Time-dependent density-functional determination of arbitrary singlet and triplet excited-state potential energy surfaces: Application to the water molecule

Virtual photon exchange vs electron transfer in interparticle Coulombic electron capture

We have investigated Interparticle Coulombic Electron Capture (ICEC) using an ab initio approach for two systems, H+ + H2O and H + H2O+. In this work, we have determined the contribution of virtual photon exchange and electron transfer to the total ICEC cross section as a function of the distance between the charged and neutral particles. Furthermore, we have shown that the relative orientation of the electron acceptor and neighbor systems affects the magnitude of the ICEC cross sections by at least two orders at relatively small distances. This geometry dependence, present even for distances as large as 10 a0, is due to the electron transfer contribution. The relative magnitude of each contribution to ICEC seems to depend on the system studied. By replacing the projectile electron with a positron, we have confirmed that electron transfer also takes place in positron collisions and that the charge of the projectile has a noticeable effect on the process, particularly at low scattering energies.

Density functionals with asymptotic-potential corrections are required for the simulation of spectroscopic properties of materials

Five effects of correction of the asymptotic potential error in density functionals are identified that significantly improve calculated properties of molecular excited states involving charge-transfer character. Newly developed materials-science computational methods are used to demonstrate how these effects manifest in materials spectroscopy. Connection is made considering chlorophyll-a as a paradigm for molecular spectroscopy, 22 iconic materials as paradigms for 3D materials spectroscopy, and the VN - defect in hexagonal boron nitride as an example of the spectroscopy of defects in 2D materials pertaining to nanophotonics. Defects can equally be thought of as being "molecular" and "materials" in nature and hence bridge the relms of molecular and materials spectroscopies. It is concluded that the density functional HSE06, currently considered as the standard for accurate calculations of materials spectroscopy, should be replaced, in most instances, by the computationally similar but asymptotically corrected CAM-B3LYP functional, with some specific functionals for materials-use only providing further improvements.

Rotovibrational states of the water molecule on the sun

The infrared spectrum of water observed in sunspots is complex and dense, with bands separated by approximately 0.01 cm^-1. For top asymmetrical molecules, there is no theoretical approach that allows for the calculation of rotovibrational energy with such precision. Experimentally derived rotovibracional energy levels of water at high temperatures combined with variational calculations have been used for the band assignments. These energy levels are employed to refine the analysis of a small portion of the infrared absorption spectrum. Such procedure has allowed for the identification of additional 55 bands to the 70 already identified as rotovibrational transitions of the water molecule. Our new assignments, which include pure and cross transitions, offer additional evidence of the existence of water on the sun, but above all they illustrate the complexity of the solar spectrum that involves states with higher levels of rotational excitation. Given the conditions on the sun, more molecules of water would occur in excited electronic states, which include apolar and paramagnetic states, generating intense bands in the spectrum. Since there is an analytical solution for the rotovibrational transitions of linear molecules, we were able to identify 16 bands relative to the excited electronic states ¹B₂ and ³A₁ in the sunspot spectrum. Density functional B3LYP/AUG-cc-pVTZ calculations of the electric and magnetic dipole are employed to discuss some consequences of the presence of excited states of water in the dynamics of sunspots and solar magnetic field.

Putting David Craig’s Legacy to Work in Nanotechnology and Biotechnology

David Craig (1919–2015) left us with a lasting legacy concerning basic understanding of chemical spectroscopy and bonding. This is expressed in terms of some of the recent achievements of my own research career, with a focus on integration of Craig’s theories with those of Noel Hush to solve fundamental problems in photosynthesis, molecular electronics (particularly in regard to the molecules synthesized by Maxwell Crossley), and self-assembled monolayer structure and function. Reviewed in particular is the relation of Craig’s legacy to: the 50-year struggle to assign the visible absorption spectrum of arguably the world’s most significant chromophore, chlorophyll; general theories for chemical bonding and structure extending Hush’s adiabatic theory of electron-transfer processes; inelastic electron-tunnelling spectroscopy (IETS); chemical quantum entanglement and the Penrose–Hameroff model for quantum consciousness; synthetic design strategies for NMR quantum computing; Gibbs free-energy measurements and calculations for formation and polymorphism of organic self-assembled monolayers on graphite surfaces from organic solution; and understanding the basic chemical processes involved in the formation of gold surfaces and nanoparticles protected by sulfur-bound ligands, ligands whose form is that of Au0-thiyl rather than its commonly believed AuI-thiolate tautomer.

Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations

In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N(4)). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as ⟨Ŝ(2)⟩ are also developed and tested.

Ab initio calculation of the electronic absorption spectrum of liquid water

The electronic absorption spectrum of liquid water was investigated by coupling a one-body energy decomposition scheme to configurations generated by classical and Born-Oppenheimer Molecular Dynamics (BOMD). A Frenkel exciton Hamiltonian formalism was adopted and the excitation energies in the liquid phase were calculated with the equation of motion coupled cluster with single and double excitations method. Molecular dynamics configurations were generated by different approaches. Classical MD were carried out with the TIP4P-Ew and AMOEBA force fields. The BLYP and BLYP-D3 exchange-correlation functionals were used in BOMD. Theoretical and experimental results for the electronic absorption spectrum of liquid water are in good agreement. Emphasis is placed on the relationship between the structure of liquid water predicted by the different models and the electronic absorption spectrum. The theoretical gas to liquid phase blue-shift of the peak positions of the electronic absorption spectrum is in good agreement with experiment. The overall shift is determined by a competition between the O-H stretching of the water monomer in liquid water that leads to a red-shift and polarization effects that induce a blue-shift. The results illustrate the importance of coupling many-body energy decomposition schemes to molecular dynamics configurations to carry out ab initio calculations of the electronic properties in liquid phase.

Insights into the ultraviolet spectrum of liquid water from model calculations

With a view toward a better molecular level understanding of the effects of hydrogen bonding on the ultraviolet absorption spectrum of liquid water, benchmark electronic structure calculations using high level wave function based methods and systematically enlarged basis sets are reported for excitation energies and oscillator strengths of valence excited states in the equilibrium water monomer and dimer and in a selection of liquid-like dimer structures. Analysis of the electron density redistribution associated with the two lowest valence excitations of the water dimer shows that these are usually localized on one or the other monomer, although valence hole delocalization can occur for certain relative orientations of the water molecules. The lowest excited state is mostly associated with the hydrogen bond donor and the significantly higher energy second excited state mostly with the acceptor. The magnitude of the lowest excitation energies is strongly dependent on where the valence hole is created, and only to a lesser degree on the perturbation of the excited electron density distribution by the neighboring water molecule. These results suggest that the lowest excitation energies in clusters and liquid water can be associated with broken acceptor hydrogen bonds, which provide energetically favorable locations for the formation of a valence hole. Higher valence excited states of the dimer typically involve delocalization of the valence hole and/or delocalization of the excited electron and/or charge transfer. Two of the higher valence excited states that involve delocalized valence holes always have particularly large oscillator strengths. Due to the pervasive delocalization and charge transfer, it is suggested that most condensed phase water valence excitations intimately involve more than one water molecule and, as a consequence, will not be adequately described by models based on perturbation of free water monomer states. The benchmark calculations are further used to evaluate a series of representative semilocal, global hybrid, and range separated hybrid functionals used in efficient time-dependent density functional methods. It is shown that such an evaluation is only meaningful when comparison is made at or near the complete basis set limit of the wave function based reference method. A functional is found that quantitatively describes the two lowest excitations of water dimer and also provides a semiquantitative description of the higher energy valence excited states. This functional is recommended for use in further studies on the absorption spectrum of large water clusters and of condensed phase water.

Excited state properties of liquid water

In this paper, we give an overview of the state of the art in calculations of the electronic band structure and absorption spectra of water. After an introduction to the main theoretical and computational schemes used, we present results for the electronic and optical excitations of water. We focus mainly on liquid water, but spectroscopic properties of ice and vapor phase are also described. The applicability and the accuracy of first-principles methods are discussed, and results are critically presented.

