A perspective on the localizability of Hartree–Fock orbitals

A common perception about molecular systems with a nonlocal electronic structure (as manifested by a nonlocal Hartree–Fock (HF) density matrix), such as conjugated π-systems, is that they can only be described in terms of nonlocal molecular orbitals. This view is mostly founded on chemical intuition, and further, this view is strengthened by traditional approaches for obtaining local occupied and virtual orbital spaces, such as the occupied Pipek–Mezey orbitals, and projected atomic orbitals. In this article, we discuss the limitations for localizability of HF orbitals in terms of restrictions posed by the delocalized character of the underlying density matrix for the molecular system and by the orthogonality constraint on the molecular orbitals. We show that the locality of the orbitals, in terms of nonvanishing charge distributions of orbitals centered far apart, is much more strongly affected by the orthogonality constraint than by the physical requirement that the occupied orbitals must represent the electron density. Thus, the freedom of carrying out unitary transformations among the orbitals provides the flexibility to obtain highly local occupied and virtual molecular orbitals, even for molecular systems with a nonlocal density matrix, provided that a proper localization function is used. As an additional consideration, we clear up the common misconception that projected atomic orbitals in general are more local than localized orthogonal virtual orbitals.     

Electronic,optical, and charge transport properties of A-π-A electron acceptors for organic solar cells: Impact of anti-aromatic π structures

Anti-aromatization and isomerization are found to be an effective way to tune the optoelectronic properties of A-π-A electron acceptors for organic photovoltaics.     

Theoretical study of novel porphyrins bearing electron donor–acceptor groups

This research project is focused on molecules that comprise a series of asymmetrically A₃B‐type meso‐substituted free‐base porphyrins and their related Zn‐metalloporphyrins. A and B were taken as electron‐donor and electron–acceptor groups. Full geometry optimizations without symmetry constrains were performed with B3LYP/6‐31G(d,P) methodology. Time‐dependent density functional theory calculations of the optimized structures indicate that there is a good agreement with the available experimental results. The highest occupied molecular orbital–lowest occupied molecular orbital (LUMO) gaps (ranging between 2.62 and 2.80 eV) are similar to those reported before for other porphyrins (2.29 eV). Also, the LUMO is situated close to the conduction band of titanium oxide, increasing the possibility of a charge transfer process. As porphyrins may act as electron transfer systems, the electron donor–acceptor capacity of these systems is characterized using two parameters; electrodonating (χ?) and electroaccepting (χ+) electronegativity. The main goal of this investigation is to analyze the electronic structure and the donor–acceptor properties of these porphyrins to see if these compounds could be useful for further applications related to the design of solar cells. © 2012 Wiley Periodicals, Inc.     

Photoelectron spectra,penning ionization electron spectra,and character of canonical molecular orbitals

When canonical molecular orbitals are expanded in terms of a set of localized molecular orbital building blocks, called bond orbitals, the character of the canonical molecular orbitals can be characterized according to the component bond orbitals resembling the core, lone pair, and localized bond building blocks in an intuitive Lewis structure. Weinhold's natural bond orbital method can produce a unique Lewis structure with total occupancy of its occupied bond orbitals exceeding 99.9% of the total electron density for simple molecules. Two useful indices, Lewis bond order and weight of lone pair orbitals, can be defined according to the weights of the bonding and lone pair components of this unique Lewis structure. Calculation results for molecules N₂, CO, CS, NO, HCN, C₂H₂, H₂O, and H₂S show that the former index can account for the vibrational structures of photoelectron spectroscopy, whereas the latter index can account for the band intensity enhancement of Penning ionization electron spectroscopy. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 882–892, 1998     

Photoinduced electron and hole transfer involving eosin conjugates of tryptophan derivatives

The preparation of several covalent conjugates of the dye, eosin Y (EY^2-) with the amino acid, L-tryptophan (Trp), the dipeptide, Trp-Trp, and with poly(L)-tryptophan is described. Intramolecular photochemical electron transfer is responsible for the quenching of dye excited singlet states (flourescence) in these systems. The sacrificial acceptor, tetranitromethane (TNM), was used to irreversibly oxidize pendant dye groups; the transfer of charge (“holes”) from the oxidized eosin moiety located at the N-terminus of the peptides was monitored by laser flash photolysis. Both modes of electron transfer involve charge transfer from indole side chains associated with Trp groups for the various peptide links. Study of the kinetics of hole transfer provided rate constants in the range of 103–104 s^-1 for several solvent media including aqueous poly(vinylpyrrolidinone) (PVP), a polymer that provides a protein-like microdomain. The observed temperature dependence of the hole transfer rate is consistent with non-adiabatic electron transfer over distances determined by molecular modeling to be about 1.0 nm (through-space) and involving through-bond interactions via a network of σ-π overlaps. Findings are discussed in terms of demonstration of the entrainment of charge along peptide chains and the efficient separation of charge in (bio)polymer structures of some size that display vectorial properties.     

