Double hybrids and time-dependent density functional theory: An implementation and benchmark on charge transfer excited states

In this paper we present the implementation and benchmarking of a Time Dependent Density Functional Theory approach in conjunction with Double Hybrid (DH) functionals. We focused on the analysis of their performance for through space charge-transfer (CT) excitations which are well known to be very problematic for commonly used functionals, such as global hybrids.Two different families of functionals were compared, each of them containing pure, hybrid and double-hybrid functionals.The results obtained show that, beside the robustness of the implementation, these functionals provide results with an accuracy comparable to that of adjusted range-separated functionals, with the relevant difference that for DHs no parameter is tuned on specific compounds thus making them more appealing for a general use. Furthermore, the algorithm described and implemented is characterized by the same computational cost scaling as that of the ground state algorithm employed for MP2 and double hybrids.     

A state-specific polarizable continuum model time dependent density functional theory method for excited state calculations in solution

An effective state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of excited electronic states has been developed and coded in the framework of the so-called polarizable continuum model (PCM). Different relaxation time regimes can be treated thus giving access to a number of different spectroscopic properties together with solvent relaxation energies of paramount relevance in electron transfer processes. SS and conventional linear response (LR) models have been compared for two benchmark systems (coumarin 153 and formaldehyde in different solvents) and in the limiting simple case of a dipolar solute embedded in a spherical cavity. The results point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents. The favorable scaling properties of PCM-TD-DFT models in both SS and LR variants and their availability in effective quantum mechanical codes pave the route for the computation of reliable spectroscopic properties of large molecules of technological and/or biological interest in their natural environments.     

Robust acceleration of self consistent field calculations for density functional theory

We show that the type 2 Broyden secant method is a robust general purpose mixer for self consistent field problems in density functional theory. The Broyden method gives reliable convergence for a large class of problems and parameter choices. We directly mix the approximation of the electronic density to provide a basis independent mixing scheme. In particular, we show that a single set of parameters can be chosen that give good results for a large range of problems. We also introduce a spin transformation to simplify treatment of spin polarized problems. The spin transformation allows us to treat these systems with the same formalism as regular fixed point iterations.     

Origin of substituent effects in the absorption spectra of peroxy radicals: time dependent density functional theory calculations.

We investigate the assignment of electronic transitions in alkyl peroxy radicals. Past experimental work has shown that the phenyl peroxy radical exhibits a transition in the visible region; however, previous high level calculations have not reproduced this observed absorption. We use time dependent density functional theory (TDDFT) to characterize the electronic excitations of the phenyl peroxy radical as well as other hydrocarbon substituted peroxy radicals. TDDFT calculations of the phenyl peroxy radical support an excitation in the visible spectrum. Further, we investigate the nature of this visible absorption using electron attachment/detachment density diagrams of the peroxy radicals and present a qualitative picture of the origin of the visible absorption based on molecular orbital perturbations. The peroxy radical substituent is also compared against isoelectronic radical groups. The visible absorption is determined to be dependent on mixing of the alkyl and radical substituent orbitals.     

Spectral analysis of acetylcholine halides by density functional theory calculations

The optimized molecular structures, vibrational frequencies and ¹H and ¹³C NMR chemical shifts of acetylcholine halides (F, Cl, and Br) have been investigated using density functional theory (B3LYP) method with 6-311G(d) basis set. The comparison of their experimental and calculated IR, R and NMR spectra of the compounds has indicated that the spectra of three optimized minimum energy conformers can simultaneously exist in one experimental spectrum. Thus, it was concluded that the compounds simultaneously exist in three conformations in the ground state. The calculated optimized geometric parameters (bond lengths and bond angles), vibrational frequencies and NMR chemical shifts for the minimum energy conformers were seen to be in a good agreement with the corresponding experimental data. All the assignments of the theoretical frequencies were performed by potential energy distributions using VEDA 4 program.     

