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- Ab initio (9)
- Electron transfer (5)
- Electronic coupling element (4)
- Excitation energy (2)
- Generalized Mulliken-Hush method (2)
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- Hydrogen bonds (2)
- Low-lying electronic state (2)
- Rotamers (2)
- Time-dependent density functional theory (2)
- 1-3-5-hexatriene (1)
- 1-3-butadiene (1)
- Ab Initio investigation (1)
- Ab initio calculations (1)
- Adiabatic excitation energy (1)
- Alkali oxides (1)
- All-trans octatetraene (1)
- Arylamine-substituted acridinium ion systems (1)
- Assembly lines (1)
- Biomimetic synthesis (1)
- Bonding (1)
- C-N bonds (1)
- CASSCF (1)
- Charge exchange (1)
- Charts (1)
- Chemical Engineering (1)
- Chemical applications (1)
- Chemical equations (1)
- Computer simulations (1)
- Cyclization (1)
- Density functional theory (1)
Articles 1 - 29 of 29
Full-Text Articles in Chemistry
Direct, Biomimetic Synthesis Of (+)-Artemone Via A Stereoselective, Organocatalytic Cyclization, Eric D. Nacsa, Brian C. Fielder, Shannon P. Wetzler, Veerasak Srisuknimit, Jonathan P. Litz, Mary J. Van Vleet, Kim Quach, David A. Vosburg
Direct, Biomimetic Synthesis Of (+)-Artemone Via A Stereoselective, Organocatalytic Cyclization, Eric D. Nacsa, Brian C. Fielder, Shannon P. Wetzler, Veerasak Srisuknimit, Jonathan P. Litz, Mary J. Van Vleet, Kim Quach, David A. Vosburg
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We present a four-step synthesis of (+)-artemone from (–)- linalool, featuring iminium organocatalysis of a doubly diastereoselective conjugate addition reaction. The strategy follows a proposed biosynthetic pathway, rapidly generates stereochemical complexity, uses no protecting groups, and minimizes redox manipulations.
Reduced Electronic Spaces For Modeling Donor/Acceptor Interactions, Robert J. Cave, Stephen T. Edwards '06, John A, Kouzelos '07, Marshall D. Newton
Reduced Electronic Spaces For Modeling Donor/Acceptor Interactions, Robert J. Cave, Stephen T. Edwards '06, John A, Kouzelos '07, Marshall D. Newton
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Diabatic states for donor (D) and acceptor (A) interactions in electron transfer (ET) processes are formulated and evaluated, along with coupling elements (HDA) and effective D/A separation distances (rDA), for reduced electronic spaces of variable size, using the generalized Mulliken Hush model (GMH), applicable to an arbitrary state space and nuclear configuration, and encompassing Robin−Day class III and as well as class II situations. Once the electronic state space is selected (a set of n ≥ 2 adiabatic states approximated by an orbital space based on an effective 1-electron (1-e) Hamiltonian), the charge-localized GMH …
The Initial And Final States Of Electron And Energy Transfer Processes: Diabatization As Motivated By System-Solvent Interactions, Joseph E. Subotnik, Robert J. Cave, Ryan P. Steele, Neil Shenvi
The Initial And Final States Of Electron And Energy Transfer Processes: Diabatization As Motivated By System-Solvent Interactions, Joseph E. Subotnik, Robert J. Cave, Ryan P. Steele, Neil Shenvi
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For a system which undergoes electron or energy transfer in a polar solvent, we define the diabatic states to be the initial and final states of the system, before and after the nonequilibrium transfer process. We consider two models for the system-solvent interactions: A solvent which is linearly polarized in space and a solvent which responds linearly to the system. From these models, we derive two new schemes for obtaining diabatic states from ab initio calculations of the isolated system in the absence of solvent. These algorithms resemble standard approaches for orbital localization, namely, the Boys and Edmiston–Ruedenberg (ER) formalisms. …
Tunneling Through Weak Interactions: Comparison Of Through-Space-, H-Bond-, And Through-Bond-Mediated Tunneling, Westin Kurlancheek '03, Robert J. Cave
Tunneling Through Weak Interactions: Comparison Of Through-Space-, H-Bond-, And Through-Bond-Mediated Tunneling, Westin Kurlancheek '03, Robert J. Cave
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Results from ab initio electronic structure theory calculations on model systems allow for the detailed comparison of tunneling through covalently bonded contacts, hydrogen bonds, and van der Waals contacts. Considerable geometrical sensitivity as well as an exponential distance dependence of the tunneling is observed for tunneling through various nonbonded contacts. However, the fundamental result from the present study is that at most a modest difference is observed between tunneling mediated by H-bonds and tunneling mediated by van der Waals contacts at typical distances for each type of interaction. These results are considered in relation to the pathways model of Beratan …
Nature's Assembly Line Logic For Natural Products, Christopher T. Walsh, Ryan G. Kruger, David A. Vosburg
Nature's Assembly Line Logic For Natural Products, Christopher T. Walsh, Ryan G. Kruger, David A. Vosburg
