Kinetic energy density for orbital‐free density functional calculations by axiomatic approach

An axiomatic approach is herein used to determine the physically acceptable forms for general D‐dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one‐point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large‐scale orbital free density functional theory calculations.     

Information‐entropic measures in free and confined hydrogen atom

Shannon entropy (S), Rényi entropy (R), Tsallis entropy (T), Fisher information (I), and Onicescu energy (E) have been explored extensively in both free H atom (FHA) and confined H atom (CHA). For a given quantum state, accurate results are presented by employing respective exact analytical wave functions in r space. The p‐space wave functions are generated from respective Fourier transforms—for FHA these can be expressed analytically in terms of Gegenbauer polynomials, whereas in CHA these are computed numerically. Exact mathematical expressions of , are derived for circular states of a FHA. Pilot calculations are done taking order of entropic moments (α, β) as in r and p spaces. A detailed, systematic analysis is performed for both FHA and CHA with respect to state indices n, l, and with confinement radius (r_c) for the latter. In a CHA, at small r_c, kinetic energy increases, whereas decrease with growth of n, signifying greater localization in high‐lying states. At moderate r_c, there exists an interplay between two mutually opposing factors: (i) radial confinement (localization) and (ii) accumulation of radial nodes with growth of n (delocalization). Most of these results are reported here for the first time, revealing many new interesting features. Comparison with literature results, wherever possible, offers excellent agreement.     

Theoretical prediction of the optical rotation of chiral molecules in ordered media: A computational study of (Ra)‐1,3‐dimethylallene, (2R)‐2‐methyloxirane,and (2R)‐N‐methyloxaziridine

A theoretical procedure has been developed and implemented to calculate the optical rotation of chiral molecules in ordered phase via origin‐independent diagonal components , of the optical activity tensor and origin‐independent components , for , of the mixed electric dipole‐electric quadrupole polarizability. Origin independence was achieved by referring these tensors to the principal axis system of the electric dipole dynamic polarizability at the same laser frequency ω. The approach has been applied, allowing for alternative quantum mechanical methods based on different gauges, to estimate near Hartree–Fock values for three chiral molecules, (2R)‐N‐methyloxaziridine C₂NOH₅, (2R)‐2‐methyloxirane (also referred to as propylene oxide) C₃OH₆, and ( )‐1,3‐dimethylallene C₅H₈, at two frequencies. The theoretical predictions can be useful for an attempt at measuring correspondent experimental values in crystal phase. © 2015 Wiley Periodicals, Inc.     

A theoretical study on the stability difference of the borane and carborane C2Bn−2Hn (5 ≤ n ≤ 7) clusters

In order to study the electronic structure and structural stability of borane and carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters, especially the stability difference between the borane and carborane C₂B₃H₅. The frontier orbital energy levels of the borane and carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters are calculated at CCSD(T)/aug‐cc‐pVXZ//B3LYP/def2‐TZVPP level. The results are further analyzed by qualitative frontier orbital method based on the cap–ring interaction. The results reveal that: (1) the larger E_gap(HOMO‐LUMO energy gap) of carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters than borane (5 ≤ n ≤ 7) clusters originates from the more effective cap–ring orbital overlap of carborane C₂B_n?2H_n (5 ≤ n ≤ 7) clusters than that of borane (5 ≤ n ≤ 7) clusters; (2) the smallest E_gap of the borane results from the highest energy level of the ring symmetry‐adapted linear combination orbital of cluster; and (3) the largest E_gap of the carborane C₂B₃H₅ is induced by the most effective cap–ring orbital interaction of C₂B₃H₅ cluster. © 2014 Wiley Periodicals, Inc.     

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.     

