UNIQUAC correlation of liquid–liquid equilibrium in systems involving ionic liquids: The DFT–PCM approach. Part II

In this work, new UNIQUAC structural parameters r and q for the ionic liquids were determined by quantum chemistry calculations performed with the Gaussian 03 and GAMESS 7.1 packages, including the density functional theory (DFT) for the optimization of the structures and the polarizable continuum method (PCM) for the calculation of molecular areas and volumes. Data liquid–liquid equilibrium (LLE) of 41 ternary systems involving 15 different ionic liquids, comprising 379 experimental tie-lines, was correlated by the UNIQUAC model for the activity coefficient. The results, expressed by deviations between experimental and calculated compositions, are very satisfactory, with deviation values about 1.93%.     

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2-106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.     

DFT description of the electronic structure and spectromagnetic properties of strongly correlated electronic systems: NiII, CuII and ZnII o-dioxolene complexes

The spectroscopic and magnetic properties of dioxolene complexes of zinc, copper and nickel were studied by DFT calculations on model complexes of formulas [(NH(3))(4)M(II)(SQ)](+) (M=Zn, Ni; SQ=semiquinonato) and [(NH(3))(2)Cu(II)(SQ)](+). Standard approaches such as time-dependent DFT (TDDFT), the Slater transition state (STS), and broken symmetry (BS) were found to be unable to completely account for the physical properties of the systems, and complete active space-configuration interaction (CAS-CI) calculations based on the Kohn-Sham (KS) orbitals was applied. The CAS-CI energies, properly corrected with multireference perturbation theory (MR-PT), were found to be in good agreement with experimental data. We present here a calculation protocol that has a low CPU cost/accuracy ratio and seems to be very promising for interpreting the properties of strongly correlated electronic systems in complexes of real chemical size.     

A dual-level state-specific time-dependent density-functional theory

A highly efficient new algorithm for time-dependent density-functional theory (TDDFT) calculations is presented. In this algorithm, a dual-level approach to speed up DFT calculations (Nakajima and Hirao, J Chem Phys 2006, 124, 184108) is combined with a state-specific (SS) algorithm for TDDFT (Chiba et al., Chem Phys Lett 2006, 420, 391). The dual-level SS-TDDFT algorithm was applied to excitation energy calculations of typical small molecules, the Q bands of the chlorophyll A molecule, the charge-transfer energy of the zincbacteriochlorin-bacteriochlorin model system, and the lowest-lying excitation of the circumcoronene molecule. As a result, it was found that the dual-level SS-TDDFT gave correct excitation energies with errors of 0.2-0.3 eV from the standard TDDFT approach, with much lower CPU times for various types of excitation energies of large-scale molecules.     

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.     

QM/MM study of the absorption spectra of DsRed.M1 chromophores

We report geometries and vertical excitation energies for the red and green chromophores of the DsRed.M1 protein in the gas phase and in the solvated protein environment. Geometries are optimized using density functional theory (DFT, B3LYP functional) for the isolated chromophores and combined quantum mechanical/molecular mechanical (QM/MM) methods for the protein (B3LYP/MM). Vertical excitation energies are computed using DFT/MRCI, OM2/MRCI, and TDDFT as QM methods. In the case of the red chromophore, there is a general blue shift in the excitation energies when going from the isolated chromophore to the protein, which is caused both by structural changes and by electrostatic interactions with the environment. For the lowest ππ* transition, these two factors contribute to a similar extent to the overall DFT/MRCI shift of 0.4 eV. An enlargement of the QM region to include active‐site residues does not change the DFT/MRCI excitation energies much. The DFT/MRCI results are closest to experiment for both chromophores. OM2/MRCI and TDDFT overestimate the first vertical excitation energy by 0.3–0.5 and 0.2–0.4 eV, respectively, relative to the experimental or DFT/MRCI values. The experimental gap of 0.35 eV between the lowest ππ* excitation energies of the red (cis‐acylimine) and green (trans‐peptide) forms is well reproduced by DFT/MRCI and TDDFT (0.32 and 0.37 eV, respectively). A histogram spectrum for an equal mixture of the two forms, generated by OM2/MRCI calculations on 450 snapshots along molecular dynamics trajectories, matches the experimental spectrum quite well, with a gap of 0.23 eV and an overall blue shift of about 0.3 eV. DFT/MRCI appears as an attractive choice for calculating excitation energies in fluorescent proteins, without the shortcomings of TDDFT and computationally more affordable than CASSCF‐based approaches. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Analytical derivative techniques for TDDFT excited-state properties: Theory and application

