Browsing by Author "Beratan, David N"

Biological electron transfer (ET) reactions are typically described in the framework of coherent two-state electron tunneling or multi-step hopping. Yet, these ET reactions may involve multiple redox cofactors in van der Waals contact with each other and with vibronic broadenings on the same scale as the energy gaps among the species. In this regime, fluctuations of the molecule and its medium can produce transient energy level matching among multiple electronic states. This transient degeneracy, or flickering electronic resonance among states, is found to support coherent (ballistic) charge transfer. Importantly, ET rates arising from a flickering resonance (FR) mechanism will decay exponentially with distance because the probability of energy matching multiple states is multiplicative. The distance dependence of FR transport thus mimics the exponential decay that is usually associated with electron tunneling, although FR transport involves real carrier population on the bridge and is not a tunneling phenomenon. Likely candidates for FR transport are macromolecules with ET groups in van der Waals contact: DNA, bacterial nanowires, multi-heme proteins, strongly coupled porphyrin arrays, and proteins with closely packed redox-active residues. The theory developed here is used to analyze DNA charge-transfer kinetics, and we find that charge transfer distances up to 3-4 bases may be accounted for with this mechanism. Thus, the observed rapid (exponential) distance dependence of DNA ET rates over distances of ≲10 Å does not necessarily prove a tunneling mechanism.

Molecular structures that direct charge transport in two or three dimensions could help to enable the development of molecule-based electrical switches and gates. As a step toward this goal, we use theory, modeling and simulation to explore DNA three-way junctions (TWJs). Molecular dynamics (MD) simulations and quantum calculations, indicate that DNA TWJs undergo dynamic interconversion among “well stacked” conformations on the time scale of nanoseconds, a feature that makes the junctions very different from linear DNA duplexes. The studies further indicate that this conformational gating would control charge flow through these TWJs, distinguishing them from conventional (larger size scale) gated devices. Simulations also find that structures with polyethylene glycol (PEG) linking groups (“extenders”) lock conformations that favor CT for 25 ns or more. The simulations explain the kinetics observed experimentally in TWJs and rationalize their transport properties compared to double-stranded DNA. Furthermore, we redesigned DNA TWJs that have equally coupled output pathways for charge. The TWJ was also designed to switch between the two conductive states in responsive to an applied electric field.

Computationally aided drug discovery confronts the problem to balance performance and computation cost. Earlier study reveals that a less-expensive docking approach is not reliable to estimate the protein-ligand affinity in exploring drug candidates targeting CARM1 (coactivator-associated arginine methyltransferase 1). However, more accurate binding free energy calculation based on molecular dynamics sampling is not affordable in a high throughput screening. A truncated MD method was developed and can be used to estimate the binding free energy with similar accuracy with the full-system MD methods, while reducing the computation cost ten fold. Thus, this truncated MD method is feasible in a high throughput screening towards drug discovery.

Molecular recognition is arguably the most elementary physical process essential for life that arises at the molecular scale. Molecular recognition drives events across virtually all length scales, from the folding of proteins and binding of ligands, to the organization of membranes and the function of muscles. Understanding such events at the molecular level is massively complicated by the unique medium in which life occurs: water. In contrast to recognition in non-aqueous solvents, which are driven largely by attractive interactions between binding partners, binding reactions in water are driven in large measure by the properties of the medium itself. Aqueous binding involves the loss of solute-solvent interactions (desolvation) and the concomitant formation of solute-solute interactions. Despite decades of research, aqueous binding remains poorly understood, a deficit that profoundly limits our ability to design effective pharmaceuticals and new enzymes. Particularly problematic is understanding the energetic consequences of aqueous desolvation, an area the Toone and Beratan groups have considered for many years.

In this dissertation, we embark on a quest to shed new light on aqueous desolvation from two perspectives. In one component of this research, we improve current computational tools to study aqueous desolvation, employing quantum mechanics (QM), molecular dynamics (MD) and Monte Carlo (MC) simulations to better understand the behavior of water near molecular surfaces. In the other, we use a synthetic host, cucurbit[7]uril (CB[7]), in conjunction with a de novo series of ligands to study the structure and thermodynamics of aqueous desolvation in the context of ligand binding with atomic precision, a feat hitherto impossible. A simple and rigid macrocycle, CB[7] alleviates the drawbacks of protein systems for the study of aqueous ligand binding, that arise from conformational heterogeneity and prohibitive computational costs to model.

We first constructed a novel host-guest system that facilitates internalization of the trimethylammonium (methonium) group from bulk water to the hydrophobic cavity of CB[7] with precise (atomic-scale) control over the position of the ligand with respect to the cavity. The process of internalization was investigated energetically using isothermal titration microcalorimetry and structurally by nuclear magnetic resonance (NMR) spectroscopy. We show that the transfer of methonium from bulk water to the CB[7] cavity is accompanied by an unfavorable desolvation enthalpy of just 0.49±0.27 kcal*mol-1, a value significantly less endothermic than those values suggested from previous gas-phase model studies. Our results offer a rationale for the wide distribution of methonium in biology and demonstrate important limitations to computational estimates of binding affinities based on simple solvent-accessible surface area approaches.

To better understand our experimental results, we developed a two-dimensional lattice model of water based on random cluster structures that successfully reproduces the temperature-density anomaly of water with minimum computational cost. Using reported well-characterized ligands of CB[7], we probed water structure within the CB[7] cavity and identified an energetically perturbed cluster of water. We offer both experimental and computational evidence that this unstable water cluster provides a significant portion of the driving force for encapsulation of hydrophobic guests.

The studies reported herein shed important light on the thermodynamic and structural nature of aqueous desolvation, and bring our previous understanding of the hydrophobic effect based on ordered water and buried surface area into question. Our approach provides new tools to quantify the thermodynamics of functional group desolvation in the context of ligand binding, which will be of tremendous value for future research on ligand/drug design.

