Bending Vibrational Levels in the Electronic Spectra of Small Radicals

The role played by bending vibrations in the spectroscopy of small carbon‐containing radicals is illustrated by the patterns and effects shown by C₃, CCH, and C₃Ar. Because of the large change in the bending frequency between the ¹Σ⁺_g and ¹Π_u states of C₃, the ¹Π_u state provides one of the best known examples of the coupling of electronic and vibrational motion in linear molecules (the Renner–Teller effect). The ²Σ⁺ and ²Π states of CCH provide a classic instance of vibronic coupling between two close‐lying electronic states, which leads very rapidly to a chaotic pattern of mixed‐state vibrational energy levels, which can only be understood by extensive high‐quality ab initio calculations. C₃Ar is an approximately T‐shaped molecule with no less than four large‐amplitude vibrations. Its state provides a beautiful example of what happens to the angular momentum of a Π state of C₃ when the symmetry is lowered by complex formation.     

Anion‐aided Dynamic One‐pot Self‐assembly of Rectangular Metallacycles

The tetracopper(I) complex [{Cu₂(μ‐dppm)₂}₂(μ‐1,4‐O₂CC₆H₄ (CO₂ )₂)](BF₄ )₂ ( 1 (BF₄ )₂) and 1,2‐bis(4‐pyridyl)ethane (bpa) can establish a dynamic equilibrium in CH₂Cl₂ . From the equilibrium mixture containing 1 (BF₄ )₂ and bpa with the molar ratio 1 (BF₄ )₂/bpa of 1:1, a supramolecular compound [{Cu₂(μ‐dppm)₂}₂(μ‐1,4‐C₆H₄ (CO₂ )₂)(μ‐bpa)]₂(BF₄ )₄ ( 2 (BF₄ )₄) was obtained as single crystals. The crystal structure was determined by X‐ray crystallography to reveal presence of one anion inside a cationic rectangular metallacycle { 2 ⊂ BF₄ }³⁺. Both structural evidence and DFT ‐calculated results indicate that the F atoms of the anion exert weak electrostatic attraction with hydrogen atoms of the bound bpa as the framework of the cationic metallacycle. The attractive interactions apparently play an important role in stabilizing some dynamically self‐assembled precursors so as to form the final anion‐included metallacycle. Without the electrostatic help from the anion, the self‐assembly of the empty metallacycle may be hindered by a rather large endothermic free energy. The favorable electrostatic stabilization is present not only for a anion but also for other anions such as , , and even when the flexible bpa is replaced by rigid 4,4′‐bipyridine (bpy). Based on the DFT results, the metallacycle 2 (BF₄ )₄ can be easily prepared in a one‐pot reaction of [Cu(MeCN )₄](BF₄ ) with three ligands.     

General build up of basis and matrix in the diagonalization approach. Determination of Kramers configuration state functions

Algorithms to build the basis and matrix representation to obtain the Kramers configuration space functions (KCSFs) via diagonalization will be formally generalized to an arbitrary number of unpaired (open shell) fermions. Effective build up of the matrix representation will be outlined (including threading and graphical processing unit parallelism) to subsequently obtain the KCSFs via calling external/numerical library routines for diagonalization. The effective build up of the matrix representation relays on a binary tree search algorithm to allow evaluation the action on a given basis vector. The binary tree search avoids the treatment of zero matrix elements which leads to an exponential acceleration. The implementation ( basis creation, matrix representation, and matrix diagonalization) will be done in an all in core and all at once manner, hence the available core memory sets the physical limits in practical applications. Memory limitations, sparsity of the matrix, general case of n fermions in m spinors, and the application of KCSFs will be put into further perspective.     

Spin–orbit effects on magnetically induced current densities in the () clusters

This study reports the spin–orbit effects on the aromaticity of the , , , , , and anionic clusters via the magnetically induced current‐density method. All‐electron density functional theory (DFT) calculations were carried out using the four‐component Dirac‐Coulomb (DC) hamiltonian, including scalar and spin–orbit relativistic effects. The magnetic index of aromaticity was calculated by numerical integration over the current flow between two atoms in the pentagonal ring. These values were compared to the spin‐free values (spin–orbit coupling switched off), in order to assess the spin–orbit effect on aromaticity. It was found that in the heavy anions, and , there is a significant influence of the spin–orbit coupling. © 2018 Wiley Periodicals, Inc.     