We review our recent work on the methodology development of the excited-state properties for the molecules in vacuum and liquid solution.The general algorithms of analytical energy derivatives for the specific properties such as the first and second geometrical derivatives and IR/Raman intensities are demonstrated in the framework of the time-dependent density functional theory(TDDFT).The performance of the analytical approaches on the calculation of excited-state energy Hessian has also been shown.It is found that the analytical approaches are superior to the finite-difference method on the computational accuracy and efficiency.The computational cost for a TDDFT excited-state Hessian calculation is only 2–3 times as that for the DFT ground-state Hessian calculation.With the low computational complexity of the developed analytical approaches,it becomes feasible to realize the large-scale numerical calculations on the excited-state vibrational frequencies,vibrational spectroscopies and the electronic-structure parameters which enter the spectrum calculations of electronic absorption and emission,and resonance Raman spectroscopies for medium-to large-sized systems.     

Computational study of iron(II) systems containing ligands with nitrogen heterocyclic groups

Density functional theory (DFT) calculations show the higher energy HOMO (highest occupied molecular orbital) orbitals of four iron(II) diimine complexes are metal centered and the lower energy LUMO (lowest unoccupied molecular orbitals) are ligand centered. The energy of the orbitals correlates with electrochemical redox potentials of the complexes. Time-dependent density functional theory (TDDFT) calculations reveal ligand centered (LC) and metal-to-ligand charge transfer (MLCT) at higher energy than experimentally observed. TDDFT calculations also reveal the presence of d-d transitions which are buried under the MLCT and LC transitions. The difference in chemical and photophysical behavior of the iron complexes compared to that of their ruthenium analogues is also addressed.     

Density functional and spin-orbit ab initio study of CF3Br: molecular properties and electronic curve crossing

Quantum chemical calculations of CF(3)Br and the CF(3) radical are performed using density functional theory (DFT) and time-dependent DFT (TDDFT). Molecular structures, vibrational frequencies, dipole moment, bond dissociation energy, and vertical excitation energies of CF(3)Br are calculated and compared with available experimental results. The performance of six hybrid and five hybrid meta functionals in DFT and TDDFT calculations are evaluated. The ωB97X, B3PW91, and M05-2X functionals give very good results for molecular structures, vibrational frequencies, and vertical excitation energies, respectively. The ωB97X functional calculates well the dipole moment of CF(3)Br. B3LYP, one of the most widely used functionals, does not perform well for calculations of the C-Br bond length, bond dissociation energy, and vertical excitation energies. Potential energy curves of the low-lying excited states of CF(3)Br are obtained using the multiconfigurational spin-orbit ab initio method. The crossing point between 2A(1) and 3E states is located near the C-Br bond length of 2.45 ?. Comparison with CH(3)Br shows that fluorination does not alter the location of the crossing point. The relation between the calculated potential energy curves and recent experimental result is briefly discussed.     

Electronic Coupling between Two Amine Redox Sites through the 5,5′‐Positions of Metal‐Chelating 2,2′‐Bipyridines

Electron delocalization of new mixed‐valent (MV) systems with the aid of lateral metal chelation is reported. 2,2′‐Bipyridine (bpy) derivatives with one or two appended di‐p‐anisylamino groups on the 5,5′‐positions and a coordinated [Ru(bpy)₂] (bpy=2,2′‐bipyridine), [Re(CO)₃Cl], or [Ir(ppy)₂] (ppy=2‐phenylpyridine) component were prepared. The single‐crystal molecular structure of the bis‐amine ligand without metal chelation is presented. The electronic properties of these complexes were studied and compared by electrochemical and spectroscopic techniques and DFT/TDDFT calculations. Compounds with two di‐p‐anisylamino groups were oxidized by a chemical or electrochemical method and monitored by near‐infrared (NIR) absorption spectral changes. Marcus–Hush analysis of the resulting intervalence charge‐transfer transitions indicated that electron coupling of these mixed‐valent systems is enhanced by metal chelation and that the iridium complex has the largest coupling. TDDFT calculations were employed to interpret the NIR transitions of these MV systems.     