Biological signaling via DNA-mediated charge transfer between high-potential [4Fe4S]2+/3+ clusters is widely discussed in the literature. Recently, it was proposed that for DNA replication on the lagging strand, primer handover from primase to polymerase α is facilitated by DNA-mediated charge transfer between the [4Fe4S] clusters housed in the respective C-terminal domains of the proteins. Using a theoretical-computational approach, I established that redox signaling between the clusters in primase and polymerase α cannot be accomplished solely by DNA-mediated charge transport, due to the unidirectionality of charge transfer between the [4Fe4S] cluster and the nucleic acid. I extended the study by developing an open-source electron hopping pathway search code to characterize hole hopping pathways in proteins and nucleic acids. I used this module to analyze protective hole escape routes in cytochrome p450, cytochrome c oxidase, and benzylsuccinate synthase. Next, I used the module to analyze molecular dynamics snapshots of a mutant primase, where the Y345C mutation (found in gastric tumors) attenuates charge transfer between the [4Fe4S] cluster and nucleic acid, which in turn, could disrupt the signaling process between primase and polymerase α. In another protein-nucleic acid system, I found that charge transfer in the p53-DNA complex plays an important role for p53 to differentiate Gadd45 DNA and p21 DNA in metabolic pathway regulation. Using density functional theory calculations on molecular dynamics snapshots, I found that hole transfer (HT) from Gadd45 DNA to the proximal cysteine residue in the DNA-binding domain of p53 is preferred over HT from p21 DNA to cysteine. This preference ensures that the p21 DNA remains bound to the transcription factor p53 which induces the transcription of the gene under cellular oxidative stress. This dissertation concludes with a study that demonstrates similar electron conductivities between an artificial nucleic acid, 2'-deoxy-2'-fluoro-arabinonucleic acid (2’F-ANA), and DNA. Compared to DNA, 2’F-ANA offers the additional benefit of chemical stability with respect to hydrolysis and nuclease degradation, thereby promoting its use as a sensor in biological systems and cellular environments.

Quantum dots (QDs), being semiconductor particles small enough to exhibit quantum mechanical properties, are leveraged in numerous applications including energy harvesting, quantum computing, and biomedical imaging. Our research theoretically examined two functional QD systems: (1) first one undergoes the electron transfer (ET) between CdSe QDs facilitated by a solvent and linker molecule, and (2) a second performs charge transfer (CT) and triplet energy transfer (TET) between CdSe/CdS core/shell QDs and ligand acceptor. These processes were scrutinized based on the electronic coupling tunneling through the shell, reaction free energy change, and reorganization energy. Furthermore, we explored chiral imprinting mechanism in perovskite nanoplatelet and the ET dynamics of organic molecules with pathway interferences.We devised a discrete variable representation (DVR) method to simulate ET between CdSe QDs, mediated by a solvent and a linker molecule. Employing the effective mass approximation (EMA), we characterized the QDs, ligand, and solvent, studying the distance dependence of donor-acceptor coupling via the energy splitting method. We found that the ET coupling decreases exponentially with the interdot distance. The decay constant is dictated by the size of the linker and the tunneling barrier through the solvent and ligand. When the donor and acceptor sizes significantly iv surpass the diameter of the linker, such as in large QDs with an alkane chain linker, the ET is predominantly regulated by through-solvent tunneling. The DVR method was also applied to simulate the CdSe/CdS core/shell QD system. Notably, experiments observe a subtle TET rate decay with an increase in shell thickness. Simulating QDs of varying shell thickness, we found a large TET coupling decay constant. Marcus analysis finds that the QD TET operates in a deeply inverted regime, where an increase in shell thickness reduces the driving force, leading to a significant increase of the Franck-Condon factor. This in turn offsets the exponential decrease of the electronic coupling with shell thickness. Further, our findings demonstrated that variations in shell thickness could further decrease the TET rate decay constant. Applying density functional theory (DFT) calculations and a charge-perturbed- particle-in-box model, we investigated chiral imprinting of perovskite nanoplatelet by chiral ligands. We found that the imprinted CD signal is sensitive to the orientation of the chiral ligand. As the proportion of chiral surface ligands grows, our model calculations find that the intensity of the CD signal from the lowest energy exciton transition saturates. v

We also examined the effects of light polarization on the ET yield in the coherent limit, using a model Zinc porphyrin as the ET donor due to its near degenerate excited states and orthogonal transition dipole moments. These two donor excited states, coupling to the acceptor state, produce pathway interference that strongly impact the ET. Introducing dissipation due to system-environment interaction via the Lindblad equation, we found that the ET yield is influenced by the initial light polarization. In the DA system, linearly polarized light (LPL) is predicted to induce an ET yield difference of up to 85% with a 100 fs dephasing time, while the yield difference elicited by R- circularly polarized light (R-CPL) and L-circularly polarized light (L-CPL) was insignificant. The model Hamiltonian was subsequently simulated and the dynamics was predicted by our collaborators with a trapped ion qutrit system.

System-environment interactions are essential in determining charge-transfer (CT) rates and mechanisms. We developed a computationally accessible

method, suitable to simulate CT in flexible molecules (i.e., DNA) with hundreds of

sites, where the system-environment interactions are explicitly treated with numerical

noise modeling of time-dependent site energies and couplings. The properties of the

noise are tunable, providing us a flexible tool to investigate the detailed effects of

correlated thermal fluctuations on CT mechanisms. The noise is parameterizable by

molecular simulation and quantum calculation results of specific molecular systems,

giving us better molecular resolution in simulating the system-environment interactions than sampling fluctuations from generic spectral density functions. The spatially correlated thermal fluctuations among different sites are naturally built-in in our method but are hard to be incorporated by approximate spectral densities. Our method has quantitative accuracy in systems with small redox potential differences ($

With the method of incorporating spatially and temporally correlated thermal fluctuations into charge transfer process, we study and engineer

coherence in guanine-rich DNA sequences.