Explicitly correlated variational estimates of the energy levels of negative hydrogen ion under spatial confinement

Comprehensive investigations on the structural modifications of negative hydrogen ion within an impenetrable spherical domain has been performed in the framework of Ritz variational method. Electron correlation plays a major role in the formation of H^– ion. The Hylleraas‐type basis set expansion of wave function considered here incorporates the effect of electron correlation in an explicit manner. Energy values of and 1sn states of H^– ion within confined domain have been calculated. Although the singly excited states do not exist for a “free” H^– ion, well converged energy values of such states have been found within a wide range of confinement radius. The thermodynamic pressure felt by the ion inside the sphere is also estimated. The general trend shows successive destabilization of the excited energy levels with increase of pressure. The contribution of angular correlation in the energy values have been estimated. Evolution of and energy levels of H^– ion as quasi‐bound states are being reported.     

(Rg = He ∼ Rn,n = 1–4): In quest of the potential trapping ability of the aromatic ring

A new series of divalent boron‐rare gas cations (Rg = He ∼ Rn, n = 1–4) have been predicted theoretically at the B3LYP, MP2, and CCSD(T) levels to present the structures, stability, charge distributions, bond natures, and aromaticity. The Rg B bond energies are quite large for heavy rare gases and increase with the size of the Rg atom. Because of steric hindrance new Rg atoms introduced to the B₄ ring will weaken the Rg B bond. Thus in the Rg B bond has the largest binding energy 90–100 kcal/mol. p‐ has a slightly shorter Rg B bond length and a larger bond energy than o‐ . NBO and AIM analyses indicate that for the heavy Rg atoms Ar ∼ Rn the B Rg bonds have character of typical covalent bonds. The energy decomposition analysis shows that the σ‐donation from rare gases to the boron ring is the major contribution to the Rg B bonding. Adaptive natural density partitioning and nuclear‐independent chemical shift analyses suggest that both and have obvious aromaticity.     

One‐range Addition Theorems for Complete Sets of Modified Exponential Type Orbitals and Noninteger n Slater Functions in Standard Convention

Using the L ‐generalized Laguerre polynomials L ‐GLPs) and φ ‐generalized exponential type orbitals φ ‐GETOs) introduced by the author in standard convention, the one‐ and two‐center onerange addition theorems are established for the complete sets of Ψ^(α*) ‐modified exponential type orbitals (Ψ^(α*) ‐METOs) and noninteger n χ‐Slater type orbitals (χ‐NISTOs), where p_l* = 2l + 2 ‐ α* and α* is the integer (α* = α, ?∞ < α ≤2) or noninteger (α* ≠ α, ?∞ < α* < 3) self‐frictional quantum number. It should be noted that the origin of the L ‐GLPs, φ ‐GETOs and Ψ^(α*) ‐METOs, therefore, of the one‐range addition theorems presented in this work is the Lorentz damping or self‐frictional field produced by the particle itself.     

The Trifluoromethyl Anion: Evidence for [K(crypt‐222)]+

[K(crypt‐222)]⁺ ( 1 ) and [K(crypt‐222)]⁺ ( 3 ) are isostructural, displaying nearly identical unit cell parameters. The two structures are similar to the extent that the previously reported [K(crypt‐222)]⁺ model can be refined against the new data for [K(crypt‐222)]⁺ , with extra electron density being observed from the fourth fluorine atom of the . In agreement with experimental observations, theoretical calculations suggest that deprotonated [K(crypt‐222)]⁺ is highly unstable even at as low as 195 K. The previously considered 1:1 CHF ₃ clathrate of deprotonated [K(crypt‐222)]⁺ (crystallographically indistinguishable from 1 ) is ruled out on the basis of all available data.     