Mutually exclusive hole and electron transfer coupling in cross stacked acenes

The topology of frontier molecular orbitals (FMOs) induces highly sensitive charge transfer coupling with variation in the intermolecular arrangement. A consistent optoelectronic property correlated to a specific aggregate architecture independent of the nature of the monomer is a rare phenomenon. Our theoretical investigation on stacked dimeric systems of linear [n]acenes (n = 2–5) and selected non-linear acenes with a D_2h point group reveals that the Greek cross (+) stacked orientation, irrespective of the molecular candidate, exhibits mutually exclusive hole and electron transfer couplings. The deactivation of either hole or electron transfer coupling is a consequence of the zero inter-orbital overlap between the highest occupied molecular orbitals (HOMOs) or lowest unoccupied molecular orbitals (LUMOs) of the monomers possessing gerade symmetry. In the Greek cross (+) stacked alignment, the (4n + 2) π-electronic acene systems with an odd number of benzenoids exhibit exclusive electron transfer coupling, while the even numbered acenes exhibit selective hole transfer coupling. The trend is reversed for representative 4n π-electronic acene systems. The effect of mutually exclusive charge transfer coupling in the hopping regime of charge transport was evaluated using semiclassical Marcus theory, and selective charge carrier mobility was exhibited by the Greek cross (+) stacks of the considered acene candidates. Additionally, the characteristic charge transfer coupling of the orthogonal acene stacks resulted in negligible short-range exciton coupling, inciting null exciton splitting at short interplanar distances. Engineering chromophores in precise angular orientations ensuring characteristic emergent properties can have tremendous potential in the rational design of advanced optoelectronic materials.

Acenes in the Greek cross (+) stack orientation exhibit selective hole and electron transfer coupling based on gerade symmetry in frontier molecular orbitals.     

Not Guilty on Every Count: The “Non‐Innocent” Nitrosyl Ligand in the Framework of IUPAC′s Oxidation‐State Formalism

Nitrosyl–metal bonding relies on the two interactions between the pair of N–O‐π* and two of the metal's d orbitals. These (back)bonds are largely covalent, which makes their allocation in the course of an oxidation‐state determination ambiguous. However, apart from M‐N‐O‐angle or net‐charge considerations, IUPAC′s “ionic approximation” is a useful tool to reliably classify nitrosyl metal complexes in an orbital‐centered approach.     

Theoretical study of electron transfer in Rhodobacter sphaeroides reaction center

We investigate the substitution effects on electron transfer in Rhodobacter (Rb.) sphaeroides reaction center using ab initio calculations. The overlap of molecular orbitals in the X-ray structure of 1PCR of the protein data bank using Gaussian09 can qualitatively explain the tendency of the experimental transition time. The charge effects of proteins on electron transfer in Rb. sphaeroides reaction center are also investigated, by employing a simple point charge approximation for proteins. We have found that the primary effect for the route A orientation is the effect of long side chains. For the route A orientation on the electron transfer, the influence of the charges of proteins operates through the long side chains indirectly as well as directly work to increase the value of overlap integrals.     

Molecular design of a “molecular syringe” mimic for metal cations using a 1,3‐alternate calix[4]arene cavity

The chemically switchable actions well imitate the function of a “molecular syringe,” has been studied in theory using the 1,3‐alternate calix [4]arene bearing a nitrogen‐containing crown cap at one side and a bis(ethoxyethoxy) group at another side by the π‐basic calixtube as a pipette and the crown ring as a rubber cap. The model is characterized by geometry optimization using density functional theory (DFT) at B3LYP/6‐31G level. The obtained optimized structures are used to perform natural bond orbital (NBO) and frequency analysis. The electron‐donating heteroatoms: O and N offer lone pair electrons to the contacting RY* (1‐center Rydberg) or LP* (1‐center valence antibond lone pair) orbitals of K⁺, Ag⁺. The results indicate that when the nitrogen atom in the crown ring is protonated, K⁺ and Ag⁺ will be pushed out to the bis(ethoxyethoxy) side through a π‐basic calixtube. When the nitrogen·H⁺ in the crown ring is deprotonated, K⁺ and Ag⁺ are sucked back to the crown‐capped side again. In the course of the coordination, both the intermolecular electrostatic interactions and the cation‐π interactions between the metal ion and π‐orbitals of the two pairs facing inverted benzene rings play a significant role. It is believed that this prototype of a “molecular syringe” is a novel molecular architecture for the action of metal cations. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