Improved description of the orbital relaxation effect by practical use of the self‐energy

The self‐energy shift in the orbital relaxation (OR) term of the polarization propagator complete through the second‐order is presented. In combination with the optimal damping parameter in the OR term, the modified propagator produces the excitation energy of the coupled‐cluster with singles and doubles (CCSD) accuracy. The self‐energy shift requires the floating‐point operation of , where N refers to the magnitude of the molecular size. Because the second‐order polarization propagator requires the floating‐point operation of , the additional computational effort to construct the self‐energy is negligibly small. Numerical results are shown for several molecules including glycine, 2,3,5,6‐tetrafluorobenzene, and naphthalene, and promising agreements with those of CCSD are confirmed within less than 0.2 eV. The basis set dependence is also tested for the water molecule using aug‐cc‐pV NZ (N = D–7), where this newly developed approach mimics the behavior of the CCSD values. The self‐energy shifting for the second‐order response matrix in combination with the use of a dumping parameter is efficiently implemented for calculations of medium‐sized molecular systems, including glycine and naphthalene. The developed approach provides CCSD‐like accuracy at a more affordable computational expense. © 2014 Wiley Periodicals, Inc.     

Prediction of the pH‐rate profile for dimethyl sulfide oxidation by hydrogen peroxide: The role of elusive H3O2+ Ion

Experimental kinetics of sulfide oxidation by hydrogen peroxide presents a pH‐dependent profile. In this article, it was carried out a detailed study of the mechanism and kinetics of dimethyl sulfide (DMS) oxidation by H₂O₂ in neutral, acid, and basic aqueous medium using ab initio calculations. The results point out that DMS oxidation in neutral aqueous medium occurs through its direct reaction with H₂O₂. In acid medium, cluster‐continuum model calculations shows that cluster is the best representation of the very reactive species. In basic medium, there is formation of the species. However, the pathway involving this species has high free energy barrier, making this pathway unfeasible. The theoretical pH‐rate profile is in good agreement with the experimental observations. © 2013 Wiley Periodicals, Inc.     

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.     

Dealing with the shifted and inverted Tietz–Hua oscillator potential using the J‐matrix method

The tridiagonal J‐matrix approach has been used to calculate the low and moderately high‐lying eigenvalues of the rotating shifted Tietz–Hua (RSTH) oscillator potential. The radial Schrödinger equation is solved efficiently by means of the diagonalization of the full Hamiltonian matrix, with the Laguerre or oscillator basis. Ro–vibrational bound state energies for 11 diatomic systems, namely , , , NO, CO, , , , , , and NO⁺, are calculated with high accuracy. Some of the energy states for molecules are reported here for the first time. The results of the last four molecules have been introduced for the first time using the oscillator basis. Higher accuracy is achieved by calculating the energy corresponding to the poles of the S‐matrix in the complex energy plane using the J‐matrix method. Furthermore, the bound states and the resonance energies for the newly proposed inverted Tietz–Hua IRSTH‐potential are calculated for the H₂‐molecule with scaled depth. A detailed analysis of variation of eigenvalues with n, quantum numbers is made. Results are compared with literature data, wherever possible. © 2015 Wiley Periodicals, Inc.     

A theoretical study on cyclacenes: Analytical tight‐binding approach

We present a theoretical study of cyclacene molecules performed at tight‐binding level. The orbital energies and eigenvectors have been analytically computed, and exact expressions for the axial component of the total position spread and polarizability tensors have been obtained. In absence of dimerization, the system has a D_nh symmetry, where n is the number of hexagonal units. The energy bands present no gap at the Fermi level, and to this fact it corresponds a diverging (per‐electron) polarizability for in the direction of the system symmetry axis. The two (degenerate) components of the polarizability on the σ_h symmetry plane, conversely, remain finite for . The total position spread tensor presents a qualitatively different behavior, since all the three components of the position spread per electron remain finite for . The results are analyzed and discussed for both axial and planar components separately as these are affected differently with respect to the increasing system size. Both dipole polarizability and total position spread have been computed using an ab initio approach for the smallest systems, to compare the analytical tight‐binding expressions with a higher‐level theory.     

Theoretical study on the electronic structures and optical properties of blue‐green and blue phosphorescent iridium(III) complexes with tetraphenylimidodiphosphinate ligand

