An efficient algorithm for energy gradients and orbital optimization in valence bond theory

An efficient algorithm for energy gradients in valence bond theory with nonorthogonal orbitals is presented. A general Hartree-Fock-like expression for the Hamiltonian matrix element between valence bond (VB) determinants is derived by introducing a transition density matrix. Analytical expressions for the energy gradients with respect to the orbital coefficients are obtained explicitly, whose scaling for computational cost is m(4), where m is the number of basis functions, and is thus approximately the same as in HF method. Compared with other existing approaches, the present algorithm has lower scaling, and thus is much more efficient. Furthermore, the expression for the energy gradient with respect to the nuclear coordinates is also presented, and it provides an effective algorithm for the geometry optimization and the evaluation of various molecular properties in VB theory. Test applications show that our new algorithm runs faster than other methods.     

Reply to comment on the paper “An efficient Algorithm for Energy Gradients and Orbital Optimization in Valence Bond Theory”

van Lenthe, Broer, and Rashid made comments on our 2009 paper [Song et al., J. Comput. Chem. 2009, 30, 399] by criticizing that we did not properly reference the work by Broer and Nieuwpoort in 1988 [Broer and Nieuwpoort, Theor. Chim. Acta. 1988, 73, 405], and we favorably compared our valence bond self‐consistent field (VBSCF) algorithm with theirs. However, both criticisms are unjustified insignificant. The Broer–Nieuwpoort algorithm, properly cited in our paper, is for the evaluations of matrix elements between determinants of nonorthogonal orbitals. Stating that this algorithm “can be used for an orbital optimization” afterwards [van Lenthe et al., submitted] is not a plausible way to require more credits or even criticize others. While we stand by our statement that our algorithms scales at O(m⁴) and van Lenthe et al.'s approximate Newton Raphson algorithm scales at O(mN⁵) (here m and N are the numbers of basis functions and electrons), as we discussed in our original paper, it becomes obvious that any strict comparison among different algorithms is difficult, unproductive, and counteractive. © 2012 Wiley Periodicals, Inc.     

An efficient algorithm for complete active space valence bond self‐consistent field calculation

This article describes a novel algorithm for the optimization of valence bond self‐consistent field (VBSCF) wave function for a complete active space (CAS), so‐called VBSCF(CAS). This was achieved by applying the strategies adopted in the optimization of CASSCF wave functions to VBSCF(CAS) wave functions, using an auxiliary orthogonal orbital set that generates the same configuration space as the original nonorthogonal orbital set. Theoretical analyses and test calculations show that the VBSCF(CAS) method shares the same computational scaling as CASSCF. The test calculations show the current capability of VBSCF method, which involves millions of VB structures. © 2012 Wiley Periodicals, Inc.     

Stoichiometric Valence and Structural Valence—Two Different Sides of the Same Coin: “Bonding Power”

Two valencies instead of one! Stoichiometric valence and structural valence are two distinct properties of atoms. The former, ^stoichV, is derived from the composition of a compound and has integer values; the latter, ^structV, depends on the structure of a compound and has non‐integer values. The scheme shows a representation of valence states of antimony and oxidation of Sb^III to Sb^V, as a function of the eccentricity parameter Φ _i.

     

The valence bond calculations for conjugated hydrocarbons having 24–28 π‐electrons

A novel algorithm is introduced for coding all Slater determinants in the covalent space with conserved S_Z, the z component of total spin S for a classical valence bond (VB) model. It effectively minimizes the search time and the storing space in the central memory of the computer. In cooperation with symmetry reductions based on molecular point group and spin inversion, the VB calculations have been extended to benzenoid hydrocarbons of up to 28 π‐electrons that have 4×10⁷ configurations. The low‐lying states of benzenoids with 24, 26, and 28 π‐electrons have been obtained for 62 species. To rationalize the aromaticity of benzenoids in a VB scheme, the resonance energy per hexagon (REPH) is defined. A linear correlation between the REPH and the energy gap of the ground (singlet) state and the first excited (triplet) state for 89 benzenoids is established. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 856–869, 2000     

Comment on “The electron‐pair origin of anti‐aromaticity: Spectroscopic manifestations”

In the article by Zilberg and Haas, “The Electron‐Pair Origin of Anti‐aromaticity: Spectroscopic Manifestations,” the relative sign of the two Kekulé valence bond functions, R and L, in conjugated cyclic hydrocarbons was discussed. It was proposed that in the ground‐state wave function of aromatic compounds, the two functions contribute with like sign, while in the ground state of anti‐aromatic compounds, the two functions contribute with opposite sign. In this Comment, it is shown that the two functions enter with like sign also into the ground‐state wave function of anti‐aromatic compounds. Furthermore, it was argued that resonance tends to (de)stabilize a symmetric ground‐state geometry in case of the (anti‐)aromatic compounds. The expression derived by Zilberg and Haas for the stabilization energy shows an unusual dependence on the ring size and distortion coordinate. An alternative formula is derived for the stabilization energy, in which the energy depends quadratically on the distortion coordinate. Without further numerical calculations, it is not possible to predict whether this term will (de)stabilize a symmetric geometry of the ground state of (anti‐)aromatic molecules. Rather, we are led to believe that the influence of term in question on the geometric stability may be small, thus not providing the main reason for the geometric distortion of anti‐aromatic compounds. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Molecular design of a “molecular syringe” mimic for metal cations using a 1,3‐alternate calix[4]arene cavity