The role of supporting electrolyte in heterogeneous electron transfer

The effects of supporting electrolyte on the kinetics of the elementary step of electron transfer are considered as unavoidable interplay of interfacial phenomena and ionic equilibria in solution. For the former, the problems to separate contributions of electrostatic electrode-reactant interactions and specific adsorption are addressed, and various aspects of the traditional Frumkin correction (“psi-prime effect”) are discussed. The construction of corrected Tafel plots is shown to be a procedure containing the internal contradiction resulting in an uncertainty. This uncertainty can be eliminated by combining the principles of traditional analysis of the “double layer” effects with physical theory instead of phenomenological approaches. Specific manifestations of parallel electron transfer to an ensemble of reacting species are presented in the context of “mean reactant charge in solution bulk.” The approach to account for non-spherical shape and inhomogeneous charge distribution in reacting species is considered in terms of “molecular psi-prime effect.” Finally, some comments are given on analogy of “double layer” effects at metal/solution interface and interfacial phenomena specific for more complex and highly relevant electrochemical systems.     

Role of electronic structure of ruthenium polypyridyl dyes in the photoconversion efficiency of dye‐sensitized solar cells: Semiempirical investigation

ZINDO/S calculations on cis‐Ru(4,4′‐dicarboxy‐2,2′‐bipyridine)₂(X)₂ and cis‐Ru(5,5′‐dicarboxy‐2,2′‐bipyridine)₂(X)₂ complexes where X = Cl^?, CN^?, and NCS^? reveal that the highest occupied molecular orbital (HOMO) of these complexes has a large amplitude on both the nonchromophoric ligand X and the central ruthenium atom. The lowest‐energy metal to ligand charge transfer (MLCT) transition in these complexes involves electron transfer from ruthenium as well as the halide/pseudohalide ligand to the polypyridyl ligand. The contribution of the halide/pseudohalide ligand(X) to the HOMO affects the total amount of charge transferred to the polypyridyl ligand and hence the photoconversion efficiency. The virtual orbitals involved in the second MLCT transition in 4,4′‐dicarboxy‐2,2′‐bipyridine complexes have higher electron density on the ? COOH group compared to the lowest unoccupied molecular orbital and hence a stronger electronic coupling with the TiO₂ surface and higher injection efficiency at shorter wavelengths. In comparison, the virtual orbitals involved in the second MLCT transition in 5,5′‐dicarboxy‐2,2′‐bipyridine complexes have lesser electron density on the ? COOH group, leading to a weaker electronic coupling with the TiO₂ surface and therefore lower efficiency for electron injection at shorter wavelengths for these complexes. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

A “vertex electron pair” scheme (VEPS) for describing the skeletal electron distribution in borane-type clusters

A predominantly localized electron pair scheme is outlined for describing the electron distribution and bonding in closo borane anions B_nH_n²⁻ and related electron deficient deltahedral clusters, in which a skeletal electron pair is assigned to each vertex, one pair being regarded as delocalized just inside the roughly spherical surface on which the skeletal atoms lie. The scheme gives a clearer picture of the electron distribution than is conveyed by resonating 2- and 3-centre bonds in the polyhedron edges and faces, and allows the bond orders of the polyhedron edge links to be calculated readily. The consequence of formal removal of BH²⁺ units from closo species B_nH_n²⁻ to generate nido species B_n−1H_n−1⁴⁻ and arachno species B_n−2H_n−2⁶⁻ is explored, and seen to allow rationalization of two features of such deltahedral-fragment clusters: (i) why a high-connectivity vertex is left vacant and (ii) why the frontier orbitals of such species concentrate electronic charge around their open faces. Moreover, in the case of D_4‘h B₄H₄⁶⁻ (cf. C₄H₄²⁻) and D_5h B₅H₅⁶⁻ (cf. C₅H₅⁻), the approach leads directly to the familiar picture for aromatic ring systems in which the highest filled, doubly degenerate π-bonding molecular orbital concentrates electronic charge in rings above and below the polygon on which the skeletal nuclei lie. It also leads to the expectation that arachno clusters with non-adjacent vacant vertices will be more stable than those with adjacent vacant vertices.     

NMR shielding tensors for density fitted local second-order Mo̸ller-Plesset perturbation theory using gauge including atomic orbitals

An efficient method for the calculation of nuclear magnetic resonance (NMR) shielding tensors is presented, which treats electron correlation at the level of second-order Mo?ller-Plesset perturbation theory. It uses spatially localized functions to span occupied and virtual molecular orbital spaces, respectively, which are expanded in a basis of gauge including atomic orbitals (GIAOs or London atomic orbitals). Doubly excited determinants are restricted to local subsets of the virtual space and pair energies with an interorbital distance beyond a certain threshold are omitted. Furthermore, density fitting is employed to factorize the electron repulsion integrals. Ordinary Gaussians are employed as fitting functions. It is shown that the errors in the resulting NMR shielding constant, introduced (i) by the local approximation and (ii) by density fitting, are very small or even negligible. The capabilities of the new program are demonstrated by calculations on some extended molecular systems, such as the cyclobutane pyrimidine dimer photolesion with adjacent nucleobases in the native intrahelical DNA double strand (ATTA sequence). Systems of that size were not accessible to correlated ab initio calculations of NMR spectra before. The presented method thus opens the door to new and interesting applications in this area.     

