On low‐lying excited states of extended nanographenes

Low‐lying excited states of planarly extended nanographenes are investigated using the long‐range corrected (LC) density functional theory (DFT) and the spin‐flip (SF) time‐dependent density functional theory (TDDFT) by exploring the long‐range exchange and double‐excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long‐range exchange interaction significantly improves the C C bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long‐range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long‐range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long‐range exchange effects, the SF‐TDDFT calculations show that the double‐excitation correlation effects are negligible in the low‐lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long‐range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP–EA values. © 2017 Wiley Periodicals, Inc.     

Through‐Space Conjugated Molecular Wire Comprising Three π‐Electron Systems

A [2.2]paracyclophane‐based through‐space conjugated oligomer comprising three π‐electron systems was designed and synthesized. The arrangement of three π‐conjugated systems in an appropriate order according to the energy band gap resulted in efficient unidirectional photoexcited energy transfer by the Förster mechanism. The energy transfer efficiency and rate constants were estimated to be >0.999 and >10¹² s^?1, respectively. The key point for the efficient energy transfer is the orientation of the transition dipole moments. The time‐dependent density functional theory (TD‐DFT) studies revealed the transition dipole moments of each stacked π‐electron system; each dipole moment was located on the long axis of each stacked π‐electron system. This alignment of the dipole moments is favorable for fluorescence resonance energy transfer (FRET).     

限制性自洽场开壳层CNDO/2方法

本文采用限制性自洽场CNDO/2方案,在IBM-PC/XT微机上实现了RHF的CNDO/2计算程序。计算了若干开壳层的小分子和含过渡金属的配合物, 得到体系总能量、电荷、键序、结合能, 与UHF的CNDO/2方法计算结果完全符合, 并且图象清晰·RHF的CNDO/2的方法的实现为半经验方法计算开壳层体系电子光谱跃迁强度, 磁超精细结构常数以及酉群的组态相互作用提供了一个好的波函数。     

Relationship between orbital energy gaps and excitation energies for long‐chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.     

A Valence Bond Study of the Low‐Lying States of the NF Molecule

The electronic structures of the three lowest‐lying states of NF are investigated by means of modern valence bond (VB) methods such as the VB self‐consistent field (VBSCF), breathing orbital VB (BOVB), and VB configuration interaction (VBCI) methods. The wave functions for the three states are expressed in terms of 9–12 VB structures, which can be further condensed into three or four classical Lewis structures, whose weights are quantitatively estimated. Despite the compactness of the wave functions, the BOVB and VBCI methods reproduce the spectroscopic properties and dipole moments of the three states well, in good agreement with previous computational studies and experimental values. By analogy to the isoelectronic O₂ molecule, the ground state ³Σ^? possesses both a σ bond and 3‐electron π bonds. However, here the polar σ bond contributes the most to the overall bonding. It is augmented by a fractional (19 %) contribution of three‐electron π bonding that arises from π charge transfer from fluorine to nitrogen. In the singlet ¹Δ and ¹Σ⁺ excited states the π‐bonding component is classically covalent, and it contributes 28 % and 37 % to the overall bonding picture for the two states, respectively. The resonance energies are calculated and reveal that π bonding contributes at least 24, 35 and 42 kcal mol^?1 to the total bonding energies of the ³Σ^?, ¹Δ and ¹Σ⁺ states, respectively. Some unusual properties of the NF molecule, like the equilibrium distance shortening and bonding energy increasing upon excitation, the counterintuitive values of the dipole moments and the reversal of the dipole moments as the bond is stretched, are interpreted in the light of the simple valence bond picture. The overall polarity of the molecule is very small in the ground state, and is opposite to the relative electronegativity of N vs F in the singlet excited states. The values of the dipole moments in the three states are quantitatively accounted for by the calculated weights of the VB structures.     