A time dependent density functional theory study of alpha-84 phycocyanobilin chromophore in C-phycocyanin

The optical characteristics of absorption and circular dichroism (CD) spectroscopy of an alpha-subunit of C-phycocyanin (C-PC) were investigated by using time dependent density functional theory (TDDFT) combined with the polarizable continuum model (PCM). When the protonation of alpha-84 phycocyanobilin (PCB) and its interaction with the protein moiety in C-PC have been taken into account, satisfactory assignment of the absorption and CD spectra of alpha-84 PCB can be achieved. The TDDFT-PCM calculations conclude that in the visible absorption region the main peak arises from the pi electron excitation of the pyrrole rings and the shoulder peak comes from the charge transfer from Asp87 (a nearby amino acid residue) to PCBH(+).     

Water chain encapsulated in carbon nanotube revealed by density functional theory

The noncovalent interactions between encapsulated water chains and single‐walled carbon nanotube (SWCNT) are studied using a self‐consistent charge density functional tight binding method with dispersion correction. The most interesting and important feature we observe is the diameter shrinking of CNTs when water chains are confined inside SWCNT. The diameter shrinking of CNTs can be suggested to the original of the van der Waals and H‐π interaction between water chains and CNTs. The calculated Raman spectra show the interactions between SWCNTs and water chains probably give rise to a kind of “mode hardening effect,” which agrees with the diameter shrinking of CNTs when water chains are confined inside SWCNT. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011.     

Recent applications of density functional theory calculations to biomolecules

The purpose of this overview is to highlight the broad scope and utility of current applications of density functional theory (DFT) methods for the study of the properties and reactions of biomolecules. This is illustrated using examples selected from research carried out within our research group and in collaboration with others. The examples include the hyperfine coupling constants of amino acid radicals, the use of an amino acid as a chiral catalyst for the formation of carbon–carbon bonds in the aldol reaction, hydrogen-bond mediated catalysis of an aminolysis reaction, radiation-induced protein–DNA cross-links, and the mechanism by which an antitumor drug cleaves DNA. We demonstrate that DFT-based methods can be applied successfully to a broad range of problems that remain beyond the scope of conventional electron-correlation methods. Furthermore, we show that contemporary computational quantum chemistry complements experiment in the study of biological systems. Received: 19 December 2001 / Accepted: 8 April 2002 / Published online: 4 July 2002     

Methylation of zebularine investigated using density functional theory calculations

Deoxyribonucleic acid (DNA) methylation is an epigenetic phenomenon, which adds methyl groups into DNA. This study reveals methylation of a nucleoside antibiotic drug 1‐(β‐D ‐ribofuranosyl)‐2‐pyrimidinone (zebularine or zeb) with respect to its methylated analog, 1‐(β‐D ‐ribofuranosyl)‐5‐methyl‐2‐pyrimidinone (d5) using density functional theory calculations in valence electronic space. Very similar infrared spectra suggest that zeb and d5 do not differ by types of the chemical bonds, but distinctly different Raman spectra of the nucleoside pair reveal that the impact caused by methylation of zeb can be significant. Further valence orbital‐based information details on valence electronic structural changes caused by methylation of zebularine. Frontier orbitals in momentum space and position space of the molecules respond differently to methylation. Based on the additional methyl electron density concentration in d5, orbitals affected by the methyl moiety are classified into primary and secondary contributors. Primary methyl contributions include MO8 (57a), MO18 (47a), and MO37 (28a) of d5, which concentrates on methyl and the base moieties, suggest certain connection to their Frontier orbitals. The primary and secondary methyl affected orbitals provide useful information on chemical bonding mechanism of the methylation in zebularine. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Studies of iridium nanoparticles using density functional theory calculations

