An ab initio method for approximation of the frozen molecular fragment

An ab initio method for calculation on many-electron molecular systems with the approximation of the inactive part of a molecule by frozen molecular fragment is presented. In the following method the SCF calculations are performed in two series. First the molecular orbitals resulting from the first SCF calculation (modest basis set) are localized. In the second SCF run, the basis set is extended for the active part of the molecule, while molecular orbitals of the inactive part, selected from the localized set, are kept frozen. The results are in good agreement with the extended basis set calculation.     

A new algorithm for inactive orbital optimization in valence bond theory

This paper presents an efficient algorithm for energy gradients in valence bond self-consistent field (VBSCF) method with non-orthogonal orbitals. The frozen core approximation method is extended to the case of non-orthogonal orbitals. The expressions for the total energy and its gradients are presented by introducing auxiliary orbitals, where inactive orbitals are orthogonal, while active orbitals are non-orthogonal themselves but orthogonal to inactive orbitals. It is shown that our new algorithm has a low scaling of (N _a + 1)m ⁴, where N _a and m are the numbers of the active orbitals and basis functions, respectively, and is more efficient than the existing VBSCF algorithms.     

The Structure–Property Correlations in the Isomerism of Au21(SR)15 Nanoclusters by Density Functional Theory Study

Isomerism of atomically precise noble metal nanoclusters provides an excellent platform to investigate the structure–property correlations of metal nanomaterials. In this study, we performed density functional theory (DFT) and time‐dependent (TD‐DFT) calculations on two Au₂₁(SR)₁₅ nanoclusters, one with a hexagonal closed packed core (denoted as Au₂₁ ^hcp ), and the other one with a face‐centered cubic core (denoted as Au₂₁ ^fcc ). The structural and electronic analysis on the typical Au–Au and Au–S bond distances, bond orders, composition of the frontier orbitals and the origin of optical absorptions shed light on the inherent correlations between these two clusters.     

The coupled cluster singles, doubles, and a hybrid treatment of connected triples based on the split virtual orbitals

We have proposed a simple strategy for splitting the virtual orbitals with a large basis set into two subgroups (active and inactive) by taking a smaller basis set as an auxiliary basis set. With the split virtual orbitals (SVOs), triple or higher excitations can be partitioned into active and inactive subgroups (according to the number of active virtual orbitals involved), which can be treated with different electron correlation methods. In this work, the coupled cluster (CC) singles, doubles, and a hybrid treatment of connected triples based on the SVO [denoted as SVO-CCSD(T)-h], has been implemented. The present approach has been applied to study the bond breaking potential energy surfaces in three molecules (HF, F(2), and N(2)), and the equilibrium properties in a number of open-shell diatomic molecules. For all systems under study, the SVO-CCSD(T)-h method based on the unrestricted Hartree-Fock (UHF) reference is an excellent approximation to the corresponding CCSDT (CC singles, doubles, and triples), and much better than the UHF-based CCSD(T) (CC singles, doubles, and perturbative triples). On the other hand, the SVO-CCSD(T)-h method based on the restricted HF (RHF) reference can also provide considerable improvement over the RHF-based CCSD(T).     

A relationship between the sizes and energies of localized molecular orbitals. I. A study of selected first-row hydrides

Ab initio calculations have been performed on selected first-row hydrides with a large Gaussian basis set. Energy localized molecular orbitals (LMO 'S ) were computed and analysed in terms of their sizes and shapes. The total molecular electronic energy was partitioned into components which may be associated with an MO , and the relationship between the sizes and energies of such orbitals was examined. It was found that a simple energy–size relationship exists for core LMO 'S but only approximately holds for bond LMO 'S .     

价键方法中的非活性轨道优化新算法

本文通过引进一组正交的辅助非活性轨道和与它正交的辅助活性轨道,将价键理论方法中的冻核近似推广到轨道非正交的情形,得到了体系能量及其对非活性轨道的梯度解析表达式,简化了价键自洽场方法中非正交轨道能量梯度的计算．该方法的标度为（Na＋1）m^4,其中Na和m分别是活性轨道和基函数的个数．分析表明,与现有的其他算法相比较,该方法具有更低的计算标度,因而计算效率更高．     

Localized molecular orbitals and chemical binding in five-membered heterocycles. II

The localized molecular orbitals (LMOs) of thiophene, furan, and pyrrole are derived from ab initio 4-31G wavefunctions using Boys' criteria for localization. From the transferability point of view, these LMOs are classified as (i) completely different and nontransferable LMOs (these are the lone-pair orbitals on O and N on one hand and those on S on the other hand), (ii) chemically similar lone pairs and inner shells on O and N (of furan and pyrrole, respectively), and (iii) chemically equivalent C? C, C?C, and C? H LMOs in the three heterocycles. The sp³ hybridization of the L core of sulfur, its appreciable polarization, and considerable involvement in bonding in the C? S bond region have been discussed. The present investigation indicates the limitation of the application of semiempirical MO methods to molecules that contain second-row atoms due to both the appreciable core—valence and π-σ interactions involving such atoms. Qualitative investigation of aromaticity and reactivity of the studied heterocycles agrees satisfactorily with experimental observations and shows that conclusions drawn based solely on static factor considerations (charge distribution in the noninteracting molecules) might very well be misleading and such factors determine the ease rather than the final orientation of the substituent.     