Density functional theory for charge transfer: the nature of the N-bands of porphyrins and chlorophylls revealed through CAM-B3LYP, CASPT2, and SAC-CI calculations

While density functional theory (DFT) has been proven to be extremely useful for the prediction of thermodynamic and spectroscopic properties of molecules, to date most functionals used in common implementations of DFT display a systematic failure to predict the properties of charge-transfer processes. While this is explicitly manifest in Rydberg transitions of atoms and molecules and in molecular charge-transfer spectroscopy, it also becomes critical for systems containing extended conjugation such as polyenes and other conducting polymers, porphyrins, chlorophylls, etc. A new density functional, a Coulomb-attenuated hybrid exchange-correlation functional (CAM-B3LYP), has recently been developed specifically to overcome these limitations, and it has been shown to properly predict molecular charge-transfer spectra. Here, we demonstrate that it predicts qualitatively reasonable spectra for porphyrin, some oligoporphyrins, and chlorophyll. However, alternate density functionals developed to overcome the same limitations such as current-density functional theory are shown, in their present implementation, to remain inadequate. The CAM-B3LYP results are shown to be in excellent agreement with complete-active-space plus second-order Møller-Plesset perturbation theory and symmetry-adapted cluster configuration interaction calculations: These depict the N and higher bands of porphyrins and chlorophylls as being charge-transfer bands associated with localization of molecular orbitals on individual pyrrole rings. The validity of the basic Gouterman model for the spectra of porphyrins and chlorophylls is confirmed, rejecting modern suggestions that non-Gouterman transitions lie close in energy to the Q-bands of chlorophylls. As porphyrins and chlorophylls provide useful paradigms for problems involving extended conjugation, the results obtained suggest that many significant areas of nanotechnology and biotechnology may now be realistically treated by cost-effective density-functional-based computational methods.

The Green's Function Density Functional Tight-Binding (gDFTB) Method for Molecular Electronic Conduction

A review is presented of the nonequilibrium Green's function (NEGF) method "gDFTB" for evaluating elastic and inelastic conduction through single molecules employing the density functional tight-binding (DFTB) electronic structure method. This focuses on the possible advantages that DFTB implementations of NEGF have over conventional methods based on density functional theory, including not only the ability to treat large irregular metal-molecule junctions with high nonequilibrium thermal distributions but perhaps also the ability to treat dispersive forces, bond breakage, and open-shell systems and to avoid large band lineup errors. New results are presented indicating that DFTB provides a useful depiction of simple gold-thiol interactions. Symmetry is implemented in DFTB, and the advantages it brings in terms of large savings of computational resources with significant increase in numerical stability are described. The power of DFTB is then harnessed to allow the use of gDFTB as a real-time tool to discover the nature of the forces that control inelastic charge transport through molecules and the role of molecular symmetry in determining both elastic and inelastic transport. Future directions for the development of the method are discussed.

Cross sections and oscillator strengths for electron-impact excitation of the ÃB11 electronic state of water

The authors report absolute differential and integral cross section measurements for electron-impact excitation of the A (1)B(1) electronic state of water. This is an important channel for the production of the OH (X (2)Pi) radical, as well as for understanding the origin of the atmospheric Meinel [Astrophys. J. 111, 555 (1950)] bands. The incident energy range of our measurements is 20-200 eV, while the angular range of the differential cross section data is 3.5 degrees -90 degrees . This is the first time such data are reported in the literature and, where possible, comparison to existing theoretical work, and new scaled Born cross sections calculated as a part of the current study, is made. The scaled Born cross sections are in good agreement with the integral cross sections deduced from the experimental differential cross sections. In addition they report (experimental) generalized oscillator strength data at the incident energies of 100 and 200 eV. These data are used to derive a value for the optical oscillator strength which is found to be in excellent agreement with that from an earlier dipole (e,e) experiment and an earlier photoabsorption experiment.

Electronically excited water aggregates and the adiabatic band gap of water

The authors report results for the electronic properties of the S(1) singlet excited state of H(3)O(+)[OH(H(2)O)((n-2))](-) aggregates, where n=2-5 is the number of water molecules. The energy of the excited state was defined relative to the ground state of neutral water clusters. Results for ionized aggregates are also reported. The results are based on configuration interaction with single excitations geometry optimizations followed by density functional theory and time dependent density functional theory calculations. Emphasis was placed on the relationship between electronic properties of the aggregates and the adiabatic band gap of liquid water. The authors' predictions for the adiabatic energy gap of water clusters are in the 6.01-6.55 eV range. These values are approximately 0.9-0.4 eV below the experimental adiabatic band gap of liquid water (6.9 eV). Comparison with experimental information for water is reported for several properties of interest including vertical and adiabatic ionization energies, excitation energies, photoemission thresholds, and conduction band edge. The results provide a description, at the molecular level, for the electronic properties of water aggregates that is consistent with the current picture for the band gap of bulk water [J. V. Coe, Int. Rev. Phys. Chem. 20, 33 (2001)].

