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Frequency domain shaped binary laser pulses were optimized to perform 2 qubitquantum gate operations in C12O16. The qubit rovibrational state representation was chosen so that all gate operations consisted of one-photon transitions. The amplitude and phase varied binary pulses were determined using a genetic algorithm optimization routine. Binary pulses have two possible amplitudes, 0 or 1, and two phases, 0 or π, for each frequency component of the pulse. Binary pulses are the simplest to shape experimentally and provide a minimum fidelity limit for amplitude and phase shaped pulses. With the current choice of qubit representation and using optimized binary pulses, fidelities of 0.80 and as high as 0.97 were achieved for the controlled-NOT and alternative controlled-NOT quantum gates. This indicates that with a judicious choice of qubits, most of the required control can be obtained with a binary pulse. Limited control was observed for 2 qubit NOT and Hadamard gates due to the need to control multiple excitations. The current choice of qubit representation produces pulses with decreased energies and superior fidelities when compared with rovibrational qubit representations consisting of two-photon transitions. The choice of input pulse energy is important and applying pulses of increased energy does not necessarily lead to a better fidelity.

We have demonstrated the use of *ab initio*molecular dynamics (AIMD) trajectories to compute the vibrational energy levels of molecular systems in the context of the semiclassical initial value representation (SC-IVR). A relatively low level of electronic structure theory (HF/3-21G) was used in this proof-of-principle study. Formaldehyde was used as a test case for the determination of accurate excited vibrational states. The AIMD-SC-IVR vibrational energies have been compared to those from curvilinear and rectilinear vibrational self-consistent field/vibrational configuration interaction with perturbation selected interactions-second-order perturbation theory (VSCF/VCIPSI-PT2) and correlation-corrected vibrational self-consistent field (cc-VSCF) methods. The survival amplitudes were obtained from selecting different reference wavefunctions using only a single set of molecular dynamics trajectories. We conclude that our approach is a further step in making the SC-IVR method a practical tool for first-principles quantum dynamics simulations.

The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT_{1} and double frequency 2-qubit NOT_{2}quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.

A fully quantum mechanical dynamical calculation on the photodissociation of molecular chlorine is presented. The magnitudes and phases of all the relevant photofragment *T*-matrices have been calculated, making this study the computational equivalent of a “complete experiment,” where all the possible parameters defining an experiment have been determined. The results are used to simulate cross-sections and angular momentumpolarization information which may be compared with experimental data. The calculations rigorously confirm the currently accepted mechanism for the UV photodissociation of Cl_{2}, in which the majority of the products exit on the C ^{1}Π_{1u }state, with non-adiabatic couplings to the A ^{3}Π_{1u }and several other Ω = 1 states, and a small contribution from the BΠ3 state present at longer wavelengths.

Deuterium kinetic isotope effects (KIEs) are reported for the first time for the dissociation of a protein–ligand complex in the gas phase. Temperature-dependent rate constants were measured for the loss of neutral ligand from the deprotonated ions of the 1:1 complex of bovine β-lactoglobulin (Lg) and palmitic acid (PA), (Lg + PA)*n*− → Lg*n*– + PA, at the 6– and 7– charge states. At 25 °C, partial or complete deuteration of the acyl chain of PA results in a measurable inverse KIE for both charge states. The magnitude of the KIEs is temperature dependent, and Arrhenius analysis of the rate constants reveals that deuteration of PA results in a decrease in activation energy. In contrast, there is no measurable deuterium KIE for the dissociation of the (Lg + PA) complex in aqueous solution at pH 8. Deuterium KIEs were calculated using conventional transition-state theory with an assumption of a late dissociative transition state (TS), in which the ligand is free of the binding pocket. The vibrational frequencies of deuterated and non-deuterated PA in the gas phase and in various solvents (*n*-hexane, 1-chlorohexane, acetone, and water) were established computationally. The KIEs calculated from the corresponding differences in zero-point energies account qualitatively for the observation of an inverse KIE but do not account for the magnitude of the KIEs nor their temperature dependence. It is proposed that the dissociation of the (Lg + PA) complex in aqueous solution also proceeds through a late TS in which the acyl chain is extensively hydrated such that there is no significant differential change in the vibrational frequencies along the reaction coordinate and, consequently, no significant KIE.