The structure of the hydrated electron. Part 2. A mixed quantum/classical molecular dynamics embedded cluster density functional theory: single-excitation configuration interaction study

Adiabatic mixed quantum/classical (MQC) molecular dynamics (MD) simulations were used to generate snapshots of the hydrated electron in liquid water at 300 K. Water cluster anions that include two complete solvation shells centered on the hydrated electron were extracted from the MQC MD simulations and embedded in a roughly 18 Ax18 Ax18 A matrix of fractional point charges designed to represent the rest of the solvent. Density functional theory (DFT) with the Becke-Lee-Yang-Parr functional and single-excitation configuration interaction (CIS) methods were then applied to these embedded clusters. The salient feature of these hybrid DFT(CIS)/MQC MD calculations is significant transfer (approximately 18%) of the excess electron's charge density into the 2p orbitals of oxygen atoms in OH groups forming the solvation cavity. We used the results of these calculations to examine the structure of the singly occupied and the lower unoccupied molecular orbitals, the density of states, the absorption spectra in the visible and ultraviolet, the hyperfine coupling (hfcc) tensors, and the infrared (IR) and Raman spectra of these embedded water cluster anions. The calculated hfcc tensors were used to compute electron paramagnetic resonance (EPR) and electron spin echo envelope modulation (ESEEM) spectra for the hydrated electron that compared favorably to the experimental spectra of trapped electrons in alkaline ice. The calculated vibrational spectra of the hydrated electron are consistent with the red-shifted bending and stretching frequencies observed in resonance Raman experiments. In addition to reproducing the visible/near IR absorption spectrum, the hybrid DFT model also accounts for the hydrated electron's 190-nm absorption band in the ultraviolet. Thus, our study suggests that to explain several important experimentally observed properties of the hydrated electron, many-electron effects must be accounted for: one-electron models that do not allow for mixing of the excess electron density with the frontier orbitals of the first-shell solvent molecules cannot explain the observed magnetic, vibrational, and electronic properties of this species. Despite the need for multielectron effects to explain these important properties, the ensemble-averaged radial wavefunctions and energetics of the highest occupied and three lowest unoccupied orbitals of the hydrated electrons in our hybrid model are close to the s- and p-like states obtained in one-electron models. Thus, one-electron models can provide a remarkably good approximation to the multielectron picture of the hydrated electron for many applications; indeed, the two approaches appear to be complementary.     

Pipek–Mezey localization of occupied and virtual orbitals

Recent advances in orbital localization algorithms are used to minimize the Pipek–Mezey localization function for both occupied and virtual Hartree–Fock orbitals. Virtual Pipek–Mezey orbitals for large molecular systems have previously not been considered in the literature. For this work, the Pipek–Mezey (PM) localization function is implemented for both the Mulliken and a Löwdin population analysis. The results show that the standard PM localization function (using either Mulliken or Löwdin population analyses) may yield local occupied orbitals, although for some systems the occupied orbitals are only semilocal as compared to state‐of‐the‐art localized occupied orbitals. For the virtual orbitals, a Löwdin population analysis shows improvement in locality compared to a Mulliken population analysis, but for both Mulliken and Löwdin population analyses, the virtual orbitals are seen to be considerably less local compared to state‐of‐the‐art localized orbitals. © 2013 Wiley Periodicals, Inc.     

Electronic properties of metal-modified DNA base pairs

The electronic properties of several metal-modified Watson-Crick guanine-cytosine base pairs are investigated by means of first-principle density functional theory calculations. Focus is placed on a new structure recently proposed as a plausible model for building an antiparallel duplex with Zn-guanine-cytosine pairs, but we also inspect several other conformations and the incorporation of Ag and Cu ions. We analyze the effects induced by the incorporation of one metal cation per base pair by comparing the structures and the electronic properties of the metalated pairs to those of the natural guanine-cytosine pair, particularly for what concerns the modifications of energy levels and charge density distributions of the frontier orbitals. Our results reveal the establishment of covalent bonding between the metal cation and the nucleobases, identified in the presence of hybrid metal-guanine and metal-cytosine orbitals. Attachment of the cation can occur either at the N1 or the N7 site of guanine and is compatible with altering or not altering the H-bond pattern of the natural pair. Cu(II) strongly contributes to the hybridization of the orbitals around the band gap, whereas Ag(I) and Zn(II) give hybrid states farther from the band gap. Most metalated pairs have smaller band gaps than the natural guanine-cytosine pair. The band gap shrinking along with the metal-base coupling suggests interesting consequences for electron transfer through DNA double helices.