Electronic delocalization in redox-active polymers may be disrupted by the heterogeneity of the environment that surrounds each monomer. When the differences in monomer redox-potential induced by the environment are small (as compared with the monomer-monomer electronic interactions), delocalization persists. Here we show that guanine (G) runs in double-stranded DNA support delocalization over 4-5 guanine bases. The weak interaction between delocalized G blocks on opposite DNA strands is known to support partially coherent long-range charge transport. The molecular-resolution model developed here finds that the coherence among these G blocks follows an even-odd orbital-symmetry rule and predicts that weakening the interaction between G blocks exaggerates the resistance oscillations. These findings indicate how sequence can be exploited to change the balance between coherent and incoherent transport. The predictions are tested and confirmed using break-junction experiments. Thus, tailored orbital symmetry and structural fluctuations may be used to produce coherent transport with a length scale of multiple nanometers in soft-matter assemblies, a length scale comparable to that of small proteins.

We extend our charge transport studies from linear molecules to branched molecules.

Self-assembling circuitry on the molecular scale demands building blocks with three or more terminals, the sine qua non for circuit elements like current splitters or combiners\cite{Molen2013,RN2,Tao2006}. A promising material for such building blocks is DNA, wherein multiple strands can self-assemble into multi-ended junctions and nucleobase stacks can transport charge over long distances\cite{Genereux2010,Cohen2005,RN6,RN7,RN8,RN9}. However, nucleobase stacking is often disrupted at the junction point, hindering electric charge transport between different terminals of the junction\cite{RN10,RN11}. Thus, the challenge of designing a multi-ended DNA circuit element remains open. Here, we address the challenge by using a guanine-quadruplex (G4) motif as the connector element of a multi-ended DNA junction, and designing the terminal groups of the motif to ensure efficient current splitting in the DNA junction with minimal carrier transport attenuation. We describe the design, assembly, and charge transport measurement\cite{RN46} of a 3-way G4 junction structure, in which charge can enter the structure from one terminal at one end of the G4, and exit from one of two terminals at the other end of the G4. We find that the charge transport characteristics are the same along the two pathways, and are also similar to those of the corresponding linear DNA duplexes. Thus, the G4-based junction indeed enables effective three-way transport, which is a necessary step towards building of DNA-based electrical networks. We optimize G4-based junction structures and interpret the charge-transport measurements with molecular dynamics and quantum chemistry simulations.

Energy transfer with an associated spin change of the donor and acceptor, Dexter energy transfer, is critically important in solar energy harvesting assemblies, damage protection schemes of photobiology, and organometallic opto-electronic materials. Dexter transfer between chemically linked donors and acceptors is bridge mediated, presenting an enticing analogy with bridge-mediated electron and hole transfer. However, Dexter coupling pathways must convey both an electron and a hole from donor to acceptor, and this adds considerable richness to the mediation process. We dissect the bridge-mediated Dexter coupling mechanisms and formulate a theory for triplet energy transfer coupling pathways. Virtual donor-acceptor charge-transfer exciton intermediates dominate at shorter distances or higher tunneling energy gaps, whereas virtual intermediates with an electron and a hole both on the bridge (virtual bridge excitons) dominate for longer distances or lower energy gaps. The effects of virtual bridge excitons were neglected in earlier treatments. The two-particle pathway framework developed here shows how Dexter energy-transfer rates depend on donor, bridge, and acceptor energetics, as well as on orbital symmetry and quantum interference among pathways.

The interactions between electronic dynamics and the molecular vibrations in a donor-­‐‑bridge-­‐‑acceptor (DBA) structure lie at the core of electron transfer (ET) reactions mechanisms. Aiming to control and characterize ET reactions via vibrational excitations of molecular modes, in this thesis, we discuss three aspects of the interplay between ET and nuclear vibrations and the charge transfer in transition metal complex compounds.

First, a theoretical framework is established to explore how transient infra-­‐‑red (IR) excitation perturbs ET kinetics and dynamics in DBA systems. Recent experiments find that IR excitation can change ET rates and can even change the relative dominance of ET and competing reactions. A comprehensive theoretical framework is formulated to describe IR-­‐‑perturbed nonadiabatic ET reactions, including the effects of IR-­‐‑induced non-­‐‑ equilibrium initial state populations and IR-­‐‑perturbed bridge-­‐‑mediated couplings. We find that these effects can produce either rate slowing or acceleration, depending on structural and energetic features of the bridge. The framework is used to interpret the origins of the observed rate slowing of charge separation and to predict rate acceleration for charge recombination in a DBA structure, and to describe the microscopic origins.

Second, a non-­‐‑equilibrium molecular dynamics (NEqMD) computational methodology is employed to explore how the molecular underpinnings of how vibrational excitation may influence non-­‐‑adiabatic electron-­‐‑transfer. NEqMD combines classical molecular dynamics simulations with nonequilibrium semiclassical initial conditions to simulate the dynamics of vibrationally excited molecules. We combine NEqMD with electronic structure computations of bridge-­‐‑mediated donor-­‐‑acceptor couplings to probe IR effects on electron transfer in two molecular species: dimethylaniline-­‐‑guanosine-­‐‑cytidine-­‐‑anthracene (DMA-­‐‑GC-­‐‑Anth) ensemble and 4-­‐‑ (pyrrolidin-­‐‑1-­‐‑yl)phenyl-­‐‑2,6,7-­‐‑triazabicyclo[2,2,2]octatriene-­‐‑10-­‐‑cyanoanthracen-­‐‑9-­‐‑yl structure (PP-­‐‑BCN-­‐‑CA). In DMA-­‐‑GC-­‐‑Anth, the simulations find that IR excitation of NH2 scissoring motion, and subsequent intramolecular vibrational energy redistribution (IVR) do not significantly alter the mean-­‐‑squared DA coupling interaction. This finding is consistent with earlier static system analysis. In PP-­‐‑BCN-­‐‑CA, IR excitation of the bridging C=N bond changes the bridge-­‐‑mediated coupling for charge separation and recombination by ~ 30 -­‐‑ 40%. These methods provide an approach to exploring out of equilibrium molecular dynamics may impact charge transfer processes at the molecular scale.