The effect of varying parameters specific to laser pulse shaping instruments on resulting fidelities for the ACNOT_{1}, NOT_{2}, and Hadamard_{2}quantum logic gates are studied for the diatomic molecule ^{12}C^{16}O. These parameters include varying the frequency resolution, adjusting the number of frequency components and also varying the amplitude and phase at each frequency component. A time domain analytic form of the original discretized frequency domain laser pulse function is derived, providing a useful means to infer the resulting pulse shape through variations to the aforementioned parameters. We show that amplitude variation at each frequency component is a crucial requirement for optimal laser pulse shaping, whereas phase variation provides minimal contribution. We also show that high fidelity laser pulses are dependent upon the frequency resolution and increasing the number of frequency components provides only a small incremental improvement to quantum gate fidelity. Analysis through use of the pulse area theorem confirms the resulting population dynamics for one or two frequency high fidelity laser pulses and implies similar dynamics for more complex laser pulse shapes. The ability to produce high fidelity laser pulses that provide both population control and global phase alignment is attributed greatly to the natural evolution phase alignment of the qubits involved within the quantum logic gate operation.

Velocity mapped ion imaging and resonantly enhanced multiphoton ionization time-of-flight methods have been used to investigate the photodissociation dynamics of the diatomic molecule Cl_{2} following excitation to the first UV absorption band. The experimental results presented here are compared with high level time dependent wavepacket calculations performed on a set of *ab initio* potential energy curves [D. B. Kokh, A. B. Alekseyev, and R. J. Buenker, J. Chem. Phys.120, 11549 (2004)10.1063/1.1753554]. The theoretical calculations provide the first determination of all dynamical information regarding the dissociation of a system of this complexity, including angular momentumpolarization. Both low rank *K* = 1, 2 and high rank *K* = 3 electronic polarization are predicted to be important for dissociation into both asymptotic product channels and, in general, good agreement is found between the recent theory and the measurements made here, which include the first experimental determination of high rank *K* = 3 orientation.

The nuclear quadrupole coupling constants (NQCCs) for the nitrogen and oxygen nuclei in N2O have been determined using a variety of computational methods (MP2, QCISD, DFT with B3LYP, PBE0, and B3PW91 functionals, CCSD, CCSD(T), CASSCF, and MRCI) combined with correlation-consistent basis sets. When compared to the available experimental determinations, the results demonstrate that only CCSD(T) and MRCI methods are capable of accurately predicting the NQCCs of the central and terminal nitrogen atoms. The spin-rotation and magnetic shielding tensors have also been determined and compared to experimental measurements where available. 14N and 17O NMR relaxation data for N2O in the gas phase and a variety of solvents is reported. The increase in the ratio of 14N spin–lattice relaxation times in solvent for the central and terminal nitrogens supports previous reports of the modification of the electric field gradients at these nuclei in van der Waals complexes. Ab initio computations for the linear FH···N2O complex confirm the large change in EFGs imposed by a single perturber.

