The ability of time-independent nonadiabatic transition state theory (NA-TST) to reproduce intersystem crossing dynamics obtained from the more computationally demanding Tully fewest switches trajectory surface hopping method is investigated. The two approaches are applied to the intersystem crossing between the ground (1)A1 state and lowest energy (3)B1 state of SiH2, coupled through the spin-orbit interaction. For NA-TST, the transition probabilities are calculated using the Landau-Zener formula and the Delos formula which accounts for tunneling. The fewest switches method produces rate constants of 7.6 × 10(11) s(-1) for the triplet to singlet transition and 5.2 × 10(11) s(-1) for the singlet to triplet transition, using a first-order kinetics model. This corresponds to a triplet electronic state lifetime of 781 fs. The NA-TST predicted rate constants are 1-2 orders of magnitude smaller, leading to a larger triplet state lifetime, as compared with the fewest switches method. This discrepancy cannot be explained by the difference in transition probabilities obtained from NA-TST and fewest switches molecular dynamics, and it is believed to be a result of the NA-TST semilocal description of nonadiabatic transitions in the vicinity of the intersystem crossing. Also, the larger triplet state lifetime obtained from NA-TST could be a result of the quantum sampling of rovibrational states, which is missing in classical trajectories traversing the crossing seam.

Teaching fundamental physical chemistry concepts such as the potential energy surface, transition state, and reaction path is a challenging task. The traditionally used oversimplified 2D representation of potential and free energy surfaces makes this task even more difficult and often confuses students. We show how this 2D representation can be expanded to more realistic potential and free energy surfaces by creating surface models using 3D printing technology. The printed models include potential energy surfaces for the hydrogen exchange reaction and for rotations of methyl groups in 1-fluoro-2-methylpropene calculated using quantum chemical methods. We also present several model surfaces created from analytical functions of two variables. These models include a free energy surface for protein folding, and potential energy surfaces for a linear triatomic molecule and surface adsorption, as well as simple double minimum, quadruple minimum, and parabolic surfaces. We discuss how these 3D models can be used in teaching different chemical kinetics, dynamics, and vibrational spectroscopy concepts including the potential energy surface, transition state, minimum energy reaction path, reaction trajectory, harmonic frequency, and anharmonicity.

We investigate the effect of H2 binding on the spin-forbidden nonadiabatic transition probability between the lowest energy singlet and triplet electronic states of [NiFe]-hydrogenase active site model, using a velocity averaged Landau-Zener theory. Density functional and multireference perturbation theories were used to provide parameters for the Landau-Zener calculations. It was found that variation of the torsion angle between the terminal thiolate ligands around the Ni center induces an intersystem crossing between the lowest energy singlet and triplet electronic states in the bare active site and in the active site with bound H2. Potential energy curves between the singlet and triplet minima along the torsion angle and H2 binding energies to the two spin states were calculated. Upon H2 binding to the active site, there is a decrease in the torsion angle at the minimum energy crossing point between the singlet and triplet states. The probability of nonadiabatic transitions at temperatures between 270 and 370 K ranges from 35% to 32% for the active site with bound H2 and from 42% to 38% for the bare active site, thus indicating the importance of spin-forbidden nonadiabatic pathways for H2 binding on the [NiFe]-hydrogenase active site.

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Frequency domain shaped binary laser pulses were optimized to perform 2 qubit quantum gate operations in (12)C(16)O. 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 pi, 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.

Three proposed mechanisms of cyclopropenone (c-H 2 C 3 O) formation from neutral species are studied using highlevel electronic structure methods in combination with nonadiabatic transition state and collision theories to deduce the likelihood of each reaction mechanism under interstellar conditions. The spin-forbidden reaction involving the singlet electronic state of cyclopenylidene (c-C 3 H 2 ) and the triplet state of atomic oxygen is studied using nonadiabatic transition state theory to predict the rate constant for c-H 2 C 3 O formation. The spin-allowed reactions of c-C 3 H 2 with molecular oxygen and acetylene with carbon monoxide were also investigated. The reaction involving the ground electronic states of acetylene and carbon monoxide has a very large reaction barrier and is unlikely to contribute to c-H 2 C 3 O formation in interstellar medium. The spin-forbidden reaction of c-C 3 H 2 with atomic oxygen, despite the high probability of nonadiabatic transition between the triplet and singlet states, was found to have a very small rate constant due to the presence of a small (3.8 kcal mol −1 ) reaction barrier. In contrast, the spin-allowed reaction between c-C 3 H 2 and molecular oxygen is found to be barrierless, and therefore can be an important path to the formation of c-H 2 C 3 O molecule in interstellar environment.

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.

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.