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Nature fashions a very large number of diverse products (molecular weights ranging from ca. 200 to 2000 daltons) from simple monomeric metabolites used in primary metabolism. These include polyketide scaffolds generated from the simple C₃ malonyl CoA and C₄ methylmalonyl CoA monomers and nonribosomal peptides made from both the 20 proteinogenic amino acids and dozens of nonpoteinogenic amino acids.¹ A large family of terpenoid skeletons are built from the Δ²- and Δ³-alkene isomers of the biological isoprene monomer, isoprenyl-pyrophosphate.²
A Theoretical Investigation Of Charge Transfer In Several Substituted Acridinium Ions, Jason Lappe '00, Robert J. Cave, Marshall D. Newton, I.V. Rostov
A Theoretical Investigation Of Charge Transfer In Several Substituted Acridinium Ions, Jason Lappe '00, Robert J. Cave, Marshall D. Newton, I.V. Rostov
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We present calculations for various properties of the ground and excited states of several arylamine-substituted acridinium ion systems that have been studied experimentally. Using ab initio and semiempirical quantum mechanical methods together with the generalized Mulliken−Hush (GMH) model, we examine the excitation energies, dipole moment shifts, and electronic coupling elements for the vertical charge shift (CSh) processes in these systems. We also examine solvent effects on these properties using a dielectric continuum reaction field model. The results are in generally good agreement with available experimental results and indicate that there is strong electronic coupling in these systems over a wide …
Theoretical Investigation Of The Ground And Excited States Of Coumarin 151 And Coumarin 120, Robert J. Cave, Kieron Burke, Edward W. Castner Jr.
Theoretical Investigation Of The Ground And Excited States Of Coumarin 151 And Coumarin 120, Robert J. Cave, Kieron Burke, Edward W. Castner Jr.
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We present calculations of various properties of the ground and excited states of Coumarins 151 and 120. These and related coumarins are important in investigating ultrafast solvation processes in liquids and complex solutions as well as being important acceptors in model electron-transfer systems. We calculate the following: (1) the electronic excitation energies to several low-lying singlet states, (2) ground and excited-state dipole moments, (3) solvation effects on excitation energies, and (4) the properties of single Coumarin 151-water complexes. We test our Time-Dependent Density Functional Theory (TDDFT) calculations against CASSCF, CASPT2 (both single and multistate versions), CIS, and ZINDO. Using TDDFT, …
Multistate Effects In Calculations Of The Electronic Coupling Element For Electron Transfer Using The Generalized Mulliken−Hush Method, Michael Rust '01, Jason Lappe '00, Robert J. Cave
Multistate Effects In Calculations Of The Electronic Coupling Element For Electron Transfer Using The Generalized Mulliken−Hush Method, Michael Rust '01, Jason Lappe '00, Robert J. Cave
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A simple diagnostic is developed for the purpose of determining when a third state must be considered to calculate the electronic coupling element for a given pair of diabatic states within the context of the generalized Mulliken−Hush approach (Chem. Phys. Lett. 1996, 275, 15−19). The diagnostic is formulated on the basis of Löwdin partitioning theory. In addition, an effective 2-state GMH expression is derived for the coupling as it is modified by the presence of the third state. Results are presented for (i) a model system involving charge transfer from ethylene to methaniminium cation, (ii) a …
Article Are Hydrogen Bonds Unique Among Weak Interactions In Their Ability To Mediate Electronic Coupling?, Emily Cukier '03, Sarah Daniels '02, Eric Vinson '01, Robert J. Cave
Article Are Hydrogen Bonds Unique Among Weak Interactions In Their Ability To Mediate Electronic Coupling?, Emily Cukier '03, Sarah Daniels '02, Eric Vinson '01, Robert J. Cave
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Superexchange effects on the electronic coupling element for electron transfer are investigated using water dimers and atomic donors and acceptors. We compare the electronic coupling elements obtained with H-bonded dimers to those obtained for other water dimer geometries at given donor−acceptor and oxygen−oxygen distances. The H-bonded orientation does not yield significantly different coupling elements from non-H-bonded orientations at a given oxygen−oxygen distance. In addition, the distance dependence of the coupling mediated by H-bonds is not significantly different from that for other dimer geometries. It is found that protonation of the intervening waters has a significant effect on coupling elements for …
Time-Dependent Density Functional Theory Investigation Of The Ground And Excited States Of Coumarins 102, 152, 153, And 343, Robert J. Cave, Edward W. Castner Jr.
