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.     

Molecular design of a π‐conjugated single‐chain electronically conductive polymer

This study demonstrates that single‐chain π‐conjugated systems can be made electrically conductive by modifying the molecular structures of both ends of the oligomers making up a polymer. That is, the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gaps of a fairly long polyyne‐type oligomer with appropriately modified molecular structures at both ends are found to be on the order of thermal energy by calculations using density functional theory (DFT) with B3LYP functionals. This result applies to molecular structures with characteristic bond alternations. The peculiar bond alternations are caused by competition between two effects of the bond alternations of the two mutually perpendicular π‐conjugated systems, which partially cancel each other out. It is probable that we can design one‐dimensional polymers with HOMO–LUMO gaps small enough to be conductive by combining the above‐mentioned oligomers with each other as monomer units in the polymer. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Theoretical study of two‐dimensionally fused zinc porphyrins: DFT calculations

Electronic structures of D_4h square‐fused zinc porphyrin sheets of two types ( SA , SB ), where SA is a directly meso‐meso‐, β‐β‐, and β‐β‐linked array and SB is a directly β‐fused array, were compared using density functional theory (DFT). The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of oligomeric SA _n are characteristically delocalized at the cyclooctatetraene‐like sites composed of β‐pyrrolic carbons and their nearest‐neighbor nitrogens. Those of oligomeric SB _n remain solitary monomeric features, reflecting weakly interacting porphyrin units. These two‐dimensionally (2D) square‐fused sheets, especially for SA _n, show effective reduction of both the HOMO–LUMO energy gaps (E_g) and the lowest Q‐like excitation energies because of LUMO's greater stabilization with increasing number of porphyrins than the corresponding one‐dimensionally (1D) linear‐fused tapes. To estimate the minimum value of E_g, the electronic band structures of the infinite‐fused SA _∞ and SB _∞ were examined in detail using modern periodic DFT. Results indicate a full metal for SA _∞, with HOMO and LUMO bands crossing the Fermi level, and a semiconductor with E_g ≈ 0.5 eV for SB _∞. Furthermore, the phonon modes and the electron–phonon coupling (EPC) constant of SA _∞ were calculated throughout the Brillouin zone using density functional perturbation theory (DFPT), yielding a weak EPC constant, λ = 0.35. Within the standard phonon‐mediated BCS mechanism, the superconducting transition temperature, T_c is demonstrated using the McMillan formula, predicting ≈0.5 K. Results show that SA _∞ will become a rare synthetic metal/superconductor without a metal‐insulator transition coming from Peierls lattice instability because it has no serious imaginary phonon modes. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical studies on the structures and electronic spectra of C75B−

Intermediate neglect of differential overlap (INDO) calculations were used to study the structure of C₇₅B^?—the isoelectronic molecule of C₇₆. It was found that the boron atom mainly substitutes the second carbon atom (there are 19 types of carbon atoms in C₇₆). The electronic spectra of all the possible isomers of C₇₅B^? were calculated based on the optimized geometries. It was shown that the UV‐Vis spectra of C₇₅B^? and C₇₆ resemble each other in many ways with the exception of the absorptions beyond 700 nm. The red shift of the absorptions was rationalized and nature of transition of the peaks discussed. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Scaling relations,virial theorem,and energy densities for long‐range and short‐range density functionals

Decomposition of the Coulomb electron–electron interaction into a long‐range and a short‐range part is described within the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local density approximation in the high‐density limit for the long‐range and the short‐range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long‐range‐only electron–electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Electronic structures and spectra for triepoxides of fullerene C78O3

The equilibrium structures and relative stabilities of the possible 21 lower‐energy isomers for C₇₈O₃ based on C₇₈ (C_2v) were studied by intermediate neglect of differential overlap (INDO) calculations. It was indicated that the most stable geometry is 28,29,30,31,52,53‐C₇₈O₃, where three oxygen atoms are added to the same hexagon passed by the longest axis of C₇₈ (C_2v) and epoxide structures are formed. Electronic spectra of C₇₈O₃ isomers were investigated based on the optimized geometries. The blue shift of the absorptions for 28,29,30,31,52,53‐C₇₈O₃ compared with that of C₇₈ (C_2v) was rationalized and nature of transition of the peaks discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Long‐range 19F–15N heteronuclear shift correlation: examination of J‐modulations associated with broad range accordion excitation