Profiling energetics and spectroscopic signatures in prototropic tautomers of asymmetric phthalocyanine analogues

Density functional theory (DFT) and time-dependent density functional theory (TDDFT) were used to explain discrepancies in UV-vis and MCD spectra of the metal-free tribenzo[b,g,l]thiopheno[3,4-q]porphyrazine (1), substituted tribenzo[b,g,l]porphyrazine (2), and 2,3-bis(methylcarboxyl)phthalocyanine (3). On the basis of gas-phase and polarized continuum solvation model (PCM) DFT and TDDFT calculations, it was suggested that both NH tautomers contribute to the spectroscopic signature of 1, whereas the Q-band region of 2 and 3 is dominated by a single NH tautomer. For all tested compounds, it was found that the combination of the BP86 exchange-correlation functional, 6-31G(d) basis set, and TDDFT-PCM approach provides the best accuracy in energies of the Q(x)- and Q(y)-bands of the individual NH tautomers as well as correctly describes their relative energy differences, which are important in understanding of experimental spectroscopy of the target systems.     

Iridium cyclometalated complexes with axial symmetry: time-dependent density functional theory investigation of trans-bis-cyclometalated complexes containing the tridentate ligand 2,6-diphenylpyridine

A new series of iridium cyclometalated complexes with a C/N/C dppy-type ligand and a N/N/N tpy-type ligand have been synthesized and characterized by various techniques such as mass spectrometry, 1H and 13C NMR, cyclic voltammetry, both steady-state and time-resolved emission and absorption studies, and time-dependent DFT (TDDFT) calculations. The complexes exhibit strong visible absorptions and long-lived (1.6-2.0 micros) emissions (lambdamax, ca. 680 nm) in room-temperature solution. DFT calculations on the ground-state geometry match that of an X-ray crystal structure. TDDFT calculations give accurate predictions of the electronic absorption energies and intensities, while geometry optimizations on the lowest energy triplet state give accurate energies for the emission. Examination of the relevant molecular orbitals shows that the inherent asymmetry of the coordination environment offers a unique directional character to the emitting excited state, which is predominately LLCT (dppy --> tpy) in nature.     

Charge delocalization of 1,4-benzenedicyclometalated ruthenium: a comparison between tris-bidentate and bis-tridentate complexes

A dimetallic biscyclometalated ruthenium complex, [(bpy)(2)Ru(dpb)Ru(bpy)(2)](2+) (bpy = 2,2'-bipyridine; dpb = 1,4-di-2-pyridylbenzene), with a tris-bidentate coordination mode has been prepared. The electronic properties of this complex were studied by electrochemical and spectroscopic analysis and DFT/TDDFT calculations on both rac and meso isomers. Complex [(bpy)(2)Ru(dpb)Ru(bpy)(2)](2+) has a similar 1,4-benzenedicyclometalated ruthenium (Ru-phenyl-Ru) structural component with a previously reported bis-tridentate complex, [(tpy)Ru(tpb)Ru(tpy)](2+) (tpy = 2,2';6',2″-terpyridine; tpb = 1,2,4,5-tetra-2-pyridylbenzene). The charge delocalizations of these complexes across the Ru-phenyl-Ru array were investigated and compared by studying the corresponding one-electron-oxidized species, generated by chemical oxidation or electrochemical electrolysis, with DFT/TDDFT calculations and spectroscopic and EPR analysis. These studies indicate that both [(bpy)(2)Ru(dpb)Ru(bpy)(2)](3+) and [(tpy)Ru(tpb)Ru(tpy)](3+) are fully delocalized systems. However, the coordination mode of the metal component plays an important role in influencing their electronic properties.     