In addition, we explore the feasibility of using transient 2D-­‐‑IR spectroscopy for examining elastic and inelastic ET pathway in DBA systems. Bridge-­‐‑mediated electron transfer interactions depend upon the quantum interferences of amplitude propagating through the bridge. The nature of these interferences is different for elastic and inelastic electron transfer. Hence, it is of great interest to develop methods that may distinguish between elastic and inelastic transport mechanisms. We show that it is feasible to use 2D-­‐‑IR spectroscopy to assess the contribution of inelastic tunneling channels to bridge-­‐‑ mediated electron transfer. 2D-­‐‑IR spectra were simulated using simple 3-­‐‑state/2-­‐‑mode models. We identified 2D-­‐‑IR spectral features that distinguish elastic and inelastic charge transfer. DBA systems with ET time scales that are shorter than the vibrational relaxation time scale should allow detection of these features. We also propose to use the change of peak volumes [J. Phys. Chem. B 2006, 110, 19998-­‐‑20013] caused by varying waiting-­‐‑times between the second and third IR pulses in the 2D-­‐‑IR pulse sequence to estimate the rates of electron transfer via elastic or inelastic mechanisms.

Finally, quantum chemistry characterization of charge transfer reactions in Rhenium complex compounds and the IR-­‐‑induced rate modulation mechanism are discussed. Electronic structure calculations and normal mode analysis indicates that in rhenium-­‐‑centered complex compounds, IR-­‐‑induced donor-­‐‑acceptor energy gap change modulates the charge transfer rates.

Electron bifurcation oxidizes a two-electron donor, using the two electrons to reduce high- and low-potential acceptors. Thus, one electron may move thermodynamically uphill, being kinetically coupled to the downhill flow of the other electron. Electron bifurcation in nature is often reversible (∆G ≈ 0) so minimal free energy is dissipated, and the reaction occurs at minimal overpotential. Thus, electron bifurcation is a compelling target for bioinspired catalysis and/or nanoscale device design.We formulate a general theory of the electron bifurcation process, using a many-electron hopping kinetics model with hopping rate constants estimated with thermally activated electron tunneling theory. We conclude that efficient and reversible electron bifurcation requires only a conserved redox potential (free energy) landscape, with steep redox potential gradients in the high- and low-potential branches (the reversible EB scheme). This energy landscape naturally builds up electron and hole populations near the bifurcating two-electron cofactor in the high- and low-potential branches, respectively, thus disfavoring short-circuiting electron-hole combination. The reversible EB scheme suppresses short-circuiting reactions by erecting a Boltzmann penalty against redox states of the enzyme that may short-circuit, and largely accounts for short-circuit insulation in complex III of the electron transport chain, although our model does not uniquely account for the slow short-circuit turnover with an inhibited low-potential branch. For electron bifurcating enzymes that reduce the low-potential substrate directly (such as bifurcating electron transfer flavoproteins), we hypothesize that a downward shift in redox potential of the low-potential substrate upon binding to the bifurcating enzyme (similar to the iron protein bound to nitrogenase) could explain how the requisite steep redox potential gradient is achieved without housing a series of redox cofactors in the low-potential branch. Electron bifurcating enzymes in nature are often found with bifurcating cofactors (for example quinones and flavins) with inverted reduction potentials (i.e., the first reduction potential lower than the second). We derive a free energy decomposition scheme for the half-reactions of a two electron species from quantum chemical calculations to find physical and chemical factors that determine whether the reduction potentials are inverted. Remarkably, two electron species such as quinones and flavins can exhibit normally-ordered or inverted reduction potentials depending on the protein environment. Using our energy decomposition scheme and an estimate of a quinone Pourbaix diagram under continuum mean-field environments with varying electrostatic permittivity, we conclude that the proton transfer events that often accompany reduction in addition to the electrostatic interactions of charged species may have a significant impact on the invertedness of two-electron compounds. Thus, we hypothesize that electrostatic interactions (including the self-interaction of a charged semiquinone) may principally explain the ability of flavins and quinones to change the order of their first and second reduction potentials so profoundly. Future studies will be required to test this hypothesis. In addition, we show that efficient and reversible electron bifurcation is possible with normally ordered potentials at the bifurcating cofactor, provided the absolute value of the difference between the first and second reduction potentials is large (on the order of the redox potential span of the high- and low-potential branches in the reversible EB scheme). This finding has implications for synthetic electron bifurcation, as engineering redox active catalytic sites with strongly normally ordered potentials seems more straightforward than sites with strongly inverted potentials. Finally, we describe kinetics schemes for thermodynamically irreversible electron bifurcation that rely on disequilibrium populations of electrons within the high potential branch (irreversible confurcation is possible with a disequilibrium population of holes within the low-potential branch). Although these schemes are yet only hypothesized, these schemes allow orders-of-magnitude regulation of the bifurcating turnover rate with the redox poise of the two-electron donor (including faster turnover than in the reversible EB scheme), with kinetics fit by a generalized Shockley ideal diode equation.

Nature is challenged to move charge efficiently over many length scales. From sub-nm to μm distances, electron-transfer proteins orchestrate energy conversion, storage, and release both inside and outside the cell. Uncovering the detailed mechanisms of biological electron-transfer reactions, which are often coupled to bond-breaking and bond-making events, is essential to designing durable, artificial energy conversion systems that mimic the specificity and efficiency of their natural counterparts. Here, we use theoretical modeling of long-distance charge hopping (Chapter 3), synthetic donor-bridge-acceptor molecules (Chapters 4, 5, and 6), and de novo protein design (Chapters 5 and 6) to investigate general principles that govern light-driven and electrochemically driven electron-transfer reactions in biology. We show that fast, μm-distance charge hopping along bacterial nanowires requires closely packed charge carriers with low reorganization energies (Chapter 3); singlet excited-state electronic polarization of supermolecular electron donors can attenuate intersystem crossing yields to lower-energy, oppositely polarized, donor triplet states (Chapter 4); the effective static dielectric constant of a small (~100 residue) de novo designed 4-helical protein bundle can change upon phototriggering an electron transfer event in the protein interior, providing a means to slow the charge-recombination reaction (Chapter 5); and a tightly-packed de novo designed 4-helix protein bundle can drastically alter charge-transfer driving forces of photo-induced amino acid radical formation in the bundle interior, effectively turning off a light-driven oxidation reaction that occurs in organic solvent (Chapter 6). This work leverages unique insights gleaned from proteins designed from scratch that bind synthetic donor-bridge-acceptor molecules that can also be studied in organic solvents, opening new avenues of exploration into the factors critical for protein control of charge flow in biology.