Development of spin‐dependent relativistic open‐shell Hartree–Fock theory with time‐reversal symmetry (II): The restricted open‐shell approach

An open‐shell Hartree–Fock (HF) theory for spin‐dependent two‐component relativistic calculations, termed the Kramers‐restricted open‐shell HF (KROHF) method, is developed. The present KROHF method is defined as a relativistic analogue of ROHF using time‐reversal symmetry and quaternion algebra, based on the Kramers‐unrestricted HF (KUHF) theory reported in our previous study (Int. J. Quantum Chem., doi: 10.1002/qua.25356 ). As seen in the nonrelativistic ROHF theory, the ambiguity of the KROHF Fock operator gives physically meaningless spinor energies. To avoid this problem, the canonical parametrization of KROHF to satisfy Koopmans' theorem is also discussed based on the procedure proposed by Plakhutin et al. (J. Chem. Phys. 2006 , 125, 204110). Numerical assessments confirmed that KROHF using Plakhutin's canonicalization procedure correctly gives physical spinor energies within the frozen‐orbital approximation under spin–orbit interactions.     

An open‐source framework for analyzing N‐electron dynamics. II. Hybrid density functional theory/configuration interaction methodology

In this contribution, we extend our framework for analyzing and visualizing correlated many‐electron dynamics to non‐variational, highly scalable electronic structure method. Specifically, an explicitly time‐dependent electronic wave packet is written as a linear combination of N‐electron wave functions at the configuration interaction singles (CIS) level, which are obtained from a reference time‐dependent density functional theory (TDDFT) calculation. The procedure is implemented in the open‐source Python program det CI@ORBKIT, which extends the capabilities of our recently published post‐processing toolbox (Hermann et al., J. Comput. Chem. 2016, 37, 1511). From the output of standard quantum chemistry packages using atom‐centered Gaussian‐type basis functions, the framework exploits the multideterminental structure of the hybrid TDDFT/CIS wave packet to compute fundamental one‐electron quantities such as difference electronic densities, transient electronic flux densities, and transition dipole moments. The hybrid scheme is benchmarked against wave function data for the laser‐driven state selective excitation in LiH. It is shown that all features of the electron dynamics are in good quantitative agreement with the higher‐level method provided a judicious choice of functional is made. Broadband excitation of a medium‐sized organic chromophore further demonstrates the scalability of the method. In addition, the time‐dependent flux densities unravel the mechanistic details of the simulated charge migration process at a glance. © 2017 Wiley Periodicals, Inc.     

Electronegativity Scaled as a Average Attracting Energy of Valence‐Shell Electrons in a Ground‐State Free Atom

The total capability of an atom attracting valence electrons can be measured by the sum of ionization energies of valence electron in a ground‐state free atom plus its electron affinity called Total Attracting Energy, TAE = Σn_iE_i + EA, where, E_i is the ionization energy of the ith valence‐shell electron in a ground‐state free atom, n_i is the number of valence‐shell electron bearing energy E_i, and EA is the electron affinity. And the electronegativity χ_CL is proportional to the average of TAE, AAE = TAE_av, divided by Σn_i, the number of atomic valence‐shell electrons. χ_CL = 0.1813 TAE_av = 0.1813 AAE = 0.1813 TAE/Σn_i, = 0.1813 (Σn_iE_I + EA)/Σn_i. Further, the atomic valence orbital electronegativity can be also obtained from the TAE value of an atom. Some discussions were made on several special aspects such as scale of rare gases, comparisons with Pauling's and Allen's scales, etc.     

Mass-spectrometric and quantum-chemical investigation of thermochemical characteristics of chlorine oxides

An electron impact technique has been used for the direct determination of the ionization potential (IP) of the ClO₃ radical and the electron affinity (EA) of the ClO₃ and ClO₄ radicals. By means of quantum-chemical calculations taking into account configuration interaction within the framework of the third-order perturbation theory of Miller and Plesset, it has been shown that, for this class of compounds, upon ionization, there are no significant excess energies related to processes of isomerization and electronic excitation. The theoretical and experimental values of the IP and EA are in agreement within 0.5 eV.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2278–2282, October, 1989.     