Time-Dependent Density Functional Theory Investigation Of The Ground And Excited States Of Coumarins 102, 152, 153, And 343, Robert J. Cave, Edward W. Castner Jr.
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We present calculations of various properties of the ground and excited electronic states of coumarins 102, 152, 153, and 343. Using density functional theory (DFT) and time-dependent density functional theory (TDDFT), we examine the excitation energies to the S1 and S2 states, the ground and excited-state dipole moments, and the lowest ionization potentials of these coumarins. In the case of C153, we locate two distinct S0 minima due to differing conformations of the julolidyl ring structure and compare properties for the syn and anti conformers. For C343, we examine the possibility of proton transfers in the ground …
Solvent As Electron Donor: Donor/Acceptor Electronic Coupling Is A Dynamical Variable, Edward W. Castner Jr., Darcy Kennedy '00, Robert J. Cave
Solvent As Electron Donor: Donor/Acceptor Electronic Coupling Is A Dynamical Variable, Edward W. Castner Jr., Darcy Kennedy '00, Robert J. Cave
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We combine analysis of measurements by femtosecond optical spectroscopy, computer simulations, and the generalized Mulliken−Hush (GMH) theory in the study of electron-transfer reactions and electron donor−acceptor interactions. Our focus is on ultrafast photoinduced electron-transfer reactions from aromatic amine solvent donors to excited-state acceptors. The experimental results from femtosecond dynamical measurements fall into three categories: six coumarin acceptors reductively quenched by N,N-dimethylaniline (DMA), eight electron-donating amine solvents reductively quenching coumarin 152 (7-(dimethylamino)-4-(trifluoromethyl)coumarin), and reductive quenching dynamics of two coumarins by DMA as a function of dilution in the nonreactive solvents toluene and chlorobenzene. Applying a combination of molecular …
On The Vertical And Adiabatic Excitation Energies Of The 21a(G), State Of Trans-1,3-Butadiene, Jason Lappe '00, Robert J. Cave
On The Vertical And Adiabatic Excitation Energies Of The 21a(G), State Of Trans-1,3-Butadiene, Jason Lappe '00, Robert J. Cave
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The excitation energy to the 21Ag state of trans-1,3-butadiene is examined using a variety of ab initio electronic structure techniques. While analogous states have been shown to be the lowest singlet excited states for all longer polyenes, for butadiene the position of the 21Ag state relative to the HOMO → LUMO excitation (11Bu) has been difficult to establish theoretically. We employ a variety of methods (CASSCF, CASPT2, MRSDCI, QDVPT) to examine both the vertical and adiabatic excitation energies for this state. At the ground-state geometry, the vertical excitation energies …
A Theoretical Study Of The Electronic Coupling Element For Electron Transfer In Water, Newt E. Miller '99, Matthew C. Wander '97, Robert J. Cave
A Theoretical Study Of The Electronic Coupling Element For Electron Transfer In Water, Newt E. Miller '99, Matthew C. Wander '97, Robert J. Cave
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The electronic coupling element for electron transfer between a donor and acceptor in water is examined using simulations combining molecular dynamics and semiempirical quantum mechanics. In the first phase of the simulations a model donor and acceptor are solvated in water, using realistic potentials. Following equilbration, molecular dynamics simulations are performed with the donor, acceptor, and water at approximately 300 K, under periodic boundary conditions. In the second phase of the simulation, the electronic coupling element between the donor and acceptor is calculated for a number of time slices, in the presence of the intervening water molecules (those having a …
An Nmr Investigation Of The Effect Of Hydrogen Bonding On The Rates Of Rotation About The C-N Bonds In Urea And Thiourea, Karl A. Haushalter, Janice Lau, John D. Roberts