The chemically switchable actions well imitate the function of a “molecular syringe,” has been studied in theory using the 1,3‐alternate calix [4]arene bearing a nitrogen‐containing crown cap at one side and a bis(ethoxyethoxy) group at another side by the π‐basic calixtube as a pipette and the crown ring as a rubber cap. The model is characterized by geometry optimization using density functional theory (DFT) at B3LYP/6‐31G level. The obtained optimized structures are used to perform natural bond orbital (NBO) and frequency analysis. The electron‐donating heteroatoms: O and N offer lone pair electrons to the contacting RY* (1‐center Rydberg) or LP* (1‐center valence antibond lone pair) orbitals of K⁺, Ag⁺. The results indicate that when the nitrogen atom in the crown ring is protonated, K⁺ and Ag⁺ will be pushed out to the bis(ethoxyethoxy) side through a π‐basic calixtube. When the nitrogen·H⁺ in the crown ring is deprotonated, K⁺ and Ag⁺ are sucked back to the crown‐capped side again. In the course of the coordination, both the intermolecular electrostatic interactions and the cation‐π interactions between the metal ion and π‐orbitals of the two pairs facing inverted benzene rings play a significant role. It is believed that this prototype of a “molecular syringe” is a novel molecular architecture for the action of metal cations. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Free energy calculations,enhanced by a gaussian ansatz,for the “chemical work” distribution

The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the “chemical work” of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the “irreversible” work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible “chemical work” minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the “chemical work,” accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the “chemical work.” For a more general free energy perturbation scheme that the Gaussian ansatz may not be valid, the free energy calculation can be expressed in terms of the moment generating function of the “chemical work” distribution. © 2014 Wiley Periodicals, Inc.     

Response to: “Comment on ‘The effect of confinement on the electronic energy and polarizability of a hydrogen molecular ion’”

In this reply we clarify questions point out in the Comment on: “The Effect of Confinement on the Electronic Energy and Polarizability of a Hydrogen Molecular Ion” by J. F. da Silva, F. R. Silva and E. Drigo Filho, Int. J. Quantum Chem.2016, 116, 497–503 written by S. A. Cruz and H. Olivares‐Pilón. In particular, we show how we made the calculations of ground state energy from the confined hydrogen molecule ion for cavities of different volumes. The internuclear distances to the excited state 2pσ_u are also presented.     

On the Origin of the “Giant” Electroclinic Effect in a “De Vries”‐Type Ferroelectric Liquid Crystal Material for Chirality Sensing Applications

W415 is a chiral smectic compound with a remarkably weak temperature dependence of its giant electroclinic effect in the liquid crystalline smectic A* phase. Furthermore it possesses a high spontaneous polarization in the smectic C* phase. The origin of this striking electroclinic effect is the co‐occurrence of a de Vries‐type ordering with a weak first‐order tilting transition (see the synchroton X‐ray scattering profiles).

     

Direct through anionic,cationic, and radical active species: Terminal carbon–halogen bond for “controlled”/living polymerizations of styrene

In this work, we examined the synthesis of novel block (co)polymers by mechanistic transformation through anionic, cationic, and radical living polymerizations using terminal carbon–halogen bond as the dormant species. First, the direct halogenation of growing species in the living anionic polymerization of styrene was examined with CCl₄ to form a carbon–halogen terminal, which can be employed as the dormant species for either living cationic or radical polymerization. The mechanistic transformation was then performed from living anionic polymerization into living cationic or radical polymerization using the obtained polymers as the macroinitiator with the SnCl₄/n‐Bu₄NCl or RuCp^*Cl(PPh₃)/Et₃N initiating system, respectively. Finally, the combination of all the polymerizations allowed the synthesis block copolymers including unprecedented gradient block copolymers composed of styrene and p‐methylstyrene. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 465–473     

DFT and ab initio potential energy scan and hydrogen bond analysis of N-substituted hydrazino acetamides: Characterization of the “hydrazinoturn” hydrogen bonding pattern

We studied a series of model primary amides in gas phase at the DFT (B3LYP) and HF at 6-31+G/6-31+G** levels of theory in order to shed light on their conformation, structure, and intramolecular hydrogen bonding network. A potential energy scan was performed by rotating around the appropriate bond for each molecule studied in this paper. In this manner, it was possible to show that the amidic group of these model compounds acts as H-bond donor and interacts with two different H-bond acceptors which stabilizes a C₈ pseudocycle, the so called “hydrazinoturn”. This study was addressed theoretically in order to understand the conformation adopted by hydrazino acetamides as model compounds for aza-β³-peptides. We thus investigated the conformational analysis of hydrazinoturns computationally and showed that these systems represent a very stabilizing folding driving force, provided that the neighboring molecular functional groups do not imply other competing hydrogen bonding patterns.     

125 Years of Chemistry in the Mirror of “Angewandte”

This Review investigates the development of Angewandte Chemie since the founding of the journal in 1887 and analyzes how its content reflects the changes in chemical research over these 125 years. Although Angewandte Chemie was originally founded as a journal for applied (“angewandte”)—technical and analytical—chemistry, numerous review articles and abstracts published even in its first 50 years enable the milestones in chemical research in a much broader sense to be traced nicely. With the introduction of the International Edition in 1962, the author base, which had until then been primarily limited to German‐speaking countries, became increasingly international, and the journal experienced impressive growth. Today, with its attractive layout, successful mix of articles, and high impact factor, Angewandte Chemie covers chemical research around the world in its full breadth, with its many achievements and future challenges.