Crystal Coulomb energies: I. Organic donor-acceptor complexes--a review. II. Classical Ewald calculations of the Coulomb binding energy of four donor-acceptor crystals and Wurster's blue perchlorate. III. A rapid-convergence quantum-mechanical formalism for crystal electronic energies

Chapter I

Theories for organic donor-acceptor (DA) complexes in solution and in the solid state are reviewed, and compared with the available experimental data. As shown by McConnell et al. (Proc. Natl. Acad. Sci. U.S., 53, 46-50 (1965)), the DA crystals fall into two classes, the holoionic class with a fully or almost fully ionic ground state, and the nonionic class with little or no ionic character. If the total lattice binding energy 2ε₁ (per DA pair) gained in ionizing a DA lattice exceeds the cost 2ε_o of ionizing each DA pair, ε₁ + ε_o less than 0, then the lattice is holoionic. The charge-transfer (CT) band in crystals and in solution can be explained, following Mulliken, by a second-order mixing of states, or by any theory that makes the CT transition strongly allowed, and yet due to a small change in the ground state of the non-interacting components D and A (or D⁺ and A^-). The magnetic properties of the DA crystals are discussed.

Chapter II

A computer program, EWALD, was written to calculate by the Ewald fast-convergence method the crystal Coulomb binding energy E_C due to classical monopole-monopole interactions for crystals of any symmetry. The precision of E_C values obtained is high: the uncertainties, estimated by the effect on E_C of changing the Ewald convergence parameter η, ranged from ± 0.00002 eV to ± 0.01 eV in the worst case. The charge distribution for organic ions was idealized as fractional point charges localized at the crystallographic atomic positions: these charges were chosen from available theoretical and experimental estimates. The uncertainty in E_C due to different charge distribution models is typically ± 0.1 eV (± 3%): thus, even the simple Hückel model can give decent results.

E_C for Wurster's Blue Perchl orate is -4.1 eV/molecule: the crystal is stable under the binding provided by direct Coulomb interactions. E_C for N-Methylphenazinium Tetracyanoquino- dimethanide is 0.1 eV: exchange Coulomb interactions, which cannot be estimated classically, must provide the necessary binding.

EWALD was also used to test the McConnell classification of DA crystals. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine: 7,7,8,8-Tetracyanoquinodimethan) E_C = -4.0 eV while 2ε_o = 4.6₅ eV: clearly, exchange forces must provide the balance. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine:para-Chloranil) E_C = -4.4 eV, while 2ε_o = 5.0 eV: again EC falls short of 2ε₁. As a Gedankenexperiment, two nonionic crystals were assumed to be ionized: for (1:1)-(Hexamethyl- benzene:para-Chloranil) E_C = -4.5 eV, 2ε_o = 6.6 eV; for (1:1)- (Napthalene:Tetracyanoethylene) E_C = -4.3 eV, 2ε_o = 6.5 eV. Thus, exchange energies in these nonionic crystals must not exceed 1 eV.

Chapter III

A rapid-convergence quantum-mechanical formalism is derived to calculate the electronic energy of an arbitrary molecular (or molecular-ion) crystal: this provides estimates of crystal binding energies which include the exchange Coulomb inter- actions. Previously obtained LCAO-MO wavefunctions for the isolated molecule(s) ("unit cell spin-orbitals") provide the starting-point. Bloch's theorem is used to construct "crystal spin-orbitals". Overlap between the unit cell orbitals localized in different unit cells is neglected, or is eliminated by Löwdin orthogonalization. Then simple formulas for the total kinetic energy Q^(XT)_λ, nuclear attraction [λ/λ]^XT, direct Coulomb [λλ/λ'λ']^XT and exchange Coulomb [λλ'/λ'λ]^XT integrals are obtained, and direct-space brute-force expansions in atomic wavefunctions are given. Fourier series are obtained for [λ/λ]^XT, [λλ/λ'λ']^XT, and [λλ/λ'λ]^XT with the help of the convolution theorem; the Fourier coefficients require the evaluation of Silverstone's two-center Fourier transform integrals. If the short-range interactions are calculated by brute-force integrations in direct space, and the long-range effects are summed in Fourier space, then rapid convergence is possible for [λ/λ]^XT, [λλ/λ'λ']^XT and [λλ'/λ'λ]^XT. This is achieved, as in the Ewald method, by modifying each atomic wavefunction by a "Gaussian convergence acceleration factor", and evaluating separately in direct and in Fourier space appropriate portions of [λ/λ]^XT, etc., where some of the portions contain the Gaussian factor.