Full–dimensional quantum molecular dynamics calculations of the rovibrationally mediated X → 2 transition of nitrous oxide

A full dimensional time‐dependent quantum wavepacket approach is used to study the photodissociation dynamics of nitrous oxide for the X → 2 bound–bound transition based on new highly accurate potential energy and transition dipole moment surfaces. The computed 2 absorption spectra at room temperature are characterized by sharp vibrational structures that contribute slightly to the diffuse vibrational structures around the maximum peak at 180 nm of the first ultraviolet absorption band (from the contribution of 2 , 1 , and 2 states) of N₂O. Transitions from different initial rovibrational states reveal that the sharp structures arise mainly from N₂? O bending vibrations, whereas, at higher temperatures, the N₂? O and N? NO stretching vibrations are responsible for enhancing the intensity of the structures. At absorption wavelengths 166 nm and 179 nm, vibrational quantum state distributions of N₂ product fragments decrease monotonically with increasing vibrational quantum number v = 0, 1, 2. At 166 nm, rotational quantum state distributions of N₂ at fixed v = 0 and v = 1 display multimodal profiles with maximum peaks at j = 77 and j = 75, respectively, whereas, the distributions at the 179 nm absorption wavelength display bimodal profiles with maximum peaks at j = 73 and j = 71, respectively. Accordingly, the presence of rotationally hot N₂ from previous experimental and theoretical works in the first band strongly implies a significant influence of the 2 state in determining the final dissociation pathway of N₂ + O. © 2016 Wiley Periodicals, Inc.     

Correlating Boron–Hydrogen Stretching Frequencies with Boron–Hydrogen Bond Lengths in Closoboranes: An Approach Using DFT Calculations

Using harmonic and anharmonic DFT calculations, we have established a general correlation between B–H stretching frequencies and B–H bond lengths valid for the closoboranes (x = 6 – 12), substituted closoboranes B₁₂H_{12 –} (with X = F, Cl, Br and n = 1 – 3 and 9 – 12) and the carboranes and , suggesting that this correlation is also applicable to other similar species. It appears that the average B–H stretching frequency observed around 2500 cm⁻¹ shift by about −100 cm⁻¹ if the average B–H bond length increases by 1 pm. In contrast to , the B–H bond in closoboranes is practically covalent and the correlation evidenced between its stretching frequency and its length proves to be similar to the one observed for the C–H bond.     

Structure,stability, and nature of bonding in carbon monoxide bound complexes (E = group 14 element; X = H,F, Cl,Br, I)

A density functional theory study is performed to predict the structures and stability of carbon monoxide (CO) bound (E = C, Si, Ge, Sn, Pb; X = H, F, Cl, Br, I) complexes. The possibility of bonding through both C‐ and O‐sides of CO is considered. Thermochemical analysis reveals that all the dissociation processes producing CO and are endothermic in nature whereas most of the dissociation reactions are endergonic in nature at room temperature. The nature of bonding in E? C/O bonds is analyzed via Wiberg bond index, natural population analysis, electron density, and energy decomposition analyses in conjunction with natural orbitals for chemical valence scheme. In comparison to C? O stretching frequency ( ) in free CO, while a red shift is noted in O‐side binding, the C‐side binding results in a blue shift in . The relative change in values in CO bound complexes on changing either E or X is scrutinized and possible explanation is provided in terms of polarization in the σ‐ and π‐orbitals and the relative strength of C→E or O→E σ‐donation and E→C or E→O π‐back‐donation. © 2016 Wiley Periodicals, Inc.     

Nuclear quantum effects induce metallization of dense solid molecular hydrogen

We present an accurate computational study of the electronic structure and lattice dynamics of solid molecular hydrogen at high pressure. The band‐gap energies of the , Pc, and structures at pressures of 250, 300, and 350 GPa are calculated using the diffusion quantum Monte Carlo (DMC) method. The atomic configurations are obtained from ab initio path‐integral molecular dynamics (PIMD) simulations at 300 K and 300 GPa to investigate the impact of zero‐point energy and temperature‐induced motion of the protons including anharmonic effects. We find that finite temperature and nuclear quantum effects reduce the band‐gaps substantially, leading to metallization of the and Pc phases via band overlap; the effect on the band‐gap of the structure is less pronounced. Our combined DMC‐PIMD simulations predict that there are no excitonic or quasiparticle energy gaps for the and Pc phases at 300 GPa and 300 K. Our results also indicate a strong correlation between the band‐gap energy and vibron modes. This strong coupling induces a band‐gap reduction of more than 2.46 eV in high‐pressure solid molecular hydrogen. Comparing our DMC‐PIMD with experimental results available, we conclude that none of the structures proposed is a good candidate for phases III and IV of solid hydrogen. © 2017 Wiley Periodicals, Inc.     