Spectroscopic constants of SiH2, GeH2, SnH2, and their cations and anions from density functional computations

Local (LSD ) and nonlocal (NLSD ) spin density calculations using different exchangecorrelation functionals have been performed to determine equilibrium geometries, harmonic vibrational frequencies (ωe), ionization potentials (IP ), electron affinities (EA ), dipole moments (μ), and singlet-triplet energy gaps (Δ E_ST) of SiH₂, GeH₂, and SnH₂. Geometrical structures as well as vibrational frequencies are in agreement with the available experimental data and compare favorably with the most sophisticated postHartree-Fock computations performed until now. Both computed IPS (9.15 and 9.25 eV for SiH₂ and GeH₂, respectively) and EA of SiH₂ (1.17 eV) compare favorably with experimental data (9.17, 9.21, and 1.2 eV). Accurate values are obtained also for singlet-triplet energy gaps. We report for the first time the electron affinities of all neutral systems and the spectroscopic constants of the cations and anions. © 1995 John Wiley & Sons, Inc.     

The Nature of Chemical Bonds from PNOF5 Calculations

Natural orbital functional theory (NOFT) is used for the first time in the analysis of different types of chemical bonds. Concretely, the Piris natural orbital functional PNOF5 is used. It provides a localization scheme that yields an orbital picture which agrees very well with the empirical valence shell electron pair repulsion theory (VSEPR) and Bent’s rule, as well as with other theoretical pictures provided by valence bond (VB) or linear combination of atomic orbitals–molecular orbital (LCAO‐MO) methods. In this context, PNOF5 provides a novel tool for chemical bond analysis. In this work, PNOF5 is applied to selected molecules that have ionic, polar covalent, covalent, multiple (σ and π), 3c–2e, and 3c–4e bonds.     

Calculation of vertical ionization potentials with the Piris natural orbital functional

The Piris natural orbital functional (PNOF) based on a new approach for the two-electron cummulant has been used to predict vertical ionization potentials of 15 molecules. The ionization energies have been calculated using the extended Koopmans' theorem. The calculated PNOF values are in good agreement with the corresponding experimental data.     

A theoretical study on three conformational structures of 2,6‐distyrylpyridine

Ab initio methods at the levels HF/cc‐pVDZ, HF/6‐31G(d,p), MP2/cc‐pVDZ, and MP2/6‐31G(d,p), as well as methods based on density functional theory (DFT) employing the hybrid functional B3LYP with the basis sets cc‐pVDZ and 6‐31G(d,p), have been applied to study the conformers of 2,6‐distyrylpyridine. Bond distances, bond angles, and dihedral angles have been calculated at the B3LYP level. The calculated values were in good agreement with those measured by X‐ray diffraction analysis of 2,6‐distyrylpyridine. The values calculated using the Hartree‐Fock method and second‐order perturbation theory (MP2) were inconsistent. The optimized lowest‐energy geometries were calculated from the reported X‐ray structural data by the B3LYP/cc‐pVDZ method. Three conformations, A, B, and C, were proposed for 2,6‐distyrylpyridine. Calculations at the three levels of theory indicated that conformation A was the most stable structure, with conformations C and B being higher in energy by 1.10 and 2.57 kcal/mol, respectively, using the same method and basis function. The same trend in the relative energies of the three possible conformations was observed at the two levels of theory and with the different basis sets employed. The reported X‐ray data were utilized to optimize total molecular energy of conformation A at the different calculation levels. The bond lengths, bond angles, and dihedral angles were then obtained from the optimized geometries by ab initio methods and by applying DFT using the two basis functions cc‐pVDZ and 6‐31G(d,p). The values were analyzed and compared. The calculated total energies, the relative energies of the molecular orbitals, the gap between them, and the dipole moment for each conformational structure proposed for 2,6‐distyrylpyridine are also reported. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

A theoretical description of charge reorganization energies in molecular organic P‐type semiconductors

