only over every short chain segment. The results are in almost exact agreement, suggesting that the second method can be safely used with other molecules. The calculated configurational entropy is in line with that suggested by the entropy of fusion, assuming the chains to acquire a configurational freedom in the melt which approaches that of independent chains.     

A BSSE-free SCF algorithm for intermolecular interactions

A very simple modification of the usual (～N⁴) SCF procedure is proposed, permitting the exclusion of basis set superposition errors (BSSE ) in problems of intermolecular interactions. No a posteriori corrections are required. The results of this “CHA /F method” are numerically close to those of the Boys–Bernardi correction scheme but are free from the “overcompensation” characteristic of the latter at smaller distances.     

Statistical representation of atomic systems structure. II. classification of the representation; entropy dependence of the total energy for isoelectronic series

The energies of the ground states of the mononuclear atomic systems, until now determined merely by approximate methods, turn out to exhibit some almost exact interdependencies. A simple statistical functional of the electronic structure (the “γ representation”) turns out to be decisive for the system energy. In this paper that interdependence is further traced for the N-electron systems in isoelectronic series (with constant N and varying Z). The resulting “combinatorial formula” reproduces the experimental data with the errors at least ten times smaller than those of the conventional Hartree–Fock approximation. The reason why there is such an exact formula for the ground-state energy remains to be clarified. The limiting behavior of our energy formula for large Z exhibits consistency with the Thomas–Fermi and the Z^?1perturbation expansion models.     

Improved intermolecular SCF theory and the BSSE problem

Analytical and numerical studies are performed concerning the exclusion of the basis set superposition error (BSSE ) from the SCF calculations of intermolecular interactions. Based on these studies a new procedure is proposed, which consists of the following steps: (1) determine the orbitals by the SCF scheme based on the recent “chemical Hamiltonian approach” (CHA-SCF method), i.e., excluding the delocalization effects caused by BSSE , and then (2) calculate the usual energy expectation value. (This gives results superior to those obtained by the previous nonsymmetric CHA energy formula.) The actual numerical calculations performed for different simple systems (He₂, water dimer) by using various basis sets indicate that the CHA/CE (CHA with “conventional energy” formula) potential curves are well-balanced and are close to those obtained by the Boys–Bernardi (BB ) method and usually (but not necessarily) go slightly beyond the latter. So our method gives results better than (or close to) those given by the BB method by performing only a single ～N⁴ calculation at each geometrical arrangement of the system.     

Variation of the ℏω with the particle number and the appearance of “kinks” for atomic clusters

The dependence of the harmonic oscillator (HO) energy level spacing ?ω on the particle number N is studied analytically for atomic (metal) clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to “kinks,” that is, to “marked discontinuities in the slope” of ?ω at the closed shells. These discontinuities diminish as N increases. For large N, ?ω becomes simply: ?ω?c₁N^?1/3+c₂N^?1. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

An integral direct, distributed-data, parallel MP2 algorithm

Summary A scalable integral direct, distributed-data parallel algorithm for four-index transformation is presented. The algorithm was implemented in the context of the second-order M?ller-Plesset (MP2) energy evaluation, yet it is easily adopted for other electron correlation methods, where only MO integrals with two indices in the virtual orbitals space are required. The major computational steps of the MP2 energy are the two-electron integral evaluationO(N ⁴) and transformation into the MO basisO(ON ⁴), whereN is the number of basis functions, andO the number of occupied orbitals, respectively. The associated maximal communication costs scale asO(n _Σ O ² V N), whereV andn _Σ denote the number of virtual orbitals, and the number of symmetry-unique shells. The largest local and global memory requirements areO(N ²) for the MO coefficients andO(OV N) for the three-quarter transformed integrals, respectively. Several aspects of the implementation such as symmetry-treatment, integral prescreening, and the distribution of data and computational tasks are discussed. The parallel efficiency of the algorithm is demonstrated by calculations on the phenanthrene molecule, with 762 primitive Gaussians, contracted to 412 basis functions. The calculations were performed on an IBM SP2 with 48 nodes. The measured wall clock time on 48 nodes is less than 15 min for this calculation, and the speedup relative to single-node execution is estimated to 527. This superlinear speedup is a result of exploiting both the compute power and the aggregate memory of the parallel computer. The latter reduces the number of passes through the AO integral list, and hence the operation count of the calculation. The test calculations also show that the evaluation of the two-electron integrals dominates the calculation, despite the higher scaling of the transformation step.     

A method for the calculation of normal-mode vibrational frequencies using symmetry coordinates. Application to the calculation of secondary deuterium isotope effects on carbocations

A method is introduced for the calculation of normal-mode vibrational frequencies of polyatomic molecules based on numerical differencing of analytical gradients in symmetry coordinates. This procedure requires a number of gradient evaluations equal to the largest number of symmetry coordinates belonging to any single irreducible representation of the molecular point group (plus a single gradient evaluation at the equilibrium configuration), which is fewer than the 3N-6 (N atoms) gradient evaluations needed for schemes based on Cartesian or internal coordinates. While the proposed method will not generally be as efficient as procedures which involve the direct calculation of energy second derivatives analytically (as are now available for single-determinant wavefunctions) it appears to be equally accurate, and it should be the method of choice for frequency calculations involving multideterminant wavefunctions for which analytical second-derivative algorithms have yet to be developed. The method is illustrated by the calculation of equilibrium secondary deuterium-isotope effects on a number of reactions involving simple carbocations.     