The first demonstrated example of ¹⁹F–¹⁵N long‐range heteronuclear shift correlation spectroscopy at natural abundance is reported. Because of the very large variation in the size of ²J(N,F) vs ³J(N,F) long‐range heteronuclear couplings, the utilization of one of the new accordion‐optimized long‐range heteronuclear shift correlations experiments is essential if all possible correlations are to be observed in a single experiment. A modified IMPEACH‐MBC pulse sequence was used in conjunction with an optimization range from 4 to 50 Hz to demonstrate the technique using a mixture of 2‐ and 3‐fluoropyridine, which had ²J(N,F) and ³J(N,F) long‐range couplings of ?52 and 3.6 Hz, respectively. Because of the size of the ²J(N,F) long‐range coupling constant, a J‐modulation of the long‐range correlation response is observed in the spectrum resulting in a ‘doublet’ in F₁ due to amplitude modulation. The size of the ‘doublet’ is shown to be a function of the parameter selection (t_1max,T_max,T_min and spectral width in F₁). This behavior is similar to F₁ ‘skew’ associated with long‐range correlation responses in ACCORD‐HMBC spectra which has been analyzed in detail previously. Copyright © 2002 John Wiley & Sons, Ltd.     

Converging ligand‐binding free energies obtained with free‐energy perturbations at the quantum mechanical level

In this article, the convergence of quantum mechanical (QM) free‐energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa‐acid deep‐cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158–224 atoms). We use single‐step exponential averaging (ssEA) and the non‐Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi‐empirical PM6‐DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free‐energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Relationship between the energy of donor–acceptor bond and the reorganization energy in molecular complexes

Donor–acceptor complexes of silicon halides with ammonia, pyridine, and 2,2′bipyridine SiX₄ · nD (X = F, Cl, Br) have been studied at the B3LYP/pVDZ level of theory. Energies of the donor–acceptor bond have been estimated taking into account the reorganization energy of the donor and acceptor fragments and basis set superposition error correction. Despite of the very low (or even negative) dissociation energy of SiX₄ · nD into free fragments, the Si–N bonding in all complexes is rather strong (75–220 kJ mol^?1). It is the reorganization energy of the acceptor SiX₄ (75–280 kJ mol^?1) that governs the dissociation energy of the complex. Thus, in contrast to the complexes of group 13 halides, the reorganization effects are crucial for the complexes of group 14 halides, and their neglecting leads to erroneous conclusions about the strength of the donor–acceptor bond in these systems. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Measurement of long‐range proton–carbon coupling constants from pure in‐phase 1D multiplets

The SELective INverse detection of carbon–proton CORrelation pulse sequence that yields a 1D spectrum of a proton directly bonded to a selected carbon resonance has been converted into a proton and carbon double‐selective variant that provides a ¹H spectrum of a selected proton that is long‐range coupled to a specific carbon resonance. The resulting 1D proton multiplet exhibits a pure absorptive in‐phase lineshape for precise measurement of specific long‐range proton–carbon coupling constants in small organic molecules at natural abundance. Copyright © 2011 John Wiley & Sons, Ltd.     

High‐temperature superconductivity and long‐range order in strongly correlated electronic systems