The effectiveness of solar energy capture and conversion materials derives from their ability to absorb light and to transform the excitation energy into energy stored in free carriers or chemical bonds. The Thomas-Reiche-Kuhn sum rule mandates that the integrated (electronic) oscillator strength of an absorber equals the total number of electrons in the structure. Typical molecular chromophores place only about 1% of their oscillator strength in the UV/Vis window, so individual chromophores operate at about 1% of their theoretical limit. We explore the distribution of oscillator strength as a function of excitation energy to understand this circumstance. To this aim, we use familiar independent-electron model Hamiltonians as well as first-principles electronic structure methods. While model Hamiltonians capture the qualitative electronic spectra associated with π-electron chromophores, these Hamiltonians mistakenly focus the oscillator strength in the fewest low-energy transitions. Advanced electronic structure methods, in contrast, spread the oscillator strength over a very wide excitation energy range, including transitions to Rydberg and continuum states, consistent with experiment. Our analysis rationalizes the low oscillator strength in the UV/Vis spectral region in molecules, a step toward the goal of oscillator strength manipulation and focusing.

Two types of oscillator strength focusing strategies are proposed. The first one is to borrow conclusions made in optics to build one-dimensional potential models through quantum-optical analogy. We prove that by using this analogy, oscillator strength associated with the HOMO→LUMO transition in the model can be maximized. However, using model potentials as a guide for the design of linear absorbers by simply matching the HOMO energy of each molecular building block to the potential in the model is not sufficient to fully reproduce the model’s results in real molecules qualitatively. This might result from the overestimation of the potential models.

The second strategy for oscillator strength focusing is to perturb the electronic structure of molecules. Mechanical stress (stretching or compression) applied along the molecular axis of polyenes is simulated by adding spring bond constraints in ab initial calculations, with the hypothesis that σ bonds would be greatly disturbed and the σ–σ* energy gap would be reduced. By stretching polyene molecules by 20%, the oscillator strength associated with the σ → σ* transition is significantly enhanced and becomes comparable to the π → π* value, while the excitation energy drops by up to 4 eV. We also show that electrostatic fields can be used to alter the electronic structure of polyenes so as to enhance their absorption in the UV/Vis region. Our time-dependent density functional theory calculations on single molecules (either in gas phase or absorbed on gold) and on molecular stacks indicate that the oscillator strength integrated over the visible spectral range up to the near UV can be increased by an order of magnitude depending on the strength of the applied field. This enhancement and its oscillatory response to the field intensity are rationalized using a shielded superlattice potential model and molecular orbital analysis. Our study prompts future experimental investigations of the use of electric fields to modulate the light absorption properties of materials based on linear conjugated molecules.

Red fluorescent proteins are widely used for deep-issue imaging and in super-resolution techniques due to their low photo-sensitivity and minimized light-scattering by endogenous biomolecules. mCherry is one of the most photostable red fluorescent proteins, but not the brightest. Efforts have been made but failed to enhance the fluorescent intensity of mCherry in vitro by intuitive mutagenesis aiming to create local electric field at the chromophore. In this work, we carry out a systematic exploration of the optimal field direction and intensity that maximize the electric field effect. We find that electric field applied in the +x or –x direction along the chromophore axis induces most notable changes. The enhancement of the maximum absorption is up to 45% in the presence of +x electric field with a field strength of 1.5 V/nm. Residue sites for mutagenesis are identified targeting the formation of the optimal local electric field, which is a promising strategy to improve the brightness of red fluorescent proteins.

Lastly, we elucidate basic side chain effect on the conductivity of self-assembled cyclic peptide nanotubes, an attractive bioinspired material for proton conducting devices. Experimental measurements find lysine-containing peptide nanotubes to be much better conductor than arginine- and histidine-containing counterparts. Molecular dynamics are carried out on hexamer model systems (with and without structural constraints). By analyzing four possible proton transfer configurations in the snapshots, effective proton transfer rates and mean-squared proton couplings are calculated for the three systems. Our results show that the flexibility of the lysine side chain enables a large contribution of cross-layer proton transfer to the overall proton transfer rate, yet this configuration requires certain degree of freedom in structure distortions. A relatively large mean-square proton coupling for lysine-containing peptides is another key determinant of its high conductivity. Our study sheds lights on rational designs of highly conductive synthetic peptide nanostructures, and promotes further investigations on improved accuracy in the modeling of cyclic peptide nanotube systems.

Four parts are included in this dissertation: Chapter 1 is an introduction and provides background on our research; Chapter 2 is the study of designing porphyrin chromophores with unusually large hyperpolarizability; chapter 3 is the hopping charge recombination in cytochrome c-cytochrome c peroxidase electron transfer; and chapter 4 is the parameterizations of flavin adenine dinucleotide and electron transfer coupling calculations in cryptochrome.

A new series of push-pull porphyrin-based chromophores with unusually large static first hyperpolarizabilities are designed based on coupled-perturbed Hartree-Fock and density functional calculations. The combination of critical building blocks, including a ruthenium(II) bisterpyridine complex, proquinoidal thiadiazoloquinoxaline, and (porphinato)zinc(II) units produces large enhancement of the static nonlinear optical (NLO) response, computed to be as large as 11,300  1030 esu, 2 orders of magnitude larger than the benchmark species [5-((4'-(dimethylamino)phenyl)ethynyl)-15- ((4''-nitrophenyl)ethynyl)-porphinato]zinc(II).