Theoretical investigations of the electronic states of porphyrins. II. Normal and hyper phosphorus porphyrins

Ab initio methods have been used to calculate the ground and excited states of “normal” and “hyper” porphyrins. Perturbation theory and CI methods were used to determine differential ground and excited-state correlation effects for [P^v(P)F₂]⁺ and [P^III(P)]⁺. A comparison is made to the INDO /S /CI predicted wavefunctions and spectra and to the experimental spectra of closely related molecules. The “hyper” [P^III(P)]⁺ calculations show some very low energy electronic transitions which provide an explanation for an anomalous “red” band in the spectrum and for the lack of fluorescence. Ab initio calculations also predict that (1) the lowest energy ¹A₁ state is a two-configuration wavefunction which can be described as a diradical, (2) the two lowest-energy singlet excited states are double excitations from the closed shell SCF configuration, and (3) a ³B₂ state is very close in energy to the lowest ¹A₁ state.     

A unified theory of the stability of benzenoid hydrocarbons

The spectral density operator technique is proved to be a convenient tool for derivation of approximate topological formulae for total pi-electron energy (E_pi) of benzenoid hydrocarbons (BH s). Developed mathematical formalism points out a common origin of three different measures for the stability of BH s, namely: resonance energy (RE), number of Kekule structures (K) and HOMO -LUMO separation (X_HL). In turn, a novel topological invariant corresponding to “normalized” RE is derived. Numerical calculations for a representative set of BH s demonstrate effectiveness of the present approach. Various approaches to an estimation of BH stabilities are discussed.     

VB2000: Pushing valence bond theory to new limits

Full valence bond (VB) calculations for a system of N electrons have always been hindered by the rapidly growing value of N!, which effectively imposes a limit N < 20. Often, however, not all electrons in a molecule are of interest; if we focus on a “group” G of N_G electrons (e.g., in an “active” region), then it is N_G! that sets the limit. In this work, group function (GF) theory is used to represent a molecule as a collection of interacting electron groups, each with a many‐electron wave function of any chosen form (e.g., VB, MO‐SCF, MCSCF), and each GF is optimized individually in a step‐by‐step process. An efficient VB algorithm allows for up to 14 electrons in any VB group and this combination of GF and VB methods greatly extends the range of feasibility of molecular calculations with VB‐type wave functions: Thus, (1) a large system can be divided into any number of smaller subsystems (groups); (2) each group may contain any chosen number of electrons; (3) the form of any group function (including its level of accuracy) may be chosen at will by the program user. A number of sample calculations are briefly presented. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Macrocyclization of polymers via ring‐closing metathesis and azide/alkyne‐“click”‐reactions: An approach to cyclic polyisobutylenes

The end‐to‐end cyclization of telechelic polyisobutylenes (PIB's) toward cyclic polyisobutylenes is reported, using either ring‐closing metathesis (RCM) or the azide/alkyne‐“click”‐reaction. The first approach uses bisallyl‐telchelic PIB's (M_n = 1650, 3680, 9770 g mol^?1) and Grubbs 1st‐, 2nd‐, and 3rd‐generation catalyst leading to cyclic PIB's in 60–80% yield, with narrow polydispersities (M_w/M_n = 1.25). Azide/alkyne‐“click”‐reactions of bisalkyne‐telechelic PIB's (M_n = 3840 and 9820 g mol^?1) with excess of 1,11‐diazido‐undecane leads to the formation of mixtures of linear/cyclic PIB's under formation of oligomeric cycles. Subsequent reaction of the residual azide‐moieties in the linear PIB's with excess of alkyne‐telechelic PEO enables the chromatographic removal of the resulting linear PEO‐PIB‐block copolymers by column chromatography. Thus pure cyclic PIB's can be obtained using this double‐“click”‐method, devoid of linear contaminants. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 671–680, 2010     

RAFT polymerization of tertiary sulfonium zwitterionic monomer in aqueous media for synthesis of protein stabilizing double hydrophilic block copolymers