Time-dependent density-functional theory calculations of triplet-triplet absorption

We present density-functional theory calculations of triplet-triplet absorption by three different approaches based on time-dependent density-functional theory (DFT): unrestricted DFT linear response, open-shell restricted DFT linear response applied to the triplet state, and quadratic response with triplet excitations applied to the ground state. Comparison is also made with corresponding results obtained by Hartree-Fock and multiconfiguration self-consistent-field response theory. Two main conclusions concerning triplet-triplet transitions are drawn in this study: First, the very good agreement between unrestricted and restricted DFT results indicates that spin contamination of the triplet state is not a serious problem when computing triplet-triplet spectra of common organic molecules. Second, DFT response calculations of triplet-triplet transitions can be affected by triplet instability problems, especially for the combination of DFT quadratic response with functionals containing fractional exact Hartree-Fock exchange.

The structure, energetics, and nature of the chemical bonding of phenylthiol adsorbed on the Au(111) surface: Implications for density-functional calculations of molecular-electronic conduction

The adsorption of phenylthiol on the Au(111) surface is modeled using Perdew and Wang density-functional calculations. Both direct molecular physisorption and dissociative chemisorption via S-H bond cleavage are considered as well as dimerization to form disulfides. For the major observed product, the chemisorbed thiol, an extensive potential-energy surface is produced as a function of both the azimuthal orientation of the adsorbate and the linear translation of the adsorbate through the key fcc, hcp, bridge, and top binding sites. Key structures are characterized, the lowest-energy one being a broad minimum of tilted orientation ranging from the bridge structure halfway towards the fcc one. The vertically oriented threefold binding sites, often assumed to dominate molecular electronics measurements, are identified as transition states at low coverage but become favored in dense monolayers. A similar surface is also produced for chemisorption of phenylthiol on Ag(111); this displays significant qualitative differences, consistent with the qualitatively different observed structures for thiol chemisorption on Ag and Au. Full contours of the minimum potential energy as a function of sulfur translation over the crystal face are described, from which the barrier to diffusion is deduced to be 5.8 kcal mol(-1), indicating that the potential-energy surface has low corrugation. The calculated bond lengths, adsorbate charge and spin density, and the density of electronic states all indicate that, at all sulfur locations, the adsorbate can be regarded as a thiyl species that forms a net single covalent bond to the surface of strength 31 kcal mol(-1). No detectable thiolate character is predicted, however, contrary to experimental results for alkyl thiols that indicate up to 20%-30% thiolate involvement. This effect is attributed to the asymptotic-potential error of all modern density functionals that becomes manifest through a 3-4 eV error in the lineup of the adsorbate and substrate bands. Significant implications are described for density-functional calculations of through-molecule electron transport in molecular electronics.

Single molecule conductivity: The role of junction-orbital degeneracy in the artificially high currents predicted by ab initio approaches

A priori evaluations, using Hartree-Fock self-consistent-field (SCF) theory or density-functional theory (DFT), of the current passing between two electrodes through a single bridging molecule result in predicted conductivities that may be up to one to two orders of magnitude larger than observed ones. We demonstrate that this is, in part, often due to the improper application of the computational methods. Conductivity is shown to arise from tunneling between junction states of the electrodes through the molecule; these states are inherently either quasi two-fold or four-fold degenerate and always comprise the (highest occupied molecular orbital) HOMO band at the Fermi energy of the system. Frequently, in previous cluster based molecular conduction calculations, closed-shell SCF or Kohn-Sham DFT methods have been applied to systems that we demonstrate to be intrinsically open shell in nature. Such calculations are shown to induce artificial HOMO-LUMO (LUMO-lowest unoccupied molecular orbital) band splittings that Landauer-based formalisms for steady-state conduction interpret as arising from extremely rapid through-molecule tunneling at the Fermi energy, hence, overestimating the low-voltage conductivity. It is demonstrated that these shortcomings can be eliminated, dramatically reducing calculated current magnitudes, through the alternate use of electronic-structure calculations based on the spin-restricted open-shell formalism and related multiconfigurational SCF of DFT approaches. Further, we demonstrate that most anomalies arising in DFT implementations arise through the use of hybrid density functionals such as B3LYP. While the enhanced band-gap properties of these functionals have made them the defacto standard in molecular conductivity calculations, we demonstrate that it also makes them particularly susceptible to open-shell anomalies.