A computational investigation on singlet and triplet exciton couplings in acene molecular crystals

Quantum chemical calculations (DFT, TDDFT and ZINDO/S) of singlet and triplet exciton couplings are presented and discussed for some acene derivatives (such as anthracene, tetracene, 9,10-di(phenyl)anthracene and 9,10-bis(phenylethynyl)anthracene). An accurate excited state single molecule characterization has been carried out followed by an analysis of the inter-molecular excitonic interactions, taking place in the crystalline phase. These have been correlated to exciton coupling terms obtaining guidelines for the choice of molecular materials with large exciton couplings. Such organic systems are likely to show multiexciton processes such as singlet fission (SF) and triplet-triplet annihilation (TTA) which are useful in energy conversion phenomena to be exploited in photonic and optoelectronic devices.     

Use of GAMESS/COSMO program in support of COSMO-SAC model applications in phase equilibrium prediction calculations

Thermodynamic models based on conductor-like screening models (COSMO) offer viable alternatives to existing group-contribution methods for the prediction of phase equilibria. Normally a COSMO-based model requires input of the distribution of screening charges on the molecular surface, aka. the sigma profile, determined from a specific quantum chemistry program and settings. For example, the COSMO-SAC model requires input of DMol³ generated sigma profiles. In this paper, we investigate the proper settings for an open-source quantum chemistry package GAMESS in order to generate sigma profiles to be used directly in the COSMO-SAC model. The phase behaviors (VLE and VLLE) of 45 binary mixtures from 10 commonly used solvents and the solubilities of 4 complex drug compounds in these solvents calculated from DMol³ and GAMESS generated sigma profiles are compared. While noticeable fine structure differences are observed in the individual sigma profiles for the same chemical compound generated from the two packages, it is found that the accuracy in the VLE/VLLE and solubility predictions from the two packages are comparable. Based on the systems we studied here, the open-source GAMESS/COSMO program with proper program settings could be used as an alternative sigma profile generation source in support of COSMO-SAC model applications in phase equilibrium prediction calculations.     

Improvement of parallelization performance of GAMESS: global sum and (semi-)direct integral calculation in multireference perturbation calculation

Performance benchmark tests of the multireference perturbation theory (MRPT2) calculation in the GAMESS suite of programs have been performed on a 128-node PC cluster system. The benchmark results point to two kinds of problems with GAMESS: network delay and slow access to disk files. To overcome these bottlenecks, we employ (semi-)direct atomic orbital integral calculations and a new algorithm for the "global sum" operation. These modifications produce remarkable performance improvements, especially in the 128-node PC cluster system, which was almost twice as fast in our version as in the original version. The modification of "global sum" also improved the performance of other types of molecular orbital calculations in GAMESS, such as density functional theory.     

Pigment Yellow 101: A showcase for photo-initiated processes in medium-sized molecules

Pigment Yellow 101 (P.Y.101) is a fluorescent yellow pigment which exhibits a surprisingly rich photochemistry of several competing reaction pathways as revealed by recent time-resolved femtosecond experiments. Our elaborate quantum chemical investigations employing density functional theory (DFT) and time-dependent DFT (TDDFT) show that the observed fluorescence competes with excited state intramolecular proton transfer and trans–cis isomerization processes. Moreover, the experimentally observed spectral features of the complicated excited state dynamics can be assigned to stable trans-diol, trans-keto and cis-diol, cis-keto isomers on the ground and excited state surfaces. Still, due to its molecular size P.Y.101 poses a challenge to electronic structure theory and many problems occur in particular with respect to the excited state calculations. Thus, P.Y.101 serves also as an educative example for which TDDFT yields a reasonable vertical electronic spectrum, but fails in the prediction of excited state structures, when standard GGA or hybrid functionals with low fractions of Hartree–Fock exchange are employed. This failure is attributed to the charge-transfer failure of TDDFT.     

Spectroscopic and theoretical studies of optically active porphyrin dimers: a system uninterpretable by exciton coupling theory.

The electronic excited states of a meso-meso beta-beta doubly linked bis-porphyrin are comprehensively investigated by measuring its circular dichroism (CD) and magnetic circular dichroism (MCD) spectra. The observed spectroscopic properties are rationalized by DFT calculations. The frontier molecular orbitals (MOs) are constructed by the linear combinations of the constituent monomers' four MOs. Comparison of a theoretical CD spectrum based on time-dependent DFT (TDDFT) with the experimental spectra resulted in the assignment of the helical conformation of the dimer. This assignment is contrary to the previous assignment based on the point-dipole approximation (exciton coupling theory).