Electronic structure and magnetism at the active site in ferredoxin: Ab initio approach to (Fe2S2)2+ complex with the 1st peptide shell

We have studied the iron–sulfur cluster systems which model an active site of ferredoxin proteins by using the first-principles electronic structure calculation. The modeled molecule is a complex between the (Fe₂S₂)²⁺ core and the amino acid residues which surround the core. The electronic structure of oxidized state for the molecules is presented. The antiferromagentic arrangement for Fe atomic magnetizations was obtained as the ground state. The spin polarized state of the half-filled Fe 3d orbitals is consistent with the formal valence of Fe³⁺. The induced spin density on the cysteine S atoms was found to be parallel to the direction of magnetization on the nearest Fe atom. The hybridized states consisting of N 2p and C 2p orbitals at the side chain of Arg residue appeared just above the highest occupied molecular orbital level for the free standing peptide.     

Maximal orbital analysis of molecular wavefunctions

We describe a new way to decompose one-electron orbitals of a molecule into atom-centered or fragment-centered orbitals by an approach that we call “maximal orbital analysis” (MOA). The MOA analysis is based on the corresponding orbital transformation (COT) that has the unique mathematical property of maximizing any sub-trace of the overlap matrix, in Hilbert metric sense, between two sets of nonorthogonal orbitals. Here, one set comprises the molecule orbitals (Hartree–Fock, Kohn–Sham, complete-active-space, or any set of orthonormal molecular orbitals), the other set comprises the basis functions associated with an atom or a group of atoms. We show in prototypical molecular systems such as a water dimer, metal carbonyl complexes, and a mixed-valent transition metal complex, that the MOA orbitals capture very well key aspects of wavefunctions and the ensuing chemical concepts that govern electronic interactions in molecules. © 2019 Wiley Periodicals, Inc.     

2‐(Benzoylsulfanyl)acetic acid and 2,5‐dioxopyrrolidin‐1‐yl 2‐(benzoylsulfanyl)acetate by powder X‐ray diffraction studies

The structures of the title compounds, C₉H₈O₃S, (I), and C₁₃H₁₁NO₅S, (II), were determined by X‐ray powder diffraction. Both were solved using the direct‐space parallel tempering algorithm and refined using the Rietveld method. In (I), the C—S—C bond angle is slightly smaller than normal, indicating more p character in the bonding orbitals of the S atom. The carboxylic acid group joins across an inversion centre to form a dimer. The crystal packing includes a weak C—H...O hydrogen bond between an aromatic C—H group and a carboxylic acid O atom to form a two‐dimensional network parallel to (10). The C—S—C bond angle in (II) is larger than its counterpart in (I), indicating that the S atom of (II) has less p character in its bonding orbitals than that of (I), according to Bent's rule. The crystal structure of (II) includes weak C—H...O hydrogen bonds between the H atoms of the methylene groups and carbonyl O atoms, forming a three‐dimensional network.     

Nonconventional C–H···Cu Interaction Between Copper Cun Clusters (n = 3–20) and Aromatic Compounds

The present study examines bonding patterns between copper Cu_n clusters (n?=?3–20) and aromatic compounds (benzene, phenol, and benzaldehyde) using a density-functional theory (DFT) approach. Hirshfeld population, natural bond orbital (NBO), molecular orbitals, and quantum theory of atoms in molecules (QTAIM) analyses suggested the formation of two types of interactions Cu–arene and C–H···Cu, in the complexation of copper clusters by an aromatic compound.