The electronic structures and photophysical properties of five iridium(III) complexes Ir(tfmppy)₂(tpip) (1), Ir(dfppy)₂(tpip) (2), Ir(afCNppy)₂(tpip) (3), Ir(CNpyN₃)₂(tpip) (4), and Ir(2fphpta)₂(tpip) (5) [where tfmppy = 4‐trifluoromethylphenylpyridine; dfppy =4,6‐difluorophenylpyridine; afCNppy = 6‐fluoro‐4‐octyloxy‐5‐cyano‐phenylpyridine; CNpyN₃ = 2‐(4‐cyano‐phenyl)‐[1,2,3]‐triazole; 2fphpta=2‐(2,6‐difluoro‐phenyl‐[1,2,4]‐triazol‐3‐yl)‐pyridine; tpip=tetraphenylimido‐diphosphinate] have been investigated by using density functional theory (DFT) methods and time‐dependent DFT ones, aiming at elucidating the influences of different substituents and cyclometalated ligands on the emission properties and quantum yield. The calculated results revealed that the different substituents in 1 ‐ 3 have a great influence on the energy levels, in particular highest occupied molecular orbital. Meanwhile, we have also get a further insight into the reason for different phosphorescence quantum yields of the studied complexes. The higher quantum yield (Φ) reported for 1 was found to be closely related to both its smaller S₁–T₁ splitting energy ( ) and larger transition electric dipole moment ( ) upon the S₀ → S₁ transition. Complex 5 is expected to be a potential candidate for blue‐emitting material with good organic light‐emitting diodes performances. We propose that the optical properties of this class of materials can be tuned by the modifications of the cyclometalated ligands. © 2013 Wiley Periodicals, Inc.     

Quantum control of electron‐proton symmetry breaking in dissociative ionization of H2 by intense laser pulses

Forward and backward electron/proton ionization/dissociation spectra from one‐dimensional non‐Born‐Oppenheimer H₂ molecule exposed to ultrashort intense laser pulses ( W/cm², λ = 800 nm) have been computed by numerically solving the time‐dependent Schrödinger equation. The resulting above‐threshold ionization and above‐threshold dissociation spectra exhibit the characteristic forward‐backward asymmetry and sensitivity to the carrier‐envelope phase (CEP), particularly for high energies. A general framework for understanding CEP effects in the asymmetry of dissociative ionization of H₂ has been established. It is found that the symmetry breaking of electron‐proton distribution with π periodic modulation occurs for all CEPs except for ( integer) and the largest asymmetry coming from the CEP of . At least one of the electron and proton distributions is asymmetric when measured simultaneously. Inspection of the nuclear and electron wave packet dynamics provides further information about the relative contribution of the gerade and ungerade states of to the dissociation channel and the time delay of electrons in asymmetric ionization. © 2014 Wiley Periodicals, Inc.     

Simulated annealing‐based optimal control over tunneling process through SDWP and Eckart barrier: A momentum basis representation

For a reaction to proceed via tunneling mechanism, it is essential that the reactants will cross the potential barrier (E_P), where its initial energy (E₀) is below the potential barrier E_P. Tunneling probability τ is defined as the probability of having momentum higher than k_m, where . In the momentum basis representation, τ can be directly calculated by integrating from the limit k_m to infinity, where is the wave function in the momentum space. Instead of the continuous basis, if we chose momentum grid space, τ can be expressed as . Our target here is to increase this τ by applying a polychromatic field, so that the reaction rate can be enhanced. By applying Simulated Annealing technique we have designed some polychromatic electric fields, spatially symmetric and asymmetric type, which enhances the tunneling rate in symmetric double well system and Eckart barrier confined in an infinite well.     

Catalytic action of Mn‐superoxide dismutase in scavenging superoxide radical anion by double hydrogen abstraction from dihydrolipoic acid: A theoretical study

The mechanism of scavenging superoxide radical anion ( ) by dihydrolipoic acid (diLA) in absence and presence of the enzyme Manganese‐superoxide dismutase (Mn‐SOD) has been investigated using density functional theory. Mn‐SOD was modelled by a complex of a manganese cation (Mn²⁺) bonded to three similar molecules having a histidine ring each and a water molecule. It has been shown that the scavenging mechanism involves double hydrogen abstraction by from different pairs of neighboring sites of diLA. It has been found that diLA alone cannot scavenge superoxide radical anions efficiently as the barrier energies involved in the reactions are very high. However, in presence of Mn‐SOD, owing to its catalytic action, the corresponding reactions become barrierless due to which superoxide radical anions would be scavenged highly efficiently. H₂O₂ formed from superoxide radical anion due to double hydrogen abstraction from diLA is scavenged by diLA alone barrierlessly without involving Mn‐SOD or any other catalyst.     

(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.     