A global investigation of excited state surfaces within time-dependent density-functional response theory

This work investigates the capability of time-dependent density functional response theory to describe excited state potential energy surfaces of conjugated organic molecules. Applications to linear polyenes, aromatic systems, and the protonated Schiff base of retinal demonstrate the scope of currently used exchange-correlation functionals as local, adiabatic approximations to time-dependent Kohn-Sham theory. The results are compared to experimental and ab initio data of various kinds to attain a critical analysis of common problems concerning charge transfer and long range (nondynamic) correlation effects. This analysis goes beyond a local investigation of electronic properties and incorporates a global view of the excited state potential energy surfaces.

The Appropriateness of Density-Functional Theory for the Calculation of Molecular Electronics Properties

As molecular electronics advances, efficient and reliable computation procedures are required for the simulation of the atomic structures of actual devices, as well as for the prediction of their electronic properties. Density-functional theory (DFT) has had widespread success throughout chemistry and solid-state physics, and it offers the possibility of fulfilling these roles. In its modern form it is an empirically parameterized approach that cannot be extended toward exact solutions in a prescribed way, ab initio. Thus, it is essential that the weaknesses of the method be identified and likely shortcomings anticipated in advance. We consider four known systematic failures of modern DFT: dispersion, charge transfer, extended pi conjugation, and bond cleavage. Their ramifications for molecular electronics applications are outlined and we suggest that great care is required when using modern DFT to partition charge flow across electrode-molecule junctions, screen applied electric fields, position molecular orbitals with respect to electrode Fermi energies, and in evaluating the distance dependence of through-molecule conductivity. The causes of these difficulties are traced to errors inherent in the types of density functionals in common use, associated with their inability to treat very long-range electron correlation effects. Heuristic enhancements of modern DFT designed to eliminate individual problems are outlined, as are three new schemes that each represent significant departures from modern DFT implementations designed to provide a priori improvements in at least one and possible all problem areas. Finally, fully semiempirical schemes based on both Hartree-Fock and Kohn-Sham theory are described that, in the short term, offer the means to avoid the inherent problems of modern DFT and, in the long term, offer competitive accuracy at dramatically reduced computational costs.

An atomistic approach to conduction between nanoelectrodes through a single molecule

Capacitance and other properties of nanoelectrodes, finite-size metal clusters envisaged for use in complex molecular-electronic devices, are discussed. The applicability of classical electrostatics (Coulomb's and Gauss' law, Poisson's equation, etc.) to atomistic systems is investigated and the self-energy necessary to store a finite charge on an atom is found to be of central importance. In particular, the neglect of electron exchange is found to introduce severe limitations, with quantum calculations predicting fundamentally different electronic structures. Also, the well-known poor representation of the atomic self-energy inherent to modern DFT is discussed, along with its implications for molecular electronics calculations. An INDO/S method is introduced with new parameters for gold. This is the simplest approximate computational scheme that correctly includes quantum electrostatic, resonance, and spin effects, and is capable of describing arbitrary excited electronic states. Encouraging results are obtained for some trial problems. In particular, voltage differential between the electrodes in electrode-molecule-electrode conduction is obtained, not through an a priori prescription but rather by moving whole electrons between the electrodes and analyzing the response. The voltage drops across the molecule-electrode junctions and the central molecular region are then deduced. This alternative to the current Landauer-based 1-particle transmission equations for electrode-molecule-electrode conduction is discussed in terms of the use of the electronic states of the system. It provides a proper description not only of conduction via electrode-to-molecule charge or hole transfer but also of conduction via simultaneous charge and hole transfer via low-lying excited molecular electronic states, including the ability to account for electroluminescence and other chemical effects. In addition, various aspects of our research on the quantitative prediction of the I(V) curves for electrode-molecule-electrode conduction are reviewed, including demonstration of the equivalence of the formalisms generated by the Datta and the Mujica-Ratner groups, and the development of analytically solvable paradigms, including the conduction through a linear-chain Hückel wire.