Optical properties of excited silicon and germanium at low temperatures

Part I of this thesis deals with 3 topics concerning the luminescence from bound multi-exciton complexes in Si. Part II presents a model for the decay of electron-hole droplets in pure and doped Ge.

Part I.

We present high resolution photoluminescence data for Si doped With Al, Ga, and In. We observe emission lines due to recombination of electron-hole pairs in bound excitons and satellite lines which have been interpreted in terms of complexes of several excitons bound to an impurity. The bound exciton luminescence in Si:Ga and Si:Al consists of three emission lines due to transitions from the ground state and two low lying excited states. In Si:Ga, we observe a second triplet of emission lines which precisely mirror the triplet due to the bound exciton. This second triplet is interpreted as due to decay of a two exciton complex into the bound exciton. The observation of the second complete triplet in Si:Ga conclusively demonstrates that more than one exciton will bind to an impurity. Similar results are found for Si:Al. The energy of the lines show that the second exciton is less tightly bound than the first in Si:Ga. Other lines are observed at lower energies. The assumption of ground state to ground-state transitions for the lower energy lines is shown to produce a complicated dependence of binding energy of the last exciton on the number of excitons in a complex. No line attributable to the decay of a two exciton complex is observed in Si:In.

We present measurements of the bound exciton lifetimes for the four common acceptors in Si and for the first two bound multi-exciton complexes in Si:Ga and Si:Al. These results are shown to be in agreement with a calculation by Osbourn and Smith of Auger transition rates for acceptor bound excitons in Si. Kinetics determine the relative populations of complexes of various sizes and work functions, at temperatures which do not allow them to thermalize with respect to one another. It is shown that kinetic limitations may make it impossible to form two-exciton complexes in Si:In from a gas of free excitons.

We present direct thermodynamic measurements of the work functions of bound multi-exciton complexes in Al, B, P and Li doped Si. We find that in general the work functions are smaller than previously believed. These data remove one obstacle to the bound multi-exciton complex picture which has been the need to explain the very large apparent work functions for the larger complexes obtained by assuming that some of the observed lines are ground-state to ground-state transitions. None of the measured work functions exceed that of the electron-hole liquid.

Part II.

A new model for the decay of electron-hole-droplets in Ge is presented. The model is based on the existence of a cloud of droplets within the crystal and incorporates exciton flow among the drops in the cloud and the diffusion of excitons away from the cloud. It is able to fit the experimental luminescence decays for pure Ge at different temperatures and pump powers while retaining physically reasonable parameters for the drops. It predicts the shrinkage of the cloud at higher temperatures which has been verified by spatially and temporally resolved infrared absorption experiments. The model also accounts for the nearly exponential decay of electron-hole-droplets in lightly doped Ge at higher temperatures.