The energetics and the electronic and magnetic properties of iridium nanoparticles in the range of 2-64 atoms were investigated using density functional theory calculations. A variety of different geometric configurations were studied, including planar, three-dimensional, nanowire, and single-walled nanotube. The binding energy per atom increases with size and dimensionality from 2.53 eV/atom for the iridium dimer to 6.09 eV/atom for the 64-atom cluster. The most stable geometry is planar until four atoms are reached and three-dimensional thereafter. The simple cubic structure is the most stable geometric building block until a strikingly large 48-atom cluster, when the most stable geometry transitions to face-centered cubic, as found in the bulk metal. The strong preference for cubic structure among small clusters demonstrates their rigidity. This result indicates that iridium nanoparticles intrinsically do not favor the coalescence process. Nanowires formed from linear atomic chains of up to 4-atom rings were studied, and the wires formed from 4-atom rings were extremely stable. Single-walled nanotubes were also studied. These nanotubes were formed by stacking 5- and 6-atom rings to form a tube. The ring stacking with each atom directly above the previous atom is more stable than if the alternate rings are rotated.     

Prediction of cellulose nanotube models through density functional theory calculations

We report the generation of a nano-scale tubular structure of cellulose molecules (CelNT), through density functional theory (DFT) calculations. When a cellulose III_I (1 0 0) chain sheet model is optimized by DFT calculations, the sheet models spontaneously roll into tubes. The oligomers arrange in a right-handed, four-fold helix with one-quarter chain staggering, oriented with parallel polarity similar to the original crystal structure. Based on a one-quarter chain staggering relationship, six large CelNT models, consisting of 16 cellulose chains with DP = 80, are constructed by combinations of two types of chain polarities and three types of symmetry operations to generate a circular arrangement of molecular chains. All six CelNT models are examined by molecular dynamics (MD) calculations in chloroform. While four CelNT models retain a tubular form throughout MD calculations, the remaining two deform. 3D-RISM theory model is used to estimate the solvation free energies of the four CelNT models. The results suggest that the CelNT model with a chain arrangement of parallel polarity and right-handed helical symmetry forms the most stable tube structure.     

The electronic absorption study of imide anion radicals in terms of time dependent density functional theory

The absorption spectra of the N-(2,5-di-tert-butylphenyl) phthalimide (1-), N-(2,5-di-tert-butylphenyl)-1,8-naphthalimide (2-) and N-(2,5-di-tert-butylphenyl)-perylene-3,4-dicarboximide (3-) anion radicals are studied in terms of time dependent density functional theory (TDDFT). For these anion radicals a large number electronic states (from 30 to 60) was found in the visible and near-IR regions (5000-45,000 cm(-1)). In these regions the TD/B3LYP treatment at the 6-1+G* level is shown to reproduce satisfactorily the empirical absorption spectra of all three anion radicals studied. The most apparent discrepancies between purely electronic theory and the experiment could be found in the excitation region corresponding to D0-->D1 transitions in the 2- and 3- molecules. For these species we argue that the structures seen in the lowest energy part of the absorptions of the 2- and 3- species are very likely due to Franck-Condon (FC) activity of the totally symmetric vibrations not studied in this Letter.     

Formation and relaxation of excited states in solution: a new time dependent polarizable continuum model based on time dependent density functional theory

In this paper a novel approach to study the formation and relaxation of excited states in solution is presented within the integral equation formalism version of the polarizable continuum model. Such an approach uses the excited state relaxed density matrix to correct the time dependent density functional theory excitation energies and it introduces a state-specific solvent response, which can be further generalized within a time dependent formalism. This generalization is based on the use of a complex dielectric permittivity as a function of the frequency, epsilonomega. The approach is here presented in its theoretical formulation and applied to the various steps involved in the formation and relaxation of electronic excited states in solvated molecules. In particular, vertical excitations (and emissions), as well as time dependent Stokes shift and complete relaxation from vertical excited states back to ground state, can be obtained as different applications of the same theory. Numerical results on two molecular systems are reported to better illustrate the features of the model.     