A selective review of the question of how repulsive electron correlations might give rise to off‐diagonal long‐range order (ODLRO) in high‐temperature superconductors is presented. The article makes detailed explanations of the relevance to superconductivity of reduced electronic density matrices and how these can be used to understand whether ODLRO might arise from Coulombic repulsions in strongly correlated electronic systems. Time‐reversed electron pairs on alternant Cuprate and the iron‐based pnictide and chalcogenide lattices may have a weak long‐range attractive tail and much stronger short‐range repulsive Coulomb interaction. The long‐range attractive tail may find its origin in one of the many suggested proposals for high‐T_c superconductivity and thus has an uncertain origin. A phenomenological Hamiltonian is invoked whose model parameters are obtained by fitting to experimental data. A detailed summary is given of the arguments that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed pairs of electrons effectively avoid the repulsive hard‐core of the Coulomb interaction but reside on average in the attractive well of the long‐range potential. Thus, the pairing of electrons itself provides an enhanced screening mechanism. The alternant lattice structure is the key to achieving robust high‐temperature superconductivity with dx²‐y² or sign alternating s‐wave or s± condensate symmetries in cuprates and iron‐based compounds. Some attention is also given to the question first raised by Leggett as to where the Coulombic energy is saved in the superconducting transition in cuprates. A mean‐field‐type model in which the condensate density serves as an order parameter is discussed. Many of the observed trends in the thermal properties of cuprate superconductors are reproduced giving strong support for the proposed model for high‐temperature superconductivity in such strongly correlated electronic systems. © 2015 Wiley Periodicals, Inc.     

Multiscale fast summation of long‐range charge and dipolar interactions

Here we present a linear order multiscale method for the fast summation of long range forces in a system consisting of a large number of charge and dipolar particles. For a N‐body system, our algorithm requires an order of work that is proportional to O(N), in comparison to order O(N²) of the direct pairwise computation. Our method is demonstrated on two‐dimensional homogeneous point‐charge and dipolar systems, and a combined heterogeneous particle system, for the calculation of the induced electrostatic potential and energy. The electrostatic interaction is decomposed into a local part and a smooth part. The method thus, has several potential advantages over other O(N log N) or O(N) techniques, especially for calculation with moving particles or implicit charges locations. This approach is beneficial to large‐scale problems such as molecular statics, molecular dynamics, equilibrium statistics (Monte‐Carlo simulations), molecular docking, and in areas such as magnetism and astrophysics. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 717–731, 2001     

Generalized spin orbital GW theory for spin‐frustrated and spin‐degenerate systems

We proposed the ab initio linear combination of Gaussian type orbital (LCGTO) generalized spin orbital GW (GSO–GW) method and calculated triangular hydrogen molecules as models of the noncolinear magnetic clusters. A remarkable improvement of ionized potentials (IPs) by the GW procedure for GHFS solutions is observed in comparison with calculational results by full CI. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 369–374, 2001     

Highly efficient implementation of pseudospectral time‐dependent density‐functional theory for the calculation of excitation energies of large molecules

We have developed and implemented pseudospectral time‐dependent density‐functional theory (TDDFT) in the quantum mechanics package Jaguar to calculate restricted singlet and restricted triplet, as well as unrestricted excitation energies with either full linear response (FLR) or the Tamm–Dancoff approximation (TDA) with the pseudospectral length scales, pseudospectral atomic corrections, and pseudospectral multigrid strategy included in the implementations to improve the chemical accuracy and to speed the pseudospectral calculations. The calculations based on pseudospectral time‐dependent density‐functional theory with full linear response (PS‐FLR‐TDDFT) and within the Tamm–Dancoff approximation (PS‐TDA‐TDDFT) for G2 set molecules using B3LYP/6‐31G*^* show mean and maximum absolute deviations of 0.0015 eV and 0.0081 eV, 0.0007 eV and 0.0064 eV, 0.0004 eV and 0.0022 eV for restricted singlet excitation energies, restricted triplet excitation energies, and unrestricted excitation energies, respectively; compared with the results calculated from the conventional spectral method. The application of PS‐FLR‐TDDFT to OLED molecules and organic dyes, as well as the comparisons for results calculated from PS‐FLR‐TDDFT and best estimations demonstrate that the accuracy of both PS‐FLR‐TDDFT and PS‐TDA‐TDDFT. Calculations for a set of medium‐sized molecules, including C_n fullerenes and nanotubes, using the B3LYP functional and 6‐31G^** basis set show PS‐TDA‐TDDFT provides 19‐ to 34‐fold speedups for C_n fullerenes with 450–1470 basis functions, 11‐ to 32‐fold speedups for nanotubes with 660–3180 basis functions, and 9‐ to 16‐fold speedups for organic molecules with 540–1340 basis functions compared to fully analytic calculations without sacrificing chemical accuracy. The calculations on a set of larger molecules, including the antibiotic drug Ramoplanin, the 46‐residue crambin protein, fullerenes up to C₅₄₀ and nanotubes up to 14×(6,6), using the B3LYP functional and 6‐31G^** basis set with up to 8100 basis functions show that PS‐FLR‐TDDFT CPU time scales as N^2.05 with the number of basis functions. © 2016 Wiley Periodicals, Inc.     