Measurement of the band bending and surface dipole at chemically functionalized Si(111)/vacuum interfaces

The core-level energy shifts observed using X-ray photoelectron spectroscopy (XPS) have been used to determine the band bending at Si(111) surfaces terminated with Si-Br, Si-H, and Si-CH₃ groups, respectively. The surface termination influenced the band bending, with the Si 2p_3/2 binding energy affected more by the surface chemistry than by the dopant type. The highest binding energies were measured on Si(111)-Br (whose Fermi level was positioned near the conduction band at the surface), followed by Si(111)-H, followed by Si(111)-CH₃ (whose Fermi level was positioned near mid-gap at the surface). Si(111)-CH₃ surfaces exposed to Br₂(g) yielded the lowest binding energies, with the Fermi level positioned between mid-gap and the valence band. The Fermi level position of Br₂(g)-exposed Si(111)-CH₃ was consistent with the presence of negatively charged bromine-containing ions on such surfaces. The binding energies of all of the species detected on the surface (C, O, Br) shifted with the band bending, illustrating the importance of isolating the effects of band bending when measuring chemical shifts on semiconductor surfaces. The influence of band bending was confirmed by surface photovoltage (SPV) measurements, which showed that the core levels shifted toward their flat-band values upon illumination. Where applicable, the contribution from the X-ray source to the SPV was isolated and quantified. Work functions were measured by ultraviolet photoelectron spectroscopy (UPS), allowing for calculation of the sign and magnitude of the surface dipole in such systems. The values of the surface dipoles were in good agreement with previous measurements as well as with electronegativity considerations. The binding energies of the adventitious carbon signals were affected by band bending as well as by the surface dipole. A model of band bending in which charged surface states are located exterior to the surface dipole is consistent with the XPS and UPS behavior of the chemically functionalized Si(111) surfaces investigated herein.

Dynamical stability of nascent neutron stars

This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the accretion induced collapse of rapidly rotating white dwarfs.

Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are constructed by assuming that the neutron stars have the same masses, angular momenta, and specific angular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is rapidly rotating, the collapsed object will contain a high density central core of size about 20 km, surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis. The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron stars is all found to be less than 0.27.

Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving the linearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β of the star is greater than the critical value β_d ≈ 0.25. It is expected that the unstable mode will persist until a substantial amount of angular momentum is carried away by gravitational radiation. The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect them unless the event rate is greater than 10^-6/year/galaxy.

All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3 are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic effects on the structure of these neutron stars. New techniques are developed and used to construct neutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models are qualitatively similar to the corresponding Newtonian models, but the values of β are somewhat smaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller than the Newtonian result (0.26). However, relativistic effects will also change the critical value β_d. A detailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects on the dynamical stability of these neutron stars.

Sequence-function relationships in E. coli transcriptional regulation

Understanding how transcriptional regulatory sequence maps to regulatory function remains a difficult problem in regulatory biology. Given a particular DNA sequence for a bacterial promoter region, we would like to be able to say which transcription factors bind there, how strongly they bind, and whether they interact with each other and/or RNA polymerase, with the ultimate objective of integrating knowledge of these parameters into a prediction of gene expression levels. The theoretical framework of statistical thermodynamics provides a useful framework for doing so, enabling us to predict how gene expression levels depend on transcription factor binding energies and concentrations. We used thermodynamic models, coupled with models of the sequence-dependent binding energies of transcription factors and RNAP, to construct a genotype to phenotype map for the level of repression exhibited by the lac promoter, and tested it experimentally using a set of promoter variants from E. coli strains isolated from different natural environments. For this work, we sought to ``reverse engineer'' naturally occurring promoter sequences to understand how variations in promoter sequence affects gene expression. The natural inverse of this approach is to ``forward engineer'' promoter sequences to obtain targeted levels of gene expression. We used a high precision model of RNAP-DNA sequence dependent binding energy, coupled with a thermodynamic model relating binding energy to gene expression, to predictively design and verify a suite of synthetic E. coli promoters whose expression varied over nearly three orders of magnitude.

However, although thermodynamic models enable predictions of mean levels of gene expression, it has become evident that cell-to-cell variability or ``noise'' in gene expression can also play a biologically important role. In order to address this aspect of gene regulation, we developed models based on the chemical master equation framework and used them to explore the noise properties of a number of common E. coli regulatory motifs; these properties included the dependence of the noise on parameters such as transcription factor binding strength and copy number. We then performed experiments in which these parameters were systematically varied and measured the level of variability using mRNA FISH. The results showed a clear dependence of the noise on these parameters, in accord with model predictions.

