We recently developed two fragment based ab initio molecular dynamics methods, and in this publication we have demonstrated both approaches by constructing efficient classical trajectories in agreement with trajectories obtained from “on-the-fly” CCSD. The dynamics trajectories are obtained using both Born–Oppenheimer and extended Lagrangian (Car–Parrinello-style) options, and hence, here, for the first time, we present Car–Parrinello-like AIMD trajectories that are accurate to the CCSD level of post-Hartree–Fock theory. The specific extended Lagrangian implementation used here is a generalization to atom-centered density matrix propagation (ADMP) that provides post-Hartree–Fock accuracy, and hence the new method is abbreviated as ADMP-pHF; whereas the Born–Oppenheimer version is called frag-BOMD. The fragmentation methodology is based on a set-theoretic, inclusion-exclusion principle based generalization of the well-known ONIOM method. Thus, the fragmentation scheme contains multiple overlapping “model” systems, and overcounting is compensated through the inclusion-exclusion principle. The energy functional thus obtained is used to construct Born–Oppenheimer forces (frag-BOMD) and is also embedded within an extended Lagrangian (ADMP-pHF). The dynamics is tested by computing structural and vibrational properties for protonated water clusters. The frag-BOMD trajectories yield structural and vibrational properties in excellent agreement with full CCSD-based “on-the-fly” BOMD trajectories, at a small fraction of the cost. The asymptotic (large system) computational scaling of both frag-BOMD and ADMP-pHF is inferred as , for on-the-fly CCSD accuracy. The extended Lagrangian implementation, ADMP-pHF, also provides structural features in excellent agreement with full “on-the-fly” CCSD calculations, but the dynamical frequencies are slightly red-shifted. Furthermore, we study the behavior of ADMP-pHF as a function of the electronic inertia tensor and find a monotonic improvement in the red-shift as we reduce the electronic inertia. In all cases a uniform spectral scaling factor, that in our preliminary studies appears to be independent of system and independent of level of theory (same scaling factor for both MP2 and CCSD implementations ADMP-pHF and for ADMP DFT), improves on agreement between ADMP-pHF and full CCSD calculations. Hence, we believe both frag-BOMD and ADMP-pHF will find significant utility in modeling complex systems. The computational power of frag-BOMD and ADMP-pHF is demonstrated through preliminary studies on a much larger protonated 21-water cluster, for which AIMD trajectories with “on-the-fly” CCSD are not feasible.

We present a detailed analysis of the anomalous carbocations: C2H5+ and C3H3+. This work involves (a) probing electronic structural properties, (b) ab initio dynamics simulations over a range of internal energies, (c) analysis of reduced dimensional potential surfaces directed along selected conformational transition pathways, (d) dynamically averaged vibrational spectra computed from ab initio dynamics trajectories, and (e) two-dimensional time–frequency analysis to probe conformational dynamics. Key findings are as follows: (i) as noted in our previous study on C2H3+, it appears that these non-classical carbocations are stabilized by delocalized nuclear frameworks and “proton shuttles”. We analyze this nuclear delocalization and find critical parallels between conformational changes in C2H3+, C2H5+, and C3H3+. (ii) The vibrational signatures of C2H5+ are dominated by the “bridge-proton” conformation, but also show critical contributions from the “classical” configuration, which is a transition state at almost all levels of theory. This result is further substantiated through two-dimensional time–frequency analysis and is at odds with earlier explanations of the experimental spectra, where frequencies close to the classical region were thought to arise from an impurity. While this is still possible, our results here indicate an additional (perhaps more likely) explanation that involves the “classical” isomer. (iii) Finally, in the case of C3H3+ our explanation of the experimental result includes the presence of multiple, namely, “cyclic”, “straight”, and propargyl, configurations. Proton shuttles and nuclear delocalization, reminiscent of those seen in the case of C2H3+, were seen all through and have a critical role in all our observations.

We present a hybrid ab initio molecular dynamics scheme that includes both DFT and Hartree–Fock-based extended Lagrangian and converged post-Hartree–Fock Born–Oppenheimer components, combined within the framework of a molecular fragmentation-based electronic structure. The specific fragmentation algorithm used here is derived from ONIOM but includes multiple, overlapping “model” systems. The interaction between the various overlapping model systems is approximated by invoking the principle of inclusion–exclusion at the chosen higher level of theory and within a “real” calculation performed at the chosen lower level of theory. Furthermore, here, the lower level electronic structure of the full system is propagated through an extended Lagrangian formalism, whereas the fragments, treated using post-Hartree–Fock electronic structure theories, are computed using the normal converged Born–Oppenheimer treatment. This conservative dynamical approach largely reduces the computational cost to approximate on-the-fly dynamics using post-Hartree–Fock electronic structure techniques and can be very beneficial for large systems where SCF convergence may be challenging and time consuming. Benchmarks are provided for medium-sized protonated water clusters, H9O4+ and H13O6+, and polypeptide fragments, including a proline tripeptide fragment, and alanine decamer. Structural features are in excellent agreement between the hybrid approach using an MP2:B3LYP fragment-based electronic structure and BOMD using MP2 for the full system. Vibrational properties derived from dynamical correlation functions do show a small redshift for the extended Lagrangian treatments, especially at higher frequencies. Strategies are discussed to improve this redshift. The computational methodology works in parallel using both MPI and OpenMP and shows good scaling with the processor number. The timing benchmarks are provided for the alanine decamer. A powerful feature of the computational implementation is the fact that it is completely decoupled from the electronic structure package being employed and thus allows for an integrated approach that may include several different packages. These computational aspects will be further probed in future publications.

Here, we demonstrate the application of fragment-based electronic structure calculations in (a) ab initio molecular dynamics (AIMD) and (b) reduced dimensional potential calculations, for medium- and large-sized protonated water clusters. The specific fragmentation algorithm used here is derived from ONIOM, but includes multiple, overlapping “model” systems. The interaction between the various overlapping model systems is (a) approximated by invoking the principle of inclusion-exclusion at the chosen higher level of theory and (b) within a real calculation performed at the chosen lower level of theory. The fragmentation algorithm itself is written using bit-manipulation arithmetic, which will prove to be advantageous, since the number of fragments in such methods has the propensity to grow exponentially with system size. Benchmark calculations are performed for three different protonated water clusters: H9O4+, H13O6+ and H(H2O)21+. For potential energy surface benchmarks, we sample the normal coordinates and compare our surface energies with full MP2 and CCSD(T) calculations. The mean absolute error for the fragment-based algorithm is <0.05 kcal/mol, when compared with MP2 calculations, and <0.07 kcal/mol, when compared with CCSD(T) calculations over 693 different geometries