We also studies the inter-protein ET recombination reaction between cytochrome c peroxidase-cytochrome c complex (i.e., ). ET rates in the wild type (WT) CcP:Cc complex and in four mutants of the Cc protein (i.e., F82S, F82W, F82Y and F82I) measured both in solution and in crystals, vary by no more than three fold despite large difference in the ET distances and protein-protein conformations. This theoretical study examines why large changes at the protein-protein interface and the lengthening of the heme-to-ZnP distances in the Cc F82Y(I) mutants do not slow the ET rate dramatically compared with the WT CcP:Cc and Cc F82S(W) mutants. PATHWAY and quantum chemical analysis, performed on molecular dynamics sampled geometries, indicates that the recombination mechanism for all five protein complexes involves two mechanisms: single step heme-ZnP tunneling and two step heme-Trp191-ZnP hopping. We further predict that back ET rates in double mutants W191F CcP:F82S(W) Cc will be dramatically reduced compared to the rates in the WT CcP:Cc complex. Since the recombination reaction is likely to occur in the inverted Marcus regime, an increased reorganization energy would compensate the decreased role of hopping recombination in the F82Y(I) mutants.

Finally, we examined the photo-induced tryptophan-to-flavin ET in cryptochrome. The amber force field of FAD was parameterized by antechamber using RESP fitting partial charges. The electronic couplings were calculated by generalized Mulliken-hush (GMH). Validation of GMH approach based on orbitals pictures are discussed in detail compared with many-electron coupling derivation.

Quantum chemical computations provide convenient and effective ways for molecular design using computers. In this dissertation, the molecular designs of optimal nonlinear optical (NLO) materials were investigated through three aspects. First, an inverse molecular design method was developed using a linear combination of atomic potential approach based on a Hückel-like tight-binding framework, and the optimizations of NLO properties were shown to be both efficient and effective. Second, for molecules with large first-hyperpolarizabilities, a new donor-carbon-nanotube paradigm was proposed and analyzed. Third, frequency-dependent first-hyperpolarizabilities were predicted and interpreted based on experimental linear absorption spectra and Thomas-Kuhn sum rules. Finally, molecular interferometers were designed to control charge-transfer using vibrational excitation. In particular, an ab initio vibronic pathway analysis was developed to describe inelastic electron tunneling, and the mechanism of vibronic pathway interferences was explored.

Electronic excitation energy transfer (EET) and electron transfer (ET) are of the fundamental importance to biochemical processes and solar energy conversion. The goal of this thesis is to develop and apply theoretical and computational tools to understand the mechanisms and kinetics of EET and ET in selected molecular systems with the aim to control and boost their efficacy. Specifically, this thesis focuses on three subjects: (1) computational study of energy transfer and its pathways in Ruthenium based metal organic frameworks (MOFs), (2) developing a general analytical model to describe the kinetics of energy transfer/electron transfer in condensed media, and (3) developing theoretical frameworks to describe multiple electron/exciton transfer processes.

In the study of energy transfer in Ruthenium based MOFs, we found that the excitation transport kinetics was well described by a Dexter (exchange) triplet-to-triplet incoherent multi-step hopping mechanism. The sensitive distance dependent rate for Dexter energy transfer in different MOF structures establishes unique energy transport pathways. For example, both one- and three-dimensional exciton-hopping networks were found in mixed Ru/Os MOFs. As such, Dexter energy transfer may potentially be helpful for spatially directing excitation energy along specific direction, for example, towards reaction centers, and an amenable for designing high efficiency energy transfer materials.

Significant amount EET processes happen in condense media and the nature of energy migration kinetics depends heavily on the donor (D) and acceptor (A) distribution in the media, especially for organic photovoltaic devices. The EET in the condense phase allow us to study the impact of ordered, partially ordered, and disordered DA distribution on the solar energy harvesting efficiency. To better account for the EET in condense phase, we developed a general analytical model for the description of the time-dependent luminescence decay emphasizing on the actual D-A spatial distribution. Applications of the developed model have been made to investigate the long-range excitation energy transfer in disordered polymer systems. By fitting the experimental transient luminescence spectra, we found that the derived EET kinetics showed better agreement with experimental observed luminescence decay both in short and long times, a significant improvement over the earlier models by Inokuti and Hirayama. Our model is more reliable in a wide range of time and acceptor density and can also be used for electron transfer.

The frontiers of ET and EET are moving from single particle one-step reactions to coupled multi-particle and multi-step processes. To understand the leading features that mediate the two-electron transfer in catalysis, we developed a two-electron transfer superexchange model that focuses on the roles of these features including (1) the one- and two-electron virtual intermediate states that mediate the ET, (2) the number of virtual intermediates with system size, and (3) the multiple classes of pathways interferes. Key questions, including how bridge structure and energetics influence multi-electron superexchange and interference between singly- and doubly-oxidized (or reduced) bridge virtual states are investigated. We found that even simple linear donor-bridge-acceptor systems have pathway topologies that resemble those seen for one-electron superexchange through bridges with multiple parallel pathways. The simple model two-electron transfer systems studied here exhibit a richness that is amenable to experimental exploration by manipulating the multiple pathways, pathway crosstalk, and changes in the number of donor and acceptor species. The features that emerge from these studies may assist in developing new strategies to deliver multiple electrons in condensed phase redox systems, including multiple-electron redox species, multi-metallic/multi-electron redox catalysts, and multi-exciton excited states.

Finally, to understand the role of structural and environmental disorder on incoherent ET, we developed a perturbative model based on the kinetic master equation to examine incoherent ET in non-equilibrium and non-Markovian regime. The developed method provides an effective way to explicitly investigate how a general (non-Gaussian) fluctuation in ET rate can modify the ET kinetics. Applications of this method have been made to study the ET kinetics for donor-bridge-acceptor systems with the structural and environmental fluctuations. Changing in ET kinetics with structural fluctuations of different nature was examined. Dominant fluctuation characters that significantly boost or reduce ET rate were identified. These findings may be helpful in designing efficient ET materials and provide strategies in modulating ET rate.

Biological electron transfer (ET) reactions are of both fundamental and practical interests, with their importance in redox signaling, oxidative damage protection, respiratory metabolism, and bioenergetic transport.Charge hopping through aromatic amino acids and redox cofactors occurs in many biological redox systems, extending the conventional paradigms of biological ET from intermolecular, subnanometer length scale to inter-protein, nanometer, or even micrometer length scale. We developed and applied computationally accessible models to understand the mechanisms and kinetics of biological long-range electron transfer, specifically in two major systems: Geobacter bacterial nanowire and cytochrome c peroxidase - cytochrome c (CcP:Cc) protein complex.