Finally, one shortcoming of the preceding modeling frameworks is that their applicability is largely limited to systems that are already well-characterized, such as the lac promoter. Motivated by this fact, we used a high throughput promoter mutagenesis assay called Sort-Seq to explore the completely uncharacterized transcriptional regulatory DNA of the E. coli mechanosensitive channel of large conductance (MscL). We identified several candidate transcription factor binding sites, and work is continuing to identify the associated proteins.

Theory of s-d exchange scattering in dilute magnetic alloys

The problem of s-d exchange scattering of conduction electrons off localized magnetic moments in dilute magnetic alloys is considered employing formal methods of quantum field theoretical scattering. It is shown that such a treatment not only allows for the first time, the inclusion of multiparticle intermediate states in single particle scattering equations but also results in extremely simple and straight forward mathematical analysis. These equations are proved to be exact in the thermodynamic limit. A self-consistent integral equation for electron self energy is derived and approximately solved. The ground state and physical parameters of dilute magnetic alloys are discussed in terms of the theoretical results. Within the approximation of single particle intermediate states our results reduce to earlier versions. The following additional features are found as a consequence of the inclusion of multiparticle intermediate states;

(i) A non analytic binding energy is pre sent for both, antiferromagnetic (J < o) and ferromagnetic (J > o) couplings of the electron plus impurity system.

(ii) The correct behavior of the energy difference of the conduction electron plus impurity system and the free electron system is found which is free of unphysical singularities present in earlier versions of the theories.

(iii) The ground state of the conduction electron plus impurity system is shown to be a many-body condensate state for J < o and J > o, both. However, a distinction is made between the usual terminology of "Singlet" and "Triplet" ground states and nature of our ground state.

(iv) It is shown that a long range ordering, leading to an ordering of the magnetic moments can result from a contact interaction such as the s-d exchange interaction.

(v) The explicit dependence of the excess specific heat of the Kondo systems is obtained and found to be linear in temperatures as T→ o and T ℓnT for 0.3 T_K ≤ T ≤ 0.6 T_K. A rise in (ΔC/T) for temperatures in the region 0 < T ≤ 0.1 T_K is predicted. These results are found to be in excellent agreement with experiments.

(vi) The existence of a critical temperature for Ferromagnetic coupling (J > o) is shown. On the basis of this the apparent contradiction of the simultaneous existence of giant moments and Kondo effect is resolved.

Kinetic investigations of heterogeneously catalyzed reactions on the Ru(001) and Pt(110)-(1x2) surfaces

The initial probabilities of activated, dissociative chemisorption of methane and ethane on Pt(110)-(1 x 2) have been measured. The surface temperature was varied from 450 to 900 K with the reactant gas temperature constant at 300 K. Under these conditions, we probe the kinetics of dissociation via trapping-mediated (as opposed to 'direct') mechanism. It was found that the probabilities of dissociation of both methane and ethane were strong functions of the surface temperature with an apparent activation energies of 14.4 kcal/mol for methane and 2.8 kcal/mol for ethane, which implys that the methane and ethane molecules have fully accommodated to the surface temperature. Kinetic isotope effects were observed for both reactions, indicating that the C-H bond cleavage was involved in the rate-limiting step. A mechanistic model based on the trapping-mediated mechanism is used to explain the observed kinetic behavior. The activation energies for C-H bond dissociation of the thermally accommodated methane and ethane on the surface extracted from the model are 18.4 and 10.3 kcal/mol, respectively.

