Zheng-Li Cai

Failure of density-functional theory and time-dependent density-functional theory for large extended π systems

Density-functional theory (DFT) is widely used for studying large systems such as metals, semiconductors, and large molecules, with time-dependent density-functional theory becoming a very powerful tool for investigating molecular excited states. As part of a systematic study of both the intrinsic weaknesses of DFT and the weaknesses of present implementations, we consider its application to the one and two-dimensional conjugated π systems: polyacetylene fragments and oligoporphyrins, respectively. Very poor results are obtained for the calculated spectra, and polyacetylene is predicted by all functionals considered, including gradient-corrected functionals, to have a triplet ground state. The cause of this is linked to known problems of existing density functionals concerning nonlocality and asymptotic behavior which result in the highest-occupied molecular-orbital being too high in energy so that semiconductors and low-band-gap insulators are predicted to have metal-like properties. The failure of modern density functionals to predict qualitatively realistic molecular hyperpolarizabilities for extended systems is closely related.

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

Abstract: 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 π 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.

Long-lived long-distance photochemically induced spin-polarized charge separation in β,β′-pyrrolic fused ferrocene-porphyrin-fullerene systems

The exceptionally long lived charge separation previously observed in a β,β′-pyrrolic-fused ferrocene-porphyrin-fullerene triad (lifetime 630 μs) and related porphyrin-fullerene dyad (lifetime 260 μs) is attributed to the production of triplet charge-separated states. Such molecular excited-state spin polarization maintained over distances of up to 23 A is unprecedented and offers many technological applications. Electronic absorption and emission spectra, femtosecond and nanosecond time-resolved transient absorption spectra, and cyclic voltammograms of two triads and four dyads are measured and analyzed to yield rate constants, donor–acceptor couplings, free-energy changes, and reorganization energies for charge-separation and charge-recombination processes. Production of long-lived intramolecular triplet states is confirmed by electron-paramagnetic resonance spectra at 77–223 K, as is retention of spin polarization in π-conjugated ferrocenium ions. The observed rate constants were either first predicted (singlet manifold) or later confirmed (triplet manifold) by a priori semiclassical kinetics calculations for all conceivable photochemical processes, parameterized using density-functional theory and complete-active-space self-consistent-field calculations. Identified are both a ps-timescale process attributed to singlet recombination and a μs-timescale process attributed to triplet recombination.

Demonstration and interpretation of significant asymmetry in the low-resolution and high-resolution Qy fluorescence and absorption spectra of bacteriochlorophyll a

Low- and high-resolution absorption and fluorescence emission Q(y) spectra of bacteriochlorophyll a (BChl a) were recorded, along with homogeneous band line shapes, revealing significant asymmetry between the absorption and emission profiles that are interpreted using a priori spectral calculations. The spectra were recorded in a range of organic solvents facilitating both penta- and hexa-coordination of Mg at ambient and cryogenic temperatures. Detailed vibrational structure in the ground electronic state, virtually independent of Mg coordination, was revealed at 4.5 K by a hole-burning fluorescence line-narrowing technique, complementing the high-resolution spectrum of the excited state measured previously by hole burning to provide the first complete description of the Q(y) absorption and fluorescence spectra of BChl a. Spectral asymmetry persists from 4.5 to 298 K. Time-dependent density-functional theory calculations of the gas-phase absorption and emission spectra obtained using the CAM-B3LYP density functional, curvilinear coordinates, and stretch-bend-torsion scaling factors fitted to data for free-base porphyrin quantitatively predict the observed frequencies of the most-significant vibrational modes as well as the observed absorption∕emission asymmetry. Most other semi-empirical, density-functional, and ab initio computational methods severely overestimate the electron-vibrational coupling and its asymmetry. It is shown that the asymmetry arises primarily through Duschinsky rotation.

Assignment of the Q -Bands of the Chlorophylls: Coherence Loss via Q x − Q y Mixing

We provide a new and definitive spectral assignment for the absorption, emission, high-resolution fluorescence excitation, linear dichroism, and/or magnetic circular dichroism spectra of 32 chlorophyllides in various environments. This encompases all data used to justify previous assignments and provides a simple interpretation of unexplained complex decoherence phenomena associated with Qx → Qy relaxation. Whilst most chlorophylls conform to the Gouterman model and display two independent transitions Qx (S2) and Qy (S1), strong vibronic coupling inseparably mixes these states in chlorophyll-a. This spreads x-polarized absorption intensity over the entire Q-band system to influence all exciton-transport, relaxation and coherence properties of chlorophyll-based photosystems. The fraction of the total absorption intensity attributed to Qx ranges between 7% and 33%, depending on chlorophyllide and coordination, and is between 10% and 25% for chlorophyll-a. CAM-B3LYP density-functional-theory calculations of the band origins, relative intensities, vibrational Huang-Rhys factors, and vibronic coupling strengths fully support this new assignment.