Electron‐density delocalization in many‐electron atoms confined by penetrable walls: A Hartree–Fock study

The electronic structure of several many‐electron atoms, confined within a penetrable spherical box, was studied using the Hartree–Fock (HF) method, coupling the Roothaan's approach with a new basis set to solve the corresponding one‐electron equations. The resulting HF wave‐function was employed to evaluate the Shannon entropy, , in configuration space. Confinements imposed by impenetrable walls induce decrements on when the confinement radius, R_c, is reduced and the electron‐density is localized. For confinements commanded by penetrable walls, exhibits an entirely different behavior, because when an atom starts to be confined, delivers values less than those observed for the free system, in the same way that the results presented by impenetrable walls. However, from a confinement radius, shows increments, and precisely in these regions, the spatial restrictions spread to the electron density. Thus, from results presented in this work, the Shannon entropy can be used as a tool to measure the electron density delocalization for many‐electron atoms, as the hydrogen atom confined in similar conditions.     

Theoretical study of metal‐free organic dyes based on different configurations for efficient dye‐sensitized solar cells

Considering different solar dyes configuration, four novel metal‐free organic dyes based on phenoxazine as electron donor, thiophene and cyanovinylene linkers as the ‐conjugation bridge and cyanoacrylic acid as electron acceptor were designed to optimize open circuit voltage and short circuit current parameters and theoretically inspected. Density functional theory and time‐dependent density functional theory calculations were used to study frontier molecular orbital energy states of the dyes and their optical absorption spectra. The results indicated that D2‐4 dyes can be suitable candidates as sensitizers for application in dye sensitized solar cells and among these three dyes, D3 showed a broader and more bathochromically shifted absorption band compared to the others. The dye also showed the highest molar extinction coefficient. This work suggests optimizing the configuration of metal‐free organic dyes based on simple D‐ ‐A configuration containing alkyl chain as substitution, starburst conformation, and symmetric double D‐ ‐A chains would produce good photovoltaic properties.     

Energies for cyclic and acyclic aggregations of adamantane and diamantane units sharing vertices,edges, or six‐membered rings

Diamondoids are hydrocarbons having a carbon scaffold comprised from polymer‐like composites of adamantane cages. This article describes computed total energies and “SWB‐tension” energies (often referred to as “strain” energies) for species having n adamantane or diamantane units sharing pairwise: one carbon atom (spiro‐[n]adamantane or spiro‐[n]diamantane); one C? C bond (one‐bond‐sharing‐[n]adamantane or one‐bond‐sharing‐[n]diamantane); or one chair‐shaped hexagon of carbon atoms (1234‐helical‐cata‐[n]diamantanes). Each of the five investigated polymer‐like types is considered either as an acyclic or a cyclic chain of adamantane‐ or diamantane‐unit cages. With increasing n values, SWB‐tension energies for acyclic aggregates are found to increase linearly, while the net SWB‐tension energies of cyclic aggregates often go thru a minimum at a suitable value of . In all five cases, a limiting common energy per unit ( ) is found to be approached by both cyclic and acyclic chains as , as revealed from plots of versus 1/n for acyclic chains and of versus 1/n² for cyclic chains. © 2015 Wiley Periodicals, Inc.     

Carbon–sulfur chains: A high‐resolution infrared and quantum‐chemical study of C3S and SC7S

In the course of a 5 μm high‐resolution infrared study of laser ablation products from carbon–sulfur targets, the ν₁ vibrational mode region of linear C₃S has been studied continuously from 2046 to 2065 cm^?1. Besides the prominent vibrational fundamental, the region was found to feature the , and even hot bands, the latter two of which were observed for the first time. Owing to the high signal‐to‐noise ratio obtained, the ν₁ mode of S could also be observed in natural abundance for the first time at high spectral resolution in the infrared. At 2061 cm^?1, hidden inside the branch of the C₃S ν₁ fundamental mode, a weak new band is observed which exhibits very tight line spacing and stems from a heavy both carbon and sulfur containing carrier. On the basis of high‐level quantum‐chemical calculations of selected carbon–sulfur chains and other carbon‐rich cumulenes, this feature is attributed to the ν₅ vibrational fundamental of linear SC₇S, which stands for the first gas‐phase spectroscopic detection of this long cumulenic chain.