General chemical strategies which provide controlled changes in the emission or absorption properties of biologically compatible fluorophores remain elusive. One strategy employed is the conversion of a fluorophore-attached alkyne (or azide) to a triazole through a copper-catalyzed azide–alkyne coupling (CuAAC) reaction. In this study, we have computationally examined a series of structurally related 2,1,3-benzoxadiazole (benzofurazan) fluorophores and evaluated changes in their photophysical properties upon conversion from alkyne (or azide) to triazole forms. We have also determined the photophysical properties for a known set of benzoxadiazole compounds. The absorption and emission energies have been determined computationally using time-dependent density functional theory (TD-DFT) with the Perdew, Burke, and Ernzerhof exchange-correlation density functional (PBE0) and the 6-31+G(d) basis set. The TD-DFT results consistently agreed with the experimentally determined absorption and emission wavelengths except for certain compounds where charge-transfer excited states occurred. In addition to determining the absorption and emission wavelengths, simple methods for predicting relative quantum yields previously derived from semiempirical calculations were reevaluated on the basis of the new TD-DFT results and shown to be deficient. These results provide a necessary framework for the design of new substituted benzoxadiazole fluorophores.

The photodissociation of vibrationally excited Cl_{2}(*v* = 1) has been investigated experimentally using the velocity mapped ion imaging technique. The experimental measurements presented here are compared with the results of time-dependent wavepacket calculations performed on a set of *ab initio* potential energy curves. The high level calculations allow prediction of all the dynamical information regarding the dissociation, including electronic polarization effects. Using a combination of theory and experiment it was found that there was negligible cooling of the vibrational degree of freedom of the parent molecule in the molecular beam. The results presented are compared with those following the photodissociation of Cl_{2}(*v* = 0). Although the same electronic states are found to be important for Cl_{2}(*v* = 1) as for Cl_{2}(*v* = 0), significant differences were found regarding many of the observables. The overall level of agreement between theory and experiment was found to be reasonable and confirms previous assignments of the photodissociation mechanism.

2010-2014Journal Article

J. Phys. Chem. A 117 6925-6931 (2013). [Joel M. Bowman Festschrift]

Publication year: 2013

The ground state potential energy and dipole moment surfaces for CS2 have been determined at the CASPT2/C:cc-pVTZ,S:aug-cc-pV(T+d)Z level of theory. The potential energy surface has been fit to a sum-of-products form using the neural network method with exponential neurons. A generic interface between neural network potential energy surface fitting and the Heidelberg MCTDH software package is demonstrated. The potential energy surface has also been fit using the *potfit* procedure in MCTDH. For fits to the low-energy regions of the potential, the neural network method requires fewer parameters than *potfit* to achieve high accuracy; global fits are comparable between the two methods. Using these potential energy surfaces, the vibrational energies have been computed for the four most abundant CS2 isotopomers. These results are compared to experimental and previous theoretical data. The current potential energy surfaces are shown to accurately reproduce the low-lying vibrational energies within a few wavenumbers. Hence, the potential energy and dipole moments surfaces will be useful for future study on the control of quantum dynamics in CS2.

The stability of a variety of borane (BH3 and BH2NHMe) and silane (SiH*n*Ph4–*n*, *n* = 0–4) adducts with diamino (NHC) and aminoalkyl (CAAC) carbenes has been carefully examined using M06-2X/cc-pVDZ computations, including natural bond orbital and atoms-in-molecules analyses. Moreover a potential mechanism for the hydride-mediated ring expansion of the carbene donors is reported. While the NHC adducts can undergo thermally induced ring-expansion chemistry, the CAAC adducts show increased stability due to a large energetic barrier for the insertion of boron (or silicon) atoms into the CAAC heterocycle. A series of substituted NHCs were investigated to further explore the roles of both electronic and steric effects on adduct stabilities and on their propensities for undergoing ring-expansion transformations.

In this work, we present time dependent density functional theory (TD-DFT) computations of the photophysical properties for a recently synthesized family of emissive RNA nucleobases (see: D. Shin, R.W. Sinkeldam, Y. Tor, Journal of the American Chemical Society 133 (2011) 14912–14915). These modified analogues are obtained by replacing the imidazole moiety of the RNA nucleobases with thiopene and represent a complete alphabet of emissive and isomorphic analogues derived from one heterocylic nucleus. An extensive study of absorption and emission wavelengths as well as the excited state charge transfer character for these molecules was conducted at the TD-DFT/6-311++G(2df,2p) level of theory employing the CAM-B3LYP, B3LYP and PBE0 functionals in water and dioxane. The theoretical results reveal good agreement with the reported experimental data. The nature of the low-lying excited states are compared and contrasted with their naturally occurring RNA nucleobase counterparts.