Time-dependent density functional theory calculations of the photoabsorption of fluorinated alkanes

Time-dependent density functional theory (TD-DFT) calculations of the transition energies and oscillator strengths of fluorinated alkanes have been performed. The TD-DFT method with the non-local B3LYP potential yields transition energies for the methanes, which are smaller by about 10% as compared to the experimental values. An empirical linear correlation was found between the calculated and experimental transition energies both at the B3LYP/DZ+Ryd(C, F) and B3LYP/cc-pVTZ+Ryd(C, F, H) levels for a total of 19 transitions of the fluorinated methanes with linear correlation coefficients of 0.987 for the former and 0.988 for the latter. This empirical correlation for fluorinated methane molecules is found to agree well with the previously obtained empirical correlations between calculated and experimental values for non-fluorinated molecules. The results show that a single empirical-correlation relationship can be used for both non-fluorinated and fluorinated molecules to predict transition energies. This linear relationship is then used to predict the photoabsorption spectra of ethane, propane, butane, and partially and fully fluorinated derivatives. A key result of these calculations is the dominance of Rydberg transitions in the spectral region of interest.     

Basis set dependence of phosphate frequencies in density functional theory calculations

The addition of extravalence, polarization and diffuse functions, were studied in order to conclude how they affect the P? O stretching frequencies of several biological relevant phosphate molecules. The results show that the polarization and the diffuse functions have opposite effects on the frequencies: the polarization functions downshift while the diffuse functions upshift the frequencies. The effect of the valence functions was more difficult to interpret. The effect of the conductor‐like screening model (CPCM)‐continuum model was also studied. The results show that the CPCM‐continuum model has a substantial effect on the frequencies for these small molecules. The continuum model's efficiency is mainly due to its effect on the geometries and not on the frequencies. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Theoretical Auger electron spectra of polymers by density functional theory calculations using model dimers

We propose a new approach for analysis of Auger electron spectra (AES) of polymers by density functional theory (DFT) calculations with the Slater's transition-state concept. Simulated AES and X-ray photoelectron spectra (XPS) of four polymers [(CH2CH2)n (PE), (CH2CH(CH3))n (PP), (CH2CH(OCH3))n (PVME), and (CH2CH(COCH3))n (PVMK)] by DFT calculations using model dimers are in a good accordance with the experimental ones. The experimental AES of the polymers can be classified in each range of 1s-2p2p, 1s-2s2p, and 1s-2s2s transitions for C KVV and O KVV spectra, and in individual contributions of the functional groups from the theoretical analysis.     

Surface-enhanced Raman scattering of 4,4′-bipyridine on silver by density functional theory calculations

Surface-enhanced Raman scattering (SERS) of 4,4′-bipyridine (BPy) on silver foil substrate was measured using the 488, 514.5, and 1064 nm excitation lines. Density functional theory (DFT) methods were used to calculate the structure and vibrational spectra of Ag–BPy, Ag₃–BPy and Ag₄–BPy complexes with B3LYP/6-31++G(d,p)(C,H,N)/Lanl2dz(Ag) basis set. The Raman bands of BPy were assigned on the basis of the calculation of potential energy distribution. The calculated spectra of Ag–BPy and Ag₄–BPy complexes were much closer to the experimental results of BPy adsorbed on silver surface than that of Ag₃–BPy complexes. The vibrational frequencies that are sensitive to the planar or non-planar structure of BPy and to the dihedral angle of two pyridyl rings were discussed. The DFT results showed that the angles between two pyridyl rings for Ag–BPy and Ag₄–BPy were skewed by about 38.44° and 37.1°, respectively. The energy gaps of the HOMO and LUMO from DFT were 415–912 nm for BPy–Ag complexes. The relative intensities of SERS bands changed with different excitation laser lines. Thus, a chemical enhancement mechanism should play an important role in the SERS of BPy on silver substrate.