Einstein A Coefficients,Oscillator Strengths,and Absolute Band Strengths for the First Negative System,and Franck-Condon Factors for the Second Negative System of

The Franck-Condon factors and r centroids for the first negative and the second negative band systems of the molecule, based on the Rydberg-Klein-Rees potential energy curves, have been computed. The variation of the electronic transition moment with the internuclear separation has been studied for the first negative bands and the Einstein A coefficients, the oscillator strengths, and the absolute band strengths for this system have been calculated by adopting the recent experimental data on the lifetimes of the various levels of the excited B state. On a calculé pour la molécule les facteurs de Franck-Condon et les r centroïds pour les deux premiers systèmes de bandes négatives avec des courbes de potential de Rydberg-Klein-Rees. On a étudié la variation du moment de transition éléctronique avec la séparation internucléaire pour les premières bandes négatives. Les constantes A d'Einstein, les forces d'oscillateur et les intensités absolues des bandes ont été calculé des données expérimentales récentes sur les durées de vie des niveaux différents de l'état excité B . Die Franck-Condon-Faktoren und die r-Zentroide der zwei ersten negativen Banden-systeme des -Moleküls, wurden mit den Rydberg-Klein-kees Potentialkurven berechnet. Die Variation des elektronischen Übergangsmoment mit dem Kernabstand würde für die ersten negativen Bänder studiert. Die Einsteinschen A-Koeffizienten, die Oszillatorstärken and die absoluten Bandenstärken wurden mit die neuen experimentellen Tatsachen über die Lebensdauern der verschiedenen Niveaus des angeregten B Zustands berechnet.     

Accurate,robust, and reliable calculations of Poisson–Boltzmann binding energies

Poisson–Boltzmann (PB) model is one of the most popular implicit solvent models in biophysical modeling and computation. The ability of providing accurate and reliable PB estimation of electrostatic solvation free energy, , and binding free energy, , is important to computational biophysics and biochemistry. In this work, we investigate the grid dependence of our PB solver (MIBPB) with solvent excluded surfaces for estimating both electrostatic solvation free energies and electrostatic binding free energies. It is found that the relative absolute error of obtained at the grid spacing of 1.0 Å compared to at 0.2 Å averaged over 153 molecules is less than 0.2%. Our results indicate that the use of grid spacing 0.6 Å ensures accuracy and reliability in calculation. In fact, the grid spacing of 1.1 Å appears to deliver adequate accuracy for high throughput screening. © 2017 Wiley Periodicals, Inc.     

Toward a Better Determination of Infrared Molar Absorptivities and Dimer Formation Constants in Self‐association Through Hydrogen Bonding: 3‐Ethyl‐2‐methyl‐3‐pentanol in Tetrachloroethylene as an Example

The monomer–dimer self‐association of the dilute 3‐ethyl‐2‐methyl‐3‐pentanol in tetrachloroethylene in the very dilute state was studied by infrared spectroscopy at several temperatures. The solute was deliberately chosen so that higher oligomers were suppressed by the steric hindrance arising from bulky groups on both sides of hydroxyl group. Two linear utility equations were derived to treat, respectively, the integrated absorbance of the monomer band, A _m, and of the dimer band, A _d, as functions of the initially prepared solute concentration, [B ]₀. The respective molar absorptivities were obtained by fitting these equations to the data. Unlike previous methods, the dimerization constant (K ) can be obtained from either A _m or A _d. Any discrepancy between these two values of K serves as a measure of the quality of the data. The values of K at different temperatures were employed to calculate the standard enthalpy and entropy of dimerization by using a van't Hoff plot. The dimer is predominantly in the cyclic form where both hydroxyl protons are hydrogen‐bonded. This is inferred from the following observations: (1) the spectrum displays only two bands between 3300 and 3750 cm⁻¹; (2) the constancy of as a function of [B ]₀ ; and (3) the linearity of both plots [B ]₀/A _m vs. A _m , and [B ]₀/A _d vs. .     