In the study of Geobacter bacterial nanowire, two bacterial nanowire structures have been examined: type IV pili and OmcS protein assemblies. For the type IV pili bacterial nanowire, we examined the possible electron transfer mechanisms in regimes ranging from purely incoherent hopping to purely coherent transport. Our studies shown that for plausible ET parameters, electron transfer in type IV pili bacterial nanowire is predicted to be dominated by incoherent hopping between phenylalanine (Phe) and tyrosine (Tyr) residues that are 3 to 4 angstroms apart, where Phe residues in the hopping pathways may create delocalized "islands" to accelerate the ET. This mechanism could be accessible in the presence of strong oxidants, capable of oxidizing Phe and Tyr residues. We also examined the physical requirements needed to sustain biological respiration via type IV pili bacterial nanowire. We found that the hopping regimes with ET rate on the order of 10^8s^-1 between Phe islands and Tyr residues and conductivities on the order of mS/cm can support ET fluxes that are compatible with cellular respiration rates, although sustaining this delocalization in the heterogeneous protein environment may be challenging. For the OmcS protein assemblies, we examined the temperature dependent conformational changes, and the inverse temperature dependent conductivities. Our studies shown that both reorganization energies and redox potential landscapes of the OmcS protein determine the inverse-temperature dependencies of the conductivity. In most biological reasonable ET parameter zones, conductivity increases with increasing temperatures, featuring thermally-activated redox hopping mechanisms, whereas in a strict ET parameter zone, the conductivity increases with decreasing temperatures, showing that the metallic-like characteristic in inverse-temperature dependent conductivity can be observed even in the purely incoherent hopping mechanism.

In the study of CcP:Cc protein complex, we focused on the role of tryptophan (Trp191) of CcP in supporting hole hopping charge recombination between the Cc heme and ZnPCcP Zinc porphyrin.Experimental studies find that when Trp191 is substituted by tyrosine, phenylalanine, or redox-active aniline derivatives bound in the W191G cavity, enzymatic activity and charge recombination rates both decrease. We performed theoretical analysis on these CcP:Cc complexes and found that the ET kinetics depend strongly on the chemistry of the modified Trp site. The computed electronic couplings in the W191F and W191G species are orders of magnitude smaller than in the native protein, due largely to the absence of a hopping intermediate and the large tunneling distance. Small molecules bound in the W191G cavity are weakly coupled electronically. The couplings in W191Y are not substantially weakened compared to the native species, but the redox potential difference for tyrosine compared to tryptophan oxidation accounts for the slower rate in the W191Y mutant. Our theoretical analysis explains why only the native Trp supports rapid hole hopping in the CcP:Cc complex, where both favorable free energies and electronic couplings are essential for establishing an efficient hole hopping relay in protein-protein complexes.

Besides the main theme of biological long-range electron transfer, we have studies the hole length along DNA base pairs, using a newly developed localized orbital scaling correction (LOSC) density functional theory method. We accurately characterized the quantum delocalization of the hole wave function in double helical B-DNA and found that the hole state tends to delocalize among four guanine-cytosine (GC) base pairs and among three adenine-thymine (AT) base pairs when these adjacent bases fluctuate into degeneracy. This extend of delocalization has significant implications for assessing the role of coherent, incoherent, or flickering resonant charge transfer mechanisms in DNA.

Lastly, we reforged our inhouse cheminformatics algorithm for Chemical Space Exploration with Stochastic Search (ACSESS). In the reforged version ACSESS, the cheminformatics library OpenEye is replaced by open-source RDKit for molecular manipulations, and a serious of mutation and filtering functions were added to facilitate targeted chemical space explorations.We applied the reforged ACSESS in exploring chemical space for potential RNA binders with restricted molecule scaffold.

The biological reduction of N2 to NH3 catalyzed by molybdenum nitrogenase requires eight steps to finish a completed catalysis cycle. This reaction cycle is associated with ATP-driven electron transfer (ET) from the Fe protein to the MoFe protein, and part of ET is experimentally confirmed to be ‘conformationally gated’. Although the overall sequence of ET in nitrogenase has been studied for decades, the nature of coupling between ET pathways and nucleotides binding/protein-protein docking is still unclear, especially from theoretical aspects. Here, we have utilized submicrosecond classical molecular dynamics simulations to allow the ADP-bound and ATP-bound nitrogenases to simulate their conformations in real biological systems. Then the Pathways plugin implemented by Balabin et al was employed to calculate the ET coupling and visualize the ET pathways between the F-cluster and the P-cluster in nitrogenase. The comparison of the ET couplings (the F-cluster to the P-cluster) we calculated and the edge-to-edge distance between the ET donor and acceptor suggests that the coupling pathways grow in strength more that that would be expected from simple distance changes. This result additionally indicates the electron of Fe protein is protected prior to the ATP binding and the protein-protein docking, using pathway switching effects.

Discovering functionally useful structures and materials by exploring the vastness of chemical space is an exciting undertaking. If done efficiently, one can discover structures that can have therapeutic value (such as drug like organic molecules) or technological value (such as organic light emitting diodes). While mining of chemical space has the potential to generate libraries of functional structures and materials, one can also easily be lost in its vastness (~1060 theoretically possible small organic molecule ~500 Da molecular weight or less). We have developed a strategy that allows efficient explorations of vast chemical spaces to generate libraries of functional organic molecules. The method, at its core, applies physical properties and structural diversity biased sampling of chemical space to search for new structures. We demonstrate the soundness and efficiency of this approach by searching through the known and enumerated databases to discover diverse organic molecules with optimum electronic and biophysical properties, and we also compare it to various existing approaches used for molecular search and property optimization. We also show a practical application of this approach by designing libraries of chromophores that emit light in the blue region of the spectrum as well as potential leads for protein and RNA binding.