An Nmr Investigation Of The Effect Of Hydrogen Bonding On The Rates Of Rotation About The C-N Bonds In Urea And Thiourea, Karl A. Haushalter, Janice Lau, John D. Roberts
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The interaction between urea and tetrabutylammonium acetate was investigated in dimethylformamide/ dimethyl sulfoxide solutions using ¹H and 15^N NMR. The chemical-shift behavior of the urea protons is consistent with a urea-acetate hydrogen-bonded complex involving both carboxylate oxygens and the urea hydrogens trans to the carbonyl oxygen with K_assoc = 120 ± 10. Line shape analysis of the temperature-dependent ¹H NMR spectra show that ∆G^‡ for rotation about the C-N bond of urea changes only slightly from 11.0 ± 0.1 to 11.2 ± 0.1 kcal/mol on 1:1 molar addition of tetrabutylammonium acetate to a dilute solution of urea. A parallel investigation …
Theoretical Study Of Solvent Effects On The Electronic Coupling Element In Rigidly Linked Donor-Acceptor Systems, Robert J. Cave, Marshall D. Newton, Krishna Kumar, Matthew B. Zimmt
Theoretical Study Of Solvent Effects On The Electronic Coupling Element In Rigidly Linked Donor-Acceptor Systems, Robert J. Cave, Marshall D. Newton, Krishna Kumar, Matthew B. Zimmt
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The recently developed generalized Mulliken-Hush approach for the calculation of the electronic coupling matrix element for electron-transfer processes is applied to two rigidly linked donor-bridge-acceptor systems having dimethoxyanthracene as the donor and a dicarbomethoxycyclobutene unit as the acceptor. The dependence of the electronic coupling matrix element as a function of bridge type is examined with and without solvent molecules present. For clamp-shaped bridge structures solvent can have a dramatic effect on the electronic coupling matrix element. The behavior with variation of solvent is in good agreement with that observed experimentally for these systems.
Resonance Raman Investigation Of The Radical Cation Of 1,3,5-Hexatriene, Tamas Keszthelyi, Robert Wilbrandt, Robert J. Cave, Jenifer L. Johnson
Resonance Raman Investigation Of The Radical Cation Of 1,3,5-Hexatriene, Tamas Keszthelyi, Robert Wilbrandt, Robert J. Cave, Jenifer L. Johnson
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The resonance Raman spectrum of the 1,3,5-hexatriene radical cation generated by v-irradiation in a Freon glass is reported. The spectrum is excited at 395 nm in resonance with the second absorption band. Identical spectra are obtained from ionized (E)- and (Z)-1,3,5-hexatriene. The presence of more than one rotamer has to be assumed to account for all the observed resonance Raman bands. The bands are assigned to a mixture of the two rotamers, calculated at lowest energy, the ttt an tct rotamers, on the basis of ab initio ROHF/6-31G calculated harmonic frequencies. The spectrum indicates that …
A Theoretical Investigation Of The Stability Of Hpc, Hannah S. Hong, Robert J. Cave
A Theoretical Investigation Of The Stability Of Hpc, Hannah S. Hong, Robert J. Cave
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Several ab initio methods are applied to the study of two linear isomers of methylidyne phosphine, HCP, and HPC. Single-reference correlation methods ranging from second-order Møller-Plesset theory to coupled cluster singles and doubles theory with noninterative inclusion of connected triple excitations were applied in a variety of basis sets of increasing size. In addition, complete active space self-consistent field wave functions, multireference singles and doubles configuration interaction, and averaged coupled pair functional theory were also applied to HPC. For HPC comparison of the single-reference based results is made with experimental data and previous theory to assess the accuracy …
Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92
Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92
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No abstract provided in this article.