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

Over the past few years a large number of density-functional schemes have been developed for molecular excited states, many of which have been shown to produce poor results for water. We apply the time-dependent density-functional method using hybrid and asymptotically corrected functionals to evaluate the vertical excitation energies, C2v-relaxation energies and vibration frequencies, and dissociation pathways for up to eight singlet and six triplet excited states of water. The results are compared to experimental data as well as ab initio calculated data obtained using direct and equations-of-motion coupled-cluster techniques, as well as multireference configuration-interaction techniques. For most properties, the asymptotically corrected density-functional method produces results of comparable quality to those produced by the ab initio methods. However, the time-dependent methods produce very poor results for systems involving molecular dissociation. In fact, only the multireference approaches produce ...

Application of time-dependent density-functional theory to the 3Σu− first excited state of H2

Recently, time-dependent density-functional (TDDFT) methods have been developed for determining the energies of molecular excited states. This, along with the somewhat similar equations-of-motion coupled-cluster (EOM-CCSD) methods, offer advantages of speed, reliability, and often accuracy over alternate complete-active-space self-consistent-field (CASSCF) based approaches, with the disadvantages associated with being essentially “single-reference” calculations. We compare results obtained using both approaches for the 1Σg+ (ground) and 3Σu− (first excited) states of the simplest molecule, H2. For the excited state of this two-electron system, EOM-CCSD is equivalent to full configuration interaction, while results obtained using TDDFT are good at short bond lengths but become quite poor as the bond is stretched from its equilibrium length. The poor TDDFT result is attributed to the fact that the spin-restricted Kohn–Sham (RKS) method used to generate the ground-state density is not size consistent. We sug...

Examination of the Photophysical Processes of Chlorophyll d Leading to a Clarification of Proposed Uphill Energy Transfer Processes in Cells of Acaryochloris marina

A comprehensive study of the photophysical properties of chlorophyll (Chl) d in 1:40 acetonitrile–methanol solution is performed over the temperature range 170–295 K. From comparison of absorption and emission spectra, time‐dependent density‐functional calculations and homologies with those of Chl a, we assign the key features of the absorption and fluorescence spectra. Possible photophysical energy relaxation mechanisms are summarized, and thermal equilibration processes are studied in detail by monitoring the observed emission profiles and quantum yields as a function of excitation energy. In particular, we concentrate on emission subsequent to excitation in the extreme far‐red tail of the Qy absorption spectrum, with this emission partitioned into contributions from hot‐band absorptions as well as uphill energy transfer processes that occur subsequent to absorption. No unusual photophysical processes are detected for Chl d; it appears that all intramolecular relaxation processes reach thermal equilibration on shorter timescales than the fluorescence lifetime even at 170 K. The results from these studies are used to reinterpret a previous study of photochemical processes observed in intact cells and their acetone extracts of the photosynthetic system of Acaryochloris marina. In the study of Mimuro et al., light absorbed by Chl d at 736 nm is found to give rise to emission by another species, believed to also be Chl d, at 703 nm; this uphill energy transfer process is easily rationalized in terms of the thermal equilibration processes that we deduced for Chl d. However, no evidence is found in the experimental results of Mimuro et al. to support claims that (nonequilibrium) uphill energy transfer is additionally observed to Chl a species that emit at 670–680 nm. This finding is relevant to broader issues concerning the nature of the special pair in photosystem II of A. marina because suggestions that it is comprised of Chl a can only be correct if nonthermal uphill energy transfer processes from Chl d are operative.

Spectroscopic Properties of Chlorophyll f

The absorption and fluorescence spectra of chlorophyll f (newly discovered in 2010) have been measured in acetone and methanol at different temperatures. The spectral analysis and assignment are compared with the spectra of chlorophyll a and d under the same experimental conditions. The spectroscopic properties of these chlorophylls have further been studied by the aid of density functional CAM-B3LYP and high-level symmetric adapted coupled-cluster configuration interaction calculations. The main Q and Soret bands and possible sidebands of chlorophylls have been determined. The photophysical properties of chlorophyll f are discussed.

Raman spectroscopy of chlorophyll d from Acaryochloris marina

The Raman spectroscopy of chlorophyll (Chl) d isolated from Acaryochloris marina has been measured in the range of 250-3200 cm(-1) at 77 K following excitation of its B(x) band at 488 nm. A peak at 1659 cm(-1) of medium intensity arising from Cz=O stretching vibration in the formyl group 3(1) specific to Chl d was observed clearly. Peaks due to other Cz=O stretching vibrations of the 13(1) keto-, 13(3) ester- and 17(3) groups have also been observed with much weaker intensities. Intense Raman peaks in the range of 1000-1800 cm(-1) are reported and homologous comparison with corresponding Raman shifts of Chl a, Chl b and BChl a are presented.