The studies of the catalytic decomposition of formic acid on the Ru(001) surface with thermal desorption mass spectrometry following the adsorption of DCOOH and HCOOH on the surface at 130 and 310 K are described. Formic acid (DCOOH) chemisorbs dissociatively on the surface via both the cleavage of its O-H bond to form a formate and a hydrogen adatom, and the cleavage of its C-O bond to form a carbon monoxide, a deuterium adatom and an hydroxyl (OH). The former is the predominant reaction. The rate of desorption of carbon dioxide is a direct measure of the kinetics of decomposition of the surface formate. It is characterized by a kinetic isotope effect, an increasingly narrow FWHM, and an upward shift in peak temperature with Ɵ_T, the coverage of the dissociatively adsorbed formic acid. The FWHM and the peak temperature change from 18 K and 326 K at Ɵ_T = 0.04 to 8 K and 395 K at Ɵ_T = 0.89. The increase in the apparent activation energy of the C-D bond cleavage is largely a result of self-poisoning by the formate, the presence of which on the surface alters the electronic properties of the surface such that the activation energy of the decomposition of formate is increased. The variation of the activation energy for carbon dioxide formation with Ɵ_T accounts for the observed sharp carbon dioxide peak. The coverage of surface formate can be adjusted over a relatively wide range so that the activation energy for C-D bond cleavage in the case of DCOOH can be adjusted to be below, approximately equal to, or well above the activation energy for the recombinative desorption of the deuterium adatoms. Accordingly, the desorption of deuterium was observed to be governed completely by the desorption kinetics of the deuterium adatoms at low Ɵ_T, jointly by the kinetics of deuterium desorption and C-D bond cleavage at intermediate Ɵ_T, and solely by the kinetics of C-D bond cleavage at high Ɵ_T. The overall branching ratio of the formate to carbon dioxide and carbon monoxide is approximately unity, regardless the initial coverage Ɵ_T, even though the activation energy for the production of carbon dioxide varies with Ɵ_T. The desorption of water, which implies C-O bond cleavage of the formate, appears at approximately the same temperature as that of carbon dioxide. These observations suggest that the cleavage of the C-D bond and that of the C-O bond of two surface formates are coupled, possibly via the formation of a short-lived surface complex that is the precursor to to the decomposition.

The measurement of steady-state rate is demonstrated here to be valuable in determining kinetics associated with short-lived, molecularly adsorbed precursor to further reactions on the surface, by determining the kinetic parameters of the molecular precursor of formaldehyde to its dissociation on the Pt(110)-(1 x 2) surface.

Overlayers of nitrogen adatoms on Ru(001) have been characterized both by thermal desorption mass spectrometry and low-energy electron diffraction, as well as chemically via the postadsorption and desorption of ammonia and carbon monoxide.

The nitrogen-adatom overlayer was prepared by decomposing ammonia thermally on the surface at a pressure of 2.8 x 10^(-6) Torr and a temperature of 480 K. The saturated overlayer prepared under these conditions has associated with it a (√247/10 x √247/10)R22.7° LEED pattern, has two peaks in its thermal desorption spectrum, and has a fractional surface coverage of 0.40. Annealing the overlayer to approximately 535 K results in a rather sharp (√3 x √3)R30° LEED pattern with an associated fractional surface coverage of one-third. Annealing the overlayer further to 620 K results in the disappearance of the low-temperature thermal desorption peak and the appearance of a rather fuzzy p(2x2) LEED pattern with an associated fractional surface coverage of approximately one-fourth. In the low coverage limit, the presence of the (√3 x √3)R30° N overlayer alters the surface in such a way that the binding energy of ammonia is increased by 20% relative to the clean surface, whereas that of carbon monoxide is reduced by 15%.

A general methodology for the indirect relative determination of the absolute fractional surface coverages has been developed and was utilized to determine the saturation fractional coverage of hydrogen on Ru(001). Formaldehyde was employed as a bridge to lead us from the known reference point of the saturation fractional coverage of carbon monoxide to unknown reference point of the fractional coverage of hydrogen on Ru(001), which is then used to determine accurately the saturation fractional coverage of hydrogen. We find that ƟSAT/H = 1.02 (±0.05), i.e., the surface stoichiometry is Ru : H = 1 : 1. The relative nature of the method, which cancels systematic errors, together with the utilization of a glass envelope around the mass spectrometer, which reduces spurious contributions in the thermal desorption spectra, results in high accuracy in the determination of absolute fractional coverages.