A Casscf Study Of Various Rotamers Of The Hexatriene Radical Cation, Robert J. Cave, Jenifer L. Johnson
A Casscf Study Of Various Rotamers Of The Hexatriene Radical Cation, Robert J. Cave, Jenifer L. Johnson
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Results are presented from ab initio calculations on the ground and two low-lying excited states of the hexatriene radical cation in a variety of stable conformations of the electronic ground state of the molecule. We have performed Hartree-Fock geometry optimizations using the STO-3G and 6-31g basis sets and have performed vibrational analyses for all stable conformers in the 6-31G basis. In addition, we have performed geometry optimizations in both basis sets using CASSCF wave functions where the five π electrons are correlated. No new geometrical information is obtained at this level of treatment. Excitation energies to the two lowest-lying doublet …
A Theoretical Study Of Models For X2y2 Zintl Ions, Robert J. Cave, Ernest R. Davidson, Philippe Sautet, Enric Canadell, Odile Eisenstein
A Theoretical Study Of Models For X2y2 Zintl Ions, Robert J. Cave, Ernest R. Davidson, Philippe Sautet, Enric Canadell, Odile Eisenstein
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Ab initio and extended Hückel calculations have been used to discuss the bonding scheme in X₂Y₂ neutral and ionic main group clusters. A qualitative analysis suggests that two different electron counts, 20 and 22, are possible for the butterfly structures of these systems. This results from two orbital crossings in the correlation diagram for the tetrahedral (T_d) -> butterfly (C_2v) -> square-planar (D_2h) transformation. Detailed ab initio computations substantiate this analysis and show that the 20-electron butterfly structure becomes increasingly favored over the tetrahedral one in X₂Y₂ clusters when the 2 atoms have increasing electronegativity difference. …
An Ab Initio Investigation Of The Stabilization Of Selected Β-Substituted Ethyl Cations And Α-Substituted Methyl Cations, Julia C. White, Robert J. Cave, Ernest R. Davidson
An Ab Initio Investigation Of The Stabilization Of Selected Β-Substituted Ethyl Cations And Α-Substituted Methyl Cations, Julia C. White, Robert J. Cave, Ernest R. Davidson
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In this study, we calculate the stabilization of β-substituted ethyl cations (R = H, Li, BeH, BH_2, CH_3, NH_2, OH, F, Na, MgH, AlH_2, SiH_3, PH_2, SH, Cl) and α-substituted methyl cations (R = H, Li, CH_3, NH_2, OH, F, Na, SiH_3, PH_2, SH, Cl) in order to obtain a relationship between the nature of the substituent and the degree of stabilization of the cation. Results show that the stabilization energy is related to the electronegativity of the β substituents, but not the α substituents. The rotational barrier of the β-substituted ethyl cation is linearly related to the Mulliken population …
Ab Initio Investigation Of Several Low-Lying States Of All-Trans Octatetraene, Robert J. Cave, Ernest R. Davidson
Ab Initio Investigation Of Several Low-Lying States Of All-Trans Octatetraene, Robert J. Cave, Ernest R. Davidson
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The results of ab initio calculations that examine vertical and nonvertical transitions to several low-lying states of all-trans-octatetraene are presented. It is found that the lowest vertical excitation is to a valence π → π* ¹B_u state, and the nominally doubly excited 2¹A_g state occurs approximately 0.4 eV higher at the geometry of the ground state. Using estimated excited-state equilibrium geometries, we find that the 2¹A_g state is indeed the lowest singlet excited state, having a 0-0 tarnsition energy of 4.15 eV. The 0-0 transition energy for the 1¹B_u state is calculated to be 4.56 eV. The present results …
A Theoretical Investigation Of Several Low-Lying States Of Trans, Trans-1,3,5-Hexatriene, Robert J. Cave, Ernest R. Davidson
A Theoretical Investigation Of Several Low-Lying States Of Trans, Trans-1,3,5-Hexatriene, Robert J. Cave, Ernest R. Davidson
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Results from ab initio calculations concerning several low-lying electronic states of trans,trans-1,3,5-hexatriene are presented and compared with experimental and previous theoretical results. The lowest excited singlet state is predicted to be the ¹B_u state, having essentially valencelike π → π* character. The nominally doubly excited 2¹A_g state is found to lie approximately 0.6-0.9 eV above the 1¹B_u state. Results are also presented for several Rydberg states. The implications of the present results for current parametrizations of semiempirical π molecular orbital schemes are discussed.