     

Silver Coated Platinum Core–Shell Nanostructures on Etched Si Nanowires: Atomic Layer Deposition (ALD) Processing and Application in SERS

A new method to prepare plasmonically active noble metal nanostructures on large surface area silicon nanowires (SiNWs) mediated by atomic layer deposition (ALD) technology has successfully been demonstrated for applications of surface‐enhanced Raman spectroscopy (SERS)‐based sensing. As host material for the plasmonically active nanostructures we use dense single‐crystalline SiNWs with diameters of less than 100 nm as obtained by a wet chemical etching method based on silver nitrate and hydrofluoric acid solutions. The SERS active metal nanoparticles/islands are made from silver (Ag) shells as deposited by autometallography on the core nanoislands made from platinum (Pt) that can easily be deposited by ALD in the form of nanoislands covering the SiNW surfaces in a controlled way. The density of the plasmonically inactive Pt islands as well as the thickness of noble metal Ag shell are two key factors determining the magnitude of the SERS signal enhancement and sensitivity of detection. The optimized Ag coated Pt islands on SiNWs exhibit great potential for ultrasensitive molecular sensing in terms of high SERS signal enhancement ability, good stability and reproducibility. The plasmonic activity of the core‐shell Pt//Ag system that will be experimentally realized in this paper as an example was demonstrated in numerical finite element simulations as well as experimentally in Raman measurements of SERS activity of a highly diluted model dye molecule. The morphology and structure of the core‐shell Pt//Ag nanoparticles on SiNW surfaces were investigated by scanning‐ and transmission electron microscopy. Optimized core–shell nanoparticle geometries for maximum Raman signal enhancement is discussed essentially based on the finite element modeling.     

Molecular orbital propagation to accelerate self-consistent-field convergence in an ab initio molecular dynamics simulation

Based on the idea of molecular orbital (MO) propagation, we propose a novel effective method for predicting initial guesses for the self-consistent-field calculations in direct ab initio molecular dynamics (AIMD) simulations. This method, called LIMO, adopts the Lagrange interpolation (LI) polynomial technique and predicts initial MO coefficients at the next AIMD step by using several previous results. Taking into account the crossing and/or mixing of MOs leads to orbital invariant formulas for the LIMO method. We also propose a simple method for determining the optimal degree of the LI polynomial, which corresponds to the number of previous steps. Numerical tests confirm that this proposed method is both effective and feasible.     

A combined freeze-and-cut strategy for the description of large molecular systems using a localized orbitals approach

A technique to reduce the computational effort in calculating ab initio energies using a localized orbitals approach is presented. By exploiting freeze strategy at the self-consistent field (SCF) level and a cut of the unneeded atomic orbitals, it is possible to perform a localized complete active space (CAS-SCF) calculation on a reduced system. This will open the possibility to perform ab initio treatments on very large molecular systems, provided that the chemically important phenomena happen in a localized zone of the molecule. Two test cases are discussed, to illustrate the performance of the method: the cis-trans interconversion curves for the (7Z)-13 ammoniotridec-7-enoate, which demonstrates the ability of the method to reproduce the interactions between charged groups; and the cisoid-transoid energy barrier for the aldehydic group in the C13 polyenal molecule.     

Orbital relaxation in the Rydberg series of the lithium atom. An excited state SCF calculation

Self-consistent-field (SCF ) calculations for a series of Rydberg states (1s²ns)²S of the Li atom are performed using the generalized Brillouin theorem (GBT) method. The calculated energy is a proper upper bound to the excited state energy. The SCF term values of the Rydberg states are almost the same as those of the frozen-core approximation ones. The orbital behavior shows that the core is slightly expanded by the penetration of the Rydberg orbitals, and the higher Rydberg orbitals can be very well represented by the modified hydrogen-like orbitals.     

2‐{[(3‐Fluorophenyl)amino]methylidene}‐3‐oxobutanenitrile and 5‐{[(3‐fluorophenyl)amino]methylidene}‐2,2‐dimethyl‐1,3‐dioxane‐4,6‐dione: X‐ray and DFT studies

In the crystal structures of the title compounds, C₁₁H₉FN₂O, (I), and C₁₃H₁₂FNO₄, (II), the molecules are joined pairwise via different hydrogen bonds and the constituent pairs are crosslinked by weak C—H...O hydrogen bonds. The basic structural motif in (I), which is partially disordered, comprises pairs of molecules arranged in an antiparallel fashion which enables C—H...N[triple‐bond]C interactions. The pairs of molecules are crosslinked by two weak C—H...O hydrogen bonds. The constituent pair in (II) is formed by intramolecular bifurcated C—H...O/O′ and combined inter‐ and intramolecular N—H...O hydrogen bonds. In both structures, F atoms form weak C—F...H—C interactions with the H atoms of the two neighbouring methyl groups, the H...F separations being 2.59/2.80 and 2.63/2.71 Å in (I) and (II), respectively. The bond orders in the molecules, estimated using the natural bond orbitals (NBO) formalism, correlate with the changes in bond lengths. Deviations from the ideal molecular geometry are explained by the concept of non‐equivalent hybrid orbitals. The existence of possible conformers of (I) and (II) is analysed by molecular calculations at the B3LYP/6–31+G** level of theory.