Hartree-Fock (HF) theory is one of the fundamental theories in electronic structure calculations. It can provide the basic description of the system, however, as the zeroth order approximation, it cannot describe the electronic structure accurately. Nevertheless, it is the starting reference for many beyond-HF wavefunction methods. Another fundamental theory in electronic structure is the density functional theory (DFT). It is usually ignored that DFT has an important connection with the HF theory. This connection is the single excitation (SE) contribution. In HF, SE does not contribute because of the Brillouin's theorem. On the other hand, SE contributes to DFT and plays a significant role in beyond-DFT many-body methods. One example is the correlation energy calculated by random phase approximation (RPA). Here we would like to discuss SE in different scenarios and extend the topic. First, the optimized effective potential (OEP) does not perform accurately in minimizing the RPA total energy functional. To overcome this problem, we developed a generalized optimized effective potential (GOEP) method. This method can describe the dissociation of weakly interacting diatomic systems accurately. From the analysis of the energy structure, the GOEP absorbs the SE contribution in contrast with the OEP method. We also notice that by performing GOEP for RPA, the physical density of the system is no longer the reference density, which is not traditionally recognized in DFT. This conclusion can be generally applied to any exchange-correlation functional that depends explicitly on the external potential. And we have shown that this physical density performs better than both the reference density and the original density of the starting reference calculated from HF or DFT. Second, the $GW$ approximation is widely used in different research areas. Especially, the $G_0W_0$ method can improve the ionization potential for both molecule and solids calculated from the ground state DFT calculation. However, the $G_0W_0$ method has a strong starting-point dependence. We have recognized that this starting-point dependence largely originates from the lack of SE contribution to the single-particle Green's function. We developed an effective and simple solution by using a subspace diagonalization of the HF Hamiltonian with the DFT density matrix to construct the renormalized singles Green's function and replace the reference Green's function $G_0$. Our method works extremely well for molecules and we are still testing it for solid states. Besides, we have developed a new method to extract excitation energies directly from the quasi-particle energies based on the $GW$ approximation. Starting from the $(N-1)$-electron system, we are able to calculate molecular excitation energies with orbital energies at the $GW$ level. We have demonstrated that this method can accurately capture low-lying local excitations as well as charge transfer excitations in many molecular systems. This provides a new perspective in applying the single-particle Green's function.

Electron transfer (ET) and excitation energy transfer (EET) are widely observed in various research areas, for example, electronic devices, biomolecular systems, light harvesting systems, etc. Here we discuss two topics. First, we study circularly polarized light (CPL) induced ET process. CPL induced coherent electron transfer (ET) process can be affected by the direction of the CPL. In particular, the yield on the acceptor through the CPL-induced ET can be asymmetrical. Previous study suggests that this yield asymmetry on the acceptor is related with the initial angular momentum polarization on the donor, which can be created by different directions of the CPL. Here we further investigate how the CPL affects the yield asymmetry by studying the yield asymmetry dependence on the molecular energetics, CPL field, and the environment perturbation. We have built a simple 4-state Hamiltonian with one ground state, two degenerate excited donor states and one acceptor and provided the optimal choice of parameters to maximize the yield asymmetry. Both analytical and numerical results suggest that the yield asymmetry is mainly created by the phase and population difference between two excited states under L- and R-CPL. Among different parameters, a slow dephasing rate is most important for observing a large yield asymmetry. With a 200 fs dephasing rate, the yield asymmetry can be as large as 5\%. One should perform the experiment in low temperature to slow the dephasing rate. Second, we study the hole length along the DNA base pairs. Knowing the length of the hole is important to understand the mechanism of the ET process through DNA. The length of the hole is determined by the competition between the delocalization (ionization) and localization (solvation) effect of the DNA. We have revisited the previous work in our group (10.1021/jp0132329) with more advanced quantum chemistry methods to calculate the hole length in AT and GC pairs. Localized scaling orbital correction (LOSC) is used to calculate the ionization potential (IP), which is usually underestimated by traditional DFT calculations because of the size-consistent problem. And we will use the Poisson-Boltzmann equation to calculate the solvation energy contribution. From the LOSC calculation, the IP is in agreement with the high-level ab-initio calculations. This result shows that the LOSC calculation overcomes the problem in traditional DFT. And we have also shown that the IP decreases faster for the increasing length of the GC pair as compared to the AT pair.

Quantum dots (QDs) are promising building block materials for many emerging energy-harvesting applications. We theoretically investigated the influences of the QD-QD (CdTe-CdSe) charge transfer rates and mechanisms on QD solar cells power conversion efficiencies using multi-level modeling methods including the first principle quantum chemistry calculations of QD electronic and charge transfer properties and the kinetic modeling of solar cell performances.

We developed tight-binding electronic structure models to explore the QD electronic properties, and the charge transfer kinetics including their dependences on QD sizes and QD surface-to-surface distance. We found that the QD-QD charge transfer rates follow the non-adiabatic rate expression by Marcus. The QD-QD electronic coupling strength decays exponentially as the QD surface-to-surface distance increases. The QD-QD charge transfer rates generally increase (decay) as the acceptor (donor) QD radius increases. We found that the TS coupling mechanism can dominate the QD-QD coupling over the TB coupling. The difference between the TS and TB coupling size dependences results in a dominance switch between the TS and TB charge transfer mechanisms in the QD dyad as the QD sizes grow.

We further explored the use of an external charge to modulate the QD-QD coupling strength and the coupling mechanism. We found that a positively charged group in the bridge strengthens the D-A coupling for all QD sizes. A negatively charged group in the bridge causes the D-A coupling reduction in large QDs. For small QDs, the D-A coupling variation induced by the negative charge depends on the QD sizes. Compared to the neutral bridge, we found that through-solvent and through-bridge mechanisms switch their dominance at smaller (larger) QD sizes for the positively (negatively) charged group in the molecular bridge.

Using the computed charge transfer rates, we explored the power conversion efficiencies of QD solar cells based on QD dyads and QD triads. We found that the external and internal power conversion quantum efficiencies are significantly enhanced by introducing a third QD between the donor and acceptor QDs. The improvements in the efficiencies can be further enhanced by tuning the band-edge energy offset of the middle-position QD from its neighbors.