Link between the kinetic‐ and exchange‐energy functionals in the generalized gradient approximation

An approximate kinetic‐energy functional of the generalized gradient approximation form was derived following the “conjointness conjecture” of Lee, Lee, and Parr. The functional shares the analytical form of its gradient dependency with the exchange‐energy functionals of Becke and Perdew, Burke, and Ernzerhof. The two free parameters of this functional were determined using the exact values of the kinetic energy of He and Xe atoms. A set of 12 closed‐shell atoms was used to test the accuracy of the proposed functional and more than 30 others taken from the literature. It is shown that the conjointness conjecture leads to a very good class of kinetic‐energy functionals. Moreover, the functional developed in this work is shown to be one of the most accurate despite its simple analytical form. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

BASHD‐J‐resolved‐HMBC,an efficient method for measuring proton–proton and heteronuclear long‐range coupling constants

Natural products often possess various spin systems consisting of a methine group directly bonded to a methyl group (e.g. –CH_a–CH_b(CH₃)–CH_c–). The methine proton H_b splits into a broadened multiplet by coupling with several vicinal protons, rendering analysis difficult of ⁿJ_C–H with respect to H_b in the J‐resolved HMBC‐1. In purpose of the reliable and easy measurements of ⁿJ_C–H and ⁿJ_H–H in the aforesaid spin system, we have developed a new technique, named BASHD‐J‐resolved‐HMBC. This method incorporates band selective homo decoupled pulse and J‐scaling pulse into HMBC. In this method, high resolution cross peaks can be observed along the F₁ axis by J‐scaling pulse, and band selective homo decoupled pulse simplified multiplet signals. Determinations of ⁿJ_C–H and ⁿJ_H–H of multiplet signals can easily be performed using the proposed pulse sequence. Copyright © 2013 John Wiley & Sons, Ltd.     

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ? and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Assessment and acceleration of binding energy calculations for protein–ligand complexes by the fragment molecular orbital method

In the field of drug discovery, it is important to accurately predict the binding affinities between target proteins and drug applicant molecules. Many of the computational methods available for evaluating binding affinities have adopted molecular mechanics‐based force fields, although they cannot fully describe protein–ligand interactions. A noteworthy computational method in development involves large‐scale electronic structure calculations. Fragment molecular orbital (FMO) method, which is one of such large‐scale calculation techniques, is applied in this study for calculating the binding energies between proteins and ligands. By testing the effects of specific FMO calculation conditions (including fragmentation size, basis sets, electron correlation, exchange‐correlation functionals, and solvation effects) on the binding energies of the FK506‐binding protein and 10 ligand complex molecule, we have found that the standard FMO calculation condition, FMO2‐MP2/6‐31G(d), is suitable for evaluating the protein–ligand interactions. The correlation coefficient between the binding energies calculated with this FMO calculation condition and experimental values is determined to be R = 0.77. Based on these results, we also propose a practical scheme for predicting binding affinities by combining the FMO method with the quantitative structure–activity relationship (QSAR) model. The results of this combined method can be directly compared with experimental binding affinities. The FMO and QSAR combined scheme shows a higher correlation with experimental data (R = 0.91). Furthermore, we propose an acceleration scheme for the binding energy calculations using a multilayer FMO method focusing on the protein–ligand interaction distance. Our acceleration scheme, which uses FMO2‐HF/STO‐3G:MP2/6‐31G(d) at R_int = 7.0 Å, reduces computational costs, while maintaining accuracy in the evaluation of binding energy. © 2015 Wiley Periodicals, Inc.