The reversible addition-fragmentation chain-transfer (RAFT) polymerization of a tertiary sulfonium-containing zwitterionic monomer (N-acryloyl-L-methionine methyl sulfonium salt: A-Met[S⁺]-OH) was performed in aqueous media in the presence of a water-soluble chain-transfer agent (CTA). Several parameters, such as the radical initiator, nature of the salt used as an additive, polymerization temperature, and solvent (water, buffer solution, and mixed solvents), were studied. The polymerization of A-Met(S⁺)-OH in acetate buffer using a trithiocarbonate-type CTA having two carboxylic acid moieties proceeded in a controlled fashion at 45°C, as confirmed by the low polydispersity of the products (M _w/M _n < 1.1) and pre-determined molecular weights. Poly(ethylene glycol)-based macro-CTA was also employed for the polymerization of A-Met(S⁺)-OH in mixed solvents (H₂O/EtOH and H₂O/DMF = 70/30 vol%) to afford novel nonionic-zwitterionic double hydrophilic block copolymers. The chain extension of the hydrophilic poly(N,N-dimethylacrylamide) macro-CTA with A-Met(S⁺)-OH was well controlled in pure water under the appropriate conditions, resulting in the formation of block copolymers with “as-designed” chain structures and relatively low dispersities (M _w/M _n < 1.3). The resulting sulfonium-containing double hydrophilic block copolymers having optimal nonionic/zwitterionic balance were efficient protein-stabilizing agents.     

Ab initio molecular orbital study on the gas phase SN2 reaction F + CH3Cl → CH3F + Cl

Ab-initio molecular orbital (MO) and direct ab initio dynamics calculations have been applied to the gas phase S_N2 reaction F⁻ + CH₃Cl → CH₃F + Cl⁻. Several basis sets were examined in order to select the most convenient and best fitted basis set to that of high-quality calculations. The Hartree–Fock (HF) 3−21+G(d) calculation reasonably represents a potential energy surface calculated at the MP2/6−311++G(2df,2pd) level. A direct ab initio dynamics calculation at the HF/3−21+G(d) level was carried out for the S_N2 reaction. A full dimensional ab initio potential energy surface including all degrees of freedom was used in the dynamics calculation. Total energies and gradients were calculated at each time step. Two initial configurations at time zero were examined in the direct dynamics calculations: one is a near collinear collision, and the other is a side-attack collision. It was found that in the near collinear collision almost all total available energy is partitioned into two modes: the relative translational mode between the products (40%) and the C − F stretching mode (60%). The other internal modes of CH₃F were still in the ground state. The lifetimes of the early- and late-complexes F⁻ … CH₃Cl and FCH₃ … Cl⁻ are significantly short enough to dissociate directly to the products. On the other hand, in the side-attack collision, the relative translation energy was about 20% of total available energy.     

The configurational free energy of a polymer chain

The configurational, or elastic, free energy A_el of a polymer chain is discussed in terms of the Fourier configurational approach. The importance of accounting for all degrees of freedom of the chain is shown in comparison with affine mean-field theories and with scaling theories of chain expansion and contraction. In case of strong contraction the chain does show neither affinity nor self-similarity, and we get A_el ∼ N^1/3, N being the number of chain bonds. Conversely, in case of good-solvent expansion we find A_el ∼ N. The same result holds in the vicinity of the Θ-temperature, where A_el is also proportional to [(T − Θ)/T]².     

Selection rules for classical reactive trajectories: Dynamical allowedness and forbiddenness

A simple model for a particle climbing an inclined plane limited by rigid walls, towards an exit symbolizing the entrance of a product valley, demonstrates the general existence of reactive and unreactive bands. The system can be described by a single parameter η. The dynamically “allowed” or “forbidden” outcome of the reaction is shown to depend on the dynamical number N which characterizes the number of rebounds of the particle on the rigid walls. For given total energy, each value of N defines a reactive band which is accessible only for certain intervals of the initial energy in the direction perpendicular to the reaction coordinate. Depending on the value of the parameter η, the onset energy for reactive bands can vary either quadratically with N or linearly with N.     

Computation of the Electronic and Spectroscopic Properties of Carbohydrates Using Novel Density Functional and Vibrational Self-Consistent Field Methods

ABSTRACT

A novel density functional method is presented for the calculation of electronic and thermodynamical properties of oligosaccharides. This method, termed K2-BVWN, offers two advantages; it scales as N ³, where N is the number of basis functions, and there are only two adjustable parameters. The current density functional method is tested in terms of reproducing high level gas phase ab initio calculations in eleven low energy conformers of D-glucopyranose including exo-anomeric and different hydroxymethyl orientations (G ^?, G ⁺, and T). The K2-BVWN method is also tested in terms of reproducing the spectroscopic features of D-glucopyranose and D-mannopyranose (α/β) as compared with both a vibrational self-consistent field calculation (VSCF) as well as experimental infrared spectroscopy. The VSCF calculations offer the advantage that it is possible to include higher order mode coupling and anharmonic effects directly into the calculation of the vibrational frequencies. In general, the K2-BVWN method reproduces the ab initio energetic trends of the different conformers of D-glucose. While the absolute energies are not the same between the ab initio and the K2-BVWN method, both methods do predict a preference for the α-anomer in the gas phase (0.4 kcal/mol ab initio, 0.0 – 0.5 kcal/mol K2-BVWN). The K2-BVWN method was able to reproduce the experimental and VSCF calculated spectrum of both D-glucopyranose and D-mannopyranose in the frequency range between 1500 – 800 cm^?1. Because the current density functional method is both relatively quick and accurate, it represents a significant advancement in the development of oligosaccharide force fields.