Charge transport properties of materials composed of small organic molecules are important for numerous optoelectronic applications. A material's ability to transport charges is considerably influenced by the charge reorganization energies of the composing molecules. Hence, predictions about charge‐transport properties of organic materials deserve reliable statements about these charge reorganization energies. However, using density functional theory which is mostly used for the predictions, the computed reorganization energies depend strongly on the chosen functional. To gain insight, a benchmark of various density functionals for the accurate calculation of charge reorganization energies is presented. A correlation between the charge reorganization energies and the ionization potentials is found which suggests applying IP‐tuning to obtain reliable values for charge reorganization energies. According to benchmark investigations with IP‐EOM‐CCSD single‐point calculations, the tuned functionals provide indeed more reliable charge reorganization energies. Among the standard functionals, ωB97X‐D and SOGGA11X yield accurate charge reorganization energies in comparison with IP‐EOM‐CCSD values. © 2016 Wiley Periodicals, Inc.     

Ionization potentials and electron affinities in the Perdew-Zunger self-interaction corrected density-functional theory

Using a self-consistent implementation of the Perdew-Zunger self-interaction corrected (PZ-SIC) density-functional theory, we have calculated ionization potentials (IP) and electron affinities (EA) of first- and second-row atoms and a set of small molecules. Several exchange-correlation functionals were tested. IPs and EAs were obtained by two methods: as the difference in self-consistent field (SCF) energies of neutrals and ions (deltaSCF) and as negatives of highest-occupied orbital energies. We found that, except for local spin-density approximation, PZ-SIC worsens DeltaSCF IPs and EAs. On the other hand, PZ-SIC brings orbital eigenvalues into much better agreement with electron removal energies. The Perdew-Zunger SIC seems to over-correct many-electron systems; for molecules it performs worse than for atoms. We also discuss several common approximations to PZ-SIC such as spherical averaging of orbital densities in atoms.     

Theoretical investigation of solvent effects on tautomeric equilibrium of 2‐diazo‐4,6‐dinitrophenol

The density functional theory has been used to study the tautomeric equilibrium of 2‐diazo‐4,6‐dinitrophenol(DDNP) in the gas phase and in 14 solvents at the B3LYP/6‐31G* level. The solvent effects on the tautomeric equilibria were investigated by the self‐consistent reaction field theory (SCRF) based on conductor polarized continuum model (CPCM) in apolar and polar solvents and by the hybrid continuum‐discrete model in protic solvent, respectively. Solvent effects on the computed molecular properties, such as molecular geometries, dipole moments, E_LUMO, E_HOMO, total energies for DDNP tautomers and transition state, tautomerization energies and solvation energies have been found to be evident. The tautomeric equilibrium of DDNP is solvent‐dependent to a certain extent. The tautomer I (cyclic azoxy form) is preferred in the gas phase, while in nonpolar solvents tautomer I and II (quinold form) exist in comparable amounts, and in highly polar solvents, the tautomeric equilibrium is shifted in favor of the more polar tautomer II . © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical computation of low‐lying electronic states of HCNS: A CASPT2 study

Complete active space self‐consistent field (CASSCF) and complete active space second‐order perturbation theory (CASPT2) calculations in conjunction with the aug‐cc‐pVTZ basis set have been used to investigate the low‐lying electronic states of thiofulminic acid (HCNS), HCNS⁺, and HCNS^?. The result of geometry optimization using CASPT2/aug‐cc‐pVTZ shows that theoretically determined geometric parameters and harmonic vibrational frequencies for the HCNS ground state X¹Σ⁺(X¹A′) are in agreement with previous studies. The ionization energies, the electron affinity energies, the adiabatic excitation energies, and vertical excitation energies have been calculated and the corresponding cation and anion states are identified. By calculating adiabatic electron affinity, the states of HCNS^? have been identified to contain both π orbital states (X²A′ and 1²A″) and dipole‐bond states (1⁴A′ and 1⁴A″). © 2012 Wiley Periodicals, Inc.