2010-2014Journal Article

Angewandte Chemie 52 6390-6395 (2013). (VIP article)

Publication year: 2013

**To branch or not to branch**: A mild stepwise route to various linear and branched (GeCl_{2})_{x} oligogermylenes supported by Lewis bases is reported, including the carbene-bound Ge_{4} complex NHC⋅GeCl_{2}Ge(GeCl_{3})_{2} (see picture). Dipp=2,6-*i*Pr_{2}C_{6}H_{3}, NHC=N-heterocyclic carbene.

The nuclear quadrupole coupling and spin-rotation constants of aluminum in AlH and AlD have been determined using coupled cluster theory with single and double excitations as well as perturbative inclusion of triples [CCSD(T)] combined with large correlation-consistent basis sets, cc-pCVXZ (X = T, Q and 5) and aug-cc-pCVXZ (X = T, Q). The anharmonic vibrational frequencies have been computed using second-order vibrational perturbation theory and the effects of vibrational averaging on the hyperfine constants have been determined. The ground state dipole moment has been determined for both isotopologues (AlH and AlD) and shown to depend critically on vibrational averaging. For completeness, the isotropic and anisotropic nuclear magnetic shielding tensors are also reported. All the results agree well with the best available experimental measurements, and in some cases (spin-rotation constants and dipole moments) refine the known data. The present computational results for the vibrationally averaged electric field gradients suggest that the currently accepted nuclear quadruple moment for ^{27}Al of may be slightly underestimated. Based on the experimental measurements of the nuclear quadrupole coupling for AlH (AlD) and best computational determinations of the vibrationally averaged electric field gradients, the quadruple moment of ^{27}Al is determined to be . However, this conclusion would be further strengthened with more precise experimental measurement of the ^{27}Al nuclear quadrupole coupling for AlH and AlD.

The elusive parent inorganic ethylene H2GeGeH2 has been isolated in the form of a stable complex for the first time via donor–acceptor coordination with suitable Lewis base/acid combinations (LB·H2Ge-GeH2·LA; LB = N-heterocyclic carbene or N-heterocyclic olefin; LA = W(CO)5). The nature of the bonding in these species was investigated by density functional theory calculations and revealed the presence of polarized Ge–Ge covalent σ-bonds within the H2Ge–GeH2 arrays and dative Ge–C interactions between the digermene and the carbon-based Lewis bases.

2010-2014Journal Article

Angewandte Chemie International Edition 53 9347-9351 (2014).

Publication year: 2014

We present isolable examples of formal zinc hydride cations supported by N-heterocyclic carbene (NHC) donors, and investigate the dual electrophilic and nucleophilic (hydridic) character of the encapsulated [ZnH]^{+} units by computational methods and preliminary hydrosilylation catalysis.

2010-2014Journal Article

Angewandte Chemie International Edition 53 4587-4591 (2014).

Publication year: 2014

The synthesis of the first examples of tellurophenes exhibiting phosphorescence in the solid state and under ambient conditions (room temperature and in air) is reported. Each of these main-group-element-based emitters feature pinacolboronates (BPin) as ring-appended side groups. The nature of the luminescence observed was also investigated using computational methods.