Quantum chemical prediction for complex organic molecules

Numerous types of quantum chemical calculations and protocols have been successfully applied to computing of small, uncomplicated organic molecules. Here, we argue for the need to shift attention to more challenging molecules that are marked by an interplay of complicating factors such as conformational, tautomeric, steric, and other effects. The challenge is not in choosing the right quantum chemical method and solvation model but in combining the existing methods to simultaneously and accurately describe the breadth of chemical and physical phenomena that give rise to the experimentally observed . The complexity of the phenomena that must be considered begs for the need for a greater automation of prediction workflows. We review our experience with these challenges and outline paths for future progress in the direction of tackling prediction of complex organic molecules.     

Geometric and electronic structures of silicon fluorides (N = 4 – 6) and potential energy surfaces for dissociation reactions → SiF4 + F– and → + F–

The geometric and electronic structures of a series of silicon fluorides (n = 4 ? 6) were computationally studied with the aid of density functional theory (DFT) method with B3LYP and M06‐2X functionals and coupled cluster (CCSD and CCSD(T)) methods with 6‐311++G(d,p) basis set. The nature of the Si‐F bonds in these compounds was analyzed in the framework of the natural bond orbital theory and natural resonance theory. Energy characteristics (heats of reactions and energy barriers) of the dissociation reactions → SiF₄ + F^– and → + F^– were calculated using the DFT and CCSD methods. The potential energy surface of elimination of a fluoride anion from has a specific topology with valley‐ridge inflection points corresponding to bifurcations of the minimal energy reaction path. © 2016 Wiley Periodicals, Inc.     

Theoretical investigation of the weak interactions of rare gas atoms with silver clusters by resonance Raman spectroscopy modeling

The interactions of rare gas atoms (Rg = Ar, Kr, and Xe) with small neutral and cationic silver clusters have been investigated by density functional methods and the effect of these weak interactions on the resonance Raman spectra of the complexes has been evaluated. The resonance Raman technique that depends on the properties of ground and excited state, seems deeply sensitive to the weak rare gas–metal cluster interactions, and the use of inert gases has been proven to be an excellent approach to recognize the ability of this technique to detect extremely weak interactions. In this work, for , and complexes the IR, normal and resonance Raman spectra have been calculated and the effect of rare gas–cluster stretching vibration ( ) on the pattern and the relative intensities of different spectra have been investigated. The resonance Raman spectra for the weakly interacted complexes (with the interaction energies less than ?2.0 kcal/mol) exhibit the vibration with the detectable intensity that its intensity increases by going from Ag₆–Ar to Ag₆–Xe complex. Moreover, the resonance Raman spectra (based on the excited state gradient approximation) for high intensity nearly degenerate excited states, proved the effect of accumulation of the excited state charge density on the relative intensity of vibration.     

Universality in Branching Frequencies and Molecular Dimensions during Hyperbranched Polymer Formation: Step Polymerization of AB2 Type Monomer with Equal Reactivity

Hyperbranched polymer formation during step polymerization of AB₂ type monomer with equal reactivity of two B's is investigated theoretically, focusing the attention to the degree of branching (DB) and the mean square radius of gyration for the unperturbed chains, . It is found that the DB‐value at large degree of polymerization (P) limit, = 0.5 is unchanged during the whole course of polymerization. The average value of having the same P is invariant throughout the polymerization. The universal curve between and P agrees perfectly with that for the self‐condensing vinyl polymerization (SCVP), another method to synthesize hyperbranched polymers, when the reactivity ratio for SCVP, r_SCVP, is 2.589 that gives = 0.5. The power law, is found for large values of P.