A Theoretical Investigation Of Some Low-Lying Singlet States Of 1,3-Butadiene, Robert J. Cave, Ernest R. Davidson
A Theoretical Investigation Of Some Low-Lying Singlet States Of 1,3-Butadiene, Robert J. Cave, Ernest R. Davidson
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Results are presented from extensive ab initio calculations on several low-lying singlet states of cis- and trans-1,3-butadiene. The results indicate a qualitative difference between the cis and trans isomers for the lowest π → π* transition. For the cis isomer, the first excited singlet state of the same symmetry as the ground state is found to lie above the lowest π → π* transition, and we estimate that this is also the case for the trans isomer.
Chemical Applications Of Scanning Tunneling Microscopy, Paul West, John Kramer, David V. Baxter, Robert J. Cave, John D. Baldeschwieler
Chemical Applications Of Scanning Tunneling Microscopy, Paul West, John Kramer, David V. Baxter, Robert J. Cave, John D. Baldeschwieler
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The development of a scanning tunneling microscope at the California Institute of Technology is well under way. Electron tunneling has been demonstrated, and preliminary surface images of gold films have been obtained. Additional instrumental development is required to achieve the atomic resolution which is required for the study of chemical processes on surfaces. A theoretical model is also being developed for the study of tunneling of electrons from the probe to surfaces with molecular species absorbed, and with atomic and molecular species intervening between the probe and the surface. These experimental tools and theoretical models, which are being developed concurrently, …
Mutual Orientation Effects On Electron-Transfer Reactions Between Porphyrins, Robert J. Cave, Paul Siders, R.A. Marcus
Mutual Orientation Effects On Electron-Transfer Reactions Between Porphyrins, Robert J. Cave, Paul Siders, R.A. Marcus
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Mutual orientation effects on the rate of nonadiabatic electron transfer between several diporphyrin pairs of experimental interest are examined. The electronic matrix element for electron transfer is calculated within a one-electron spheroidal model for a variety of states and orientations which are relevant to both biological and synthetic electron-transfer systems. Both the mutual orientation of the pairs and the nodal structure of the donor and acceptor orbitals can have large effects on calculated rates.
Alkali Oxides. Analysis Of Bonding And Explanation Of The Reversal Of Ordering Of The 2Σ And 2Π States, Janet N. Allison, Robert J. Cave, William A. Goddard Iii
Alkali Oxides. Analysis Of Bonding And Explanation Of The Reversal Of Ordering Of The 2Σ And 2Π States, Janet N. Allison, Robert J. Cave, William A. Goddard Iii
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We analyze the bonding in alkali oxides, MO, for M = Li, Na, K, Rb, and Cs. Using ab initio correlated wave functions we find that the ground state is ²II for M = Li, Na, and K and that the ground state is ²Ʃ^+ for M = Rb and Cs. The origin of this effect is explained.
A Survey Of Ligand Effects Upon The Reaction Entropies Of Some Transition Metal Redox Couples, Edmund L. Yee, Robert J. Cave, Kendall L. Guyer, Paul D. Tyma, Michael J. Weaver
A Survey Of Ligand Effects Upon The Reaction Entropies Of Some Transition Metal Redox Couples, Edmund L. Yee, Robert J. Cave, Kendall L. Guyer, Paul D. Tyma, Michael J. Weaver
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The reaction entropies ∆S°_rc of a number of transition metal redox couples of the form M(III)/(II) in aqueous solution have been determined using nonisothermal electrochemical cells in order to explore the effect of varying the ligand structure upon the nature of the ion-solvent interactions. Examinations of six aquo couples of the form M(OH_2)_n&3+/2+ with varying metal M yielded ∆S°_rc values in the range 36-49 eu. In order to scrutinize the effect of replacing aquo with ammine and simple anionic ligands, Ru(III)/(II) couples were employed since the relative substituion inertness of both oxidation states allowed ∆S …
A Theoretical Model For Gas Separation In A Glow Discharge: Cataphoresis, Fredrick H. Shair, Donald S. Remer
A Theoretical Model For Gas Separation In A Glow Discharge: Cataphoresis, Fredrick H. Shair, Donald S. Remer
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A theoretical model for transient and steady-state cataphoresis is developed starting with the macroscopic equations of continuity. After a brief breakdown period, the impurity ions are assumed to be closely coupled with their neutral counterparts. The basic assumptions in the model are that after breakdown, the level of ionization of the impurity, and the axial electric field remain constant; it is demonstrated that under these conditions a system involving rapid ionization-recombination reactions is equivalent to a system in which no reaction occurs, but in which the "effective'' ion mobility is a product of the true ion mobility and the fraction …