Quantum Mechanics Studies of Fuel Cell Catalysts and Proton Conducting Ceramics with Validation by Experiment

We carried out quantum mechanics (QM) studies aimed at improving the performance of hydrogen fuel cells. This led to predictions of improved materials, some of which were subsequently validated with experiments by our collaborators.

In part I, the challenge was to find a replacement for the Pt cathode that would lead to improved performance for the Oxygen Reduction Reaction (ORR) while remaining stable under operational conditions and decreasing cost. Our design strategy was to find an alloy with composition Pt3M that would lead to surface segregation such that the top layer would be pure Pt, with the second and subsequent layers richer in M. Under operating conditions we expect the surface to have significant O and/or OH chemisorbed on the surface, and hence we searched for M that would remain segregated under these conditions. Using QM we examined surface segregation for 28 Pt₃M alloys, where M is a transition metal. We found that only Pt₃Os and Pt₃Ir showed significant surface segregation when O and OH are chemisorbed on the catalyst surfaces. This result indicates that Pt₃Os and Pt3Ir favor formation of a Pt-skin surface layer structure that would resist the acidic electrolyte corrosion during fuel cell operation environments. We chose to focus on Os because the phase diagram for Pt-Ir indicated that Pt-Ir could not form a homogeneous alloy at lower temperature. To determine the performance for ORR, we used QM to examine all intermediates, reaction pathways, and reaction barriers involved in the processes for which protons from the anode reactions react with O₂ to form H₂O. These QM calculations used our Poisson-Boltzmann implicit solvation model include the effects of the solvent (water with dielectric constant 78 with pH 7 at 298K). We found that the rate determination step (RDS) was the O_ad hydration reaction (O_ad + H₂O_ad -> OH_ad + OH_ad) in both cases, but that the barrier for pure Pt of 0.50 eV is reduced to 0.48 eV for Pt₃Os, which at 80 degrees C would increase the rate by 218%. We collaborated with the Pu-Wei Wu’s group to carry out experiments, where we found that the dealloying process-treated Pt2Os catalyst showed two-fold higher activity at 25 degrees C than pure Pt and that the alloy had 272% improved stability, validating our theoretical predictions.

We also carried out similar QM studies followed by experimental validation for the Os/Pt core-shell catalyst fabricated by the underpotential deposition (UPD) method. The QM results indicated that the RDS for ORR is a compromise between the OOH formation step (0.37 eV for Pt, 0.23 eV for Pt_2ML/Os core-shell) and H₂O formation steps (0.32 eV for Pt, 0.22 eV for Pt_2ML/Os core-shell). We found that Pt_2ML/Os has the highest activity (compared to pure Pt and to the Pt₃Os alloy) because the 0.37 eV barrier decreases to 0.23 eV. To understand what aspects of the core shell structure lead to this improved performance, we considered the effect on ORR of compressing the alloy slab to the dimensions of pure Pt. However this had little effect, with the same RDS barrier 0.37 eV. This shows that the ligand effect (the electronic structure modification resulting from the Os substrate) plays a more important role than the strain effect, and is responsible for the improved activity of the core- shell catalyst. Experimental materials characterization proves the core-shell feature of our catalyst. The electrochemical experiment for Pt_2ML/Os/C showed 3.5 to 5 times better ORR activity at 0.9V (vs. NHE) in 0.1M HClO₄ solution at 25 degrees C as compared to those of commercially available Pt/C. The excellent correlation between experimental half potential and the OH binding energies and RDS barriers validate the feasibility of predicting catalyst activity using QM calculation and a simple Langmuir–Hinshelwood model.