We present a computational study on HIO2 molecules. Ground state properties such as equilibrium structures, relative energetics, vibrational frequencies, and infrared intensities were obtained for all the isomers at the coupled-cluster with single and double excitations as well as perturbative inclusion of triples (CCSD(T)) level of theory with the aug-cc-pVTZ-PP basis set and ECP-28-PP effective core potential for iodine and the aug-cc-pVTZ basis set for hydrogen and oxygen atoms. The HOIO structure is confirmed as the lowest energy isomer. The relativeenergies are shown to be HOIO < HOOI < HI(O)O. The HO(O)I isomer is only stable at the density functional theory (DFT) level of theory. The transition states determined show interconversion of the isomers is possible. In order to facilitate future experimental identification, vibrational frequencies are also determined for all corresponding deuterated species. Verticalexcitation energies for the three lowest-lying singlet and triplet excited states were determined using the configuration interaction singles, time-dependent density functional theory (TD-DFT)/B3LYP, TD-DFT/G96PW91, and equation of motion-CCSD approaches with the LANL2DZ basis set plus effective core potential for iodine and the aug-cc-pVTZ basis set for hydrogen and oxygen atoms. It is shown that HOIO and HOOI isomers have excited states accessible at solar wavelengths (<4.0 eV) but these states have very small oscillator strengths (<2 × 10^{−3}).

The resonance Raman spectrum of uracil is simulated using the Herzberg–Teller short-time dynamics formalism. The ground-state geometry is optimized at the levels of PBE0/aug-cc-pVTZ and B3LYP/aug-cc-pVTZ, respectively. The gradient of the bright excited state is computed using time-dependent density functional theory and spin-flip time-dependent density functional theory. The excited-state calculations are carried out in both the gas phase and implicit water using the conductor-like polarizable continuum model. The ground-state equilibrium structure is found to impact the resulting resonance Raman spectrum significantly. The simulated resonance Raman spectrum using the long-range corrected functionals, that is, CAMB3LYP and LC-BLYP, and based on the PBE0/aug-cc-pVTZ optimized ground-state structure shows better agreement with the experimental spectrum than using standard hybrid functionals, that is, PBE0 and B3LYP. The solvation effect leads to a change in the energetic order of the *n* → π* and π → π* excited states, and it improves the agreement with the experimental spectrum, especially with regard to the relative intensities of the peaks with frequencies greater than 1600 cm–1.

2010-2014Book Chapters

in Molecular Quantum Dynamics: From Theory to Applications (Physical Chemistry in Action), edited by F. Gatti (Springer, Berlin, 2014), pp. 249-270.

Publication year: 2014

Two-photon spectroscopy of fluorescent proteins is a powerful bioimaging tool. Considerable effort has been made to measure absolute two-photon absorption (TPA) for the available fluorescent proteins. Being a technically involved procedure, there is significant variation in the published experimental measurements even for the same protein. In this work, we present a time-dependent density functional theory (TDDFT) study on isolated chromophores comparing the ability of four functionals (PBE0, B3LYP, CAM-B3LYP, and LC-BLYP) combined with the 6-31+G(d,p) basis set to reproduce averaged experimental TPA energies and cross sections. The TDDFT energies and TPA cross sections are also compared to corresponding CC2/6-31+G(d,p) results for excitation to S1 for the five smallest chromophores. In general, the computed TPA energies are less functional dependent than the TPA cross sections. The variation between functionals is more pronounced when higher-energy transitions are studied. Changes to the conformation of a chromophore are shown to change the TPA cross-section considerably. This adds to the difficulty of comparing an isolated chromophore to the one embedded in the protein environment. All functionals considered give moderate agreement with the corresponding CC2 results; in general, the TPA cross sections determined by TDDFT are 1.5–10 times smaller than the corresponding CC2 values for excitation to S1. LC-BLYP and CAM-B3LYP give erroneously large TPA cross sections in the higher-energy regions. On the other hand, B3LYP and PBE0 yield values that are of the same order of magnitude and in some cases very close to the averaged experimental data. Thus, based on the results reported here, B3LYP and PBE0 are the preferred functionals for screening chromphores for TPA. However, at best, TDDFT can be used to semiquantitatively scan chromophores for potential TPA probes and highlight spectroscopic peaks that could be present in the mature protein.