In part II, we used QM calculations to study methane stream reforming on a Ni-alloy catalyst surfaces for solid oxide fuel cell (SOFC) application. SOFC has wide fuel adaptability but the coking and sulfur poisoning will reduce its stability. Experimental results suggested that the Ni4Fe alloy improves both its activity and stability compared to pure Ni. To understand the atomistic origin of this, we carried out QM calculations on surface segregation and found that the most stable configuration for Ni₄Fe has a Fe atom distribution of (0%, 50%, 25%, 25%, 0%) starting at the bottom layer. We calculated that the binding of C atoms on the Ni4Fe surface is 142.9 Kcal/mol, which is about 10 Kcal/mol weaker compared to the pure Ni surface. This weaker C binding energy is expected to make coke formation less favorable, explaining why Ni₄Fe has better coking resistance. This result confirms the experimental observation. The reaction energy barriers for CHx decomposition and C binding on various alloy surface, Ni₄X (X=Fe, Co, Mn, and Mo), showed Ni₄Fe, Ni₄Co, and Fe₄Mn all have better coking resistance than pure Ni, but that only Ni₄Fe and Fe₄Mn have (slightly) improved activity compared to pure Ni.

In part III, we used QM to examine the proton transport in doped perovskite-ceramics. Here we used a 2x2x2 supercell of perovskite with composition Ba₈X₇M₁(OH)₁O₂₃ where X=Ce or Zr and M=Y, Gd, or Dy. Thus in each case a 4⁺ X is replace by a 3⁺ M plus a proton on one O. Here we predicted the barriers for proton diffusion allowing both includes intra-octahedron and inter-octahedra proton transfer. Without any restriction, we only observed the inter-octahedra proton transfer with similar energy barrier as previous computational work but 0.2 eV higher than experimental result for Y doped zirconate. For one restriction in our calculations is that the O_donor-O_acceptor atoms were kept at fixed distances, we found that the barrier difference between cerates/zirconates with various dopants are only 0.02~0.03 eV. To fully address performance one would need to examine proton transfer at grain boundaries, which will require larger scale ReaxFF reactive dynamics for systems with millions of atoms. The QM calculations used here will be used to train the ReaxFF force field.

Structurally engineered cytochromes c with novel ligand-binding properties

Semisynthesis of horse heart cytochrome c and site-directed mutagenesis of Saccharomyces cerevisiae (S. c.) iso-1-cytochrome c have been utilized to substitute Ala for the cytochrome c heme axial ligand Met80 to yield ligand-binding proteins (horse heart Ala80cyt c and S.c. Ala80cyt c) with spectroscopic properties remarkably similar to those of myoglobin. Both species of Fe(II)Ala80cyt c form exceptionally stable dioxygen complexes with autoxidation rates 10-30x smaller and O₂ binding constants ~ 3x greater than those of myoglobin. The resistance of O₂-Fe(II)Ala80cyt c to autoxidation is attributed in part to protection of the heme site from solvent as exhibited by the exceptionally slow rate of CO binding to the heme as well as the low quantum yield of CO photodissociation.

UV/vis, EPR, and paramagnetic NMR spectroscopy indicate that at pH 7 the Fe(III)Ala80cyt c heme is low-spin with axial His-OH^- coordination and that below pH ~6.5, Fe(III)Ala80cyt cis high-spin with His-H₂O heme ligation. Significant differences in the pH dependence of the ¹H NMR spectra of S.c. Fe(III)Ala80cyt c compared to wild-type demonstrate that the axial ligands influence the conformational energetics of cytochrome c.

¹H NMR spectroscopy has been utilized to determine the solution structure of the cyanide derivative of S.c. Fe(III)Ala80cyt c. 82% of the resonances in the ¹H NMR spectrum of S.c. CN-Fe(III)Ala80cyt c have been assigned through 1D and 2D experiments. The RMSD values after restrained energy minimization of the family of 17 structures obtained from distance geometry calculations are 0.68 ± 0.11 Å for the backbone and 1.32 ± 0.14 Å for all heavy atoms. The solution structure indicates that a tyrosine in the "distal" pocket of CN-Fe(III)Ala80cyt c forms a hydrogen bond with the Fe(III)-CN unit, suggesting that it may play a role analogous to that of the distal histidine in myoglobin in stabilizing the dioxygen adduct.

Computational Predictions of G Protein-Coupled Receptor Structures and Binding Sites

G protein-coupled receptors (GPCRs) are the largest family of proteins within the human genome. They consist of seven transmembrane (TM) helices, with a N-terminal region of varying length and structure on the extracellular side, and a C-terminus on the intracellular side. GPCRs are involved in transmitting extracellular signals to cells, and as such are crucial drug targets. Designing pharmaceuticals to target GPCRs is greatly aided by full-atom structural information of the proteins. In particular, the TM region of GPCRs is where small molecule ligands (much more bioavailable than peptide ligands) typically bind to the receptors. In recent years nearly thirty distinct GPCR TM regions have been crystallized. However, there are more than 1,000 GPCRs, leaving the vast majority of GPCRs with limited structural information. Additionally, GPCRs are known to exist in a myriad of conformational states in the body, rendering the static x-ray crystal structures an incomplete reflection of GPCR structures. In order to obtain an ensemble of GPCR structures, we have developed the GEnSeMBLE procedure to rapidly sample a large number of variations of GPCR helix rotations and tilts. The lowest energy GEnSeMBLE structures are then docked to small molecule ligands and optimized. The GPCR family consists of five subfamilies with little to no sequence homology between them: class A, B1, B2, C, and Frizzled/Taste2. Almost all of the GPCR crystal structures have been of class A GPCRs, and much is known about their conserved interactions and binding sites. In this work we particularly focus on class B1 GPCRs, and aim to understand that family’s interactions and binding sites both to small molecules and their native peptide ligands. Specifically, we predict the full atom structure and peptide binding site of the glucagon-like peptide receptor and the TM region and small molecule binding sites for eight other class B1 GPCRs: CALRL, CRFR1, GIPR, GLR, PACR, PTH1R, VIPR1, and VIPR2. Our class B1 work reveals multiple conserved interactions across the B1 subfamily as well as a consistent small molecule binding site centrally located in the TM bundle. Both the interactions and the binding sites are distinct from those seen in the more well-characterized class A GPCRs, and as such our work provides a strong starting point for drug design targeting class B1 proteins. We also predict the full structure of CXCR4 bound to a small molecule, a class A GPCR that was not closely related to any of the class A GPCRs at the time of the work.

I. Site effects and exciton structure in molecular crystals - Benzene. II. The first and second triplet states of solid benzene

The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C₆H₆, C₆H₅D, m-C₆H₄D₂, p-C₆H₄D₂, sym-C₆H₃D₃, C₆D₅H, and C₆D₆ in either a C₆H₆ or C₆D₆ host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C₆H₆, C₆D₆, and sym-C₆H₃D₃; c) the orientational effect for the isotopes without a trigonal axis in both the ¹B_2u electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.

To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.

A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be^-Cr - A/r⁶ ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.

In part II the location and identification of the benzene first and second triplet states (³B_1u and ³E_1u) is given.

Understanding Co-translational Protein Targeting and Lithium Dendrite Formation through Free Energy Simulations and Coarse-Grained Models

We describe the application of alchemical free energy methods and coarse-grained models to study two key problems: (i) co-translational protein targeting and insertion to direct membrane proteins to the endoplasmic reticulum for proper localization and folding, (ii) lithium dendrite formation during recharging of lithium metal batteries. We show that conformational changes in the signal recognition particle, a central component of the protein targeting machinery, confer additional specificity during the the recognition of signal sequences. We then develop a three-dimensional coarse-grained model to study the long-timescale dynamics of membrane protein integration at the translocon and a framework for the calculation of binding free energies between the ribosome and translocon. Finally, we develop a coarse-grained model to capture the dynamics of lithium deposition and dissolution at the electrode interface with time-dependent voltages to show that pulse plating and reverse pulse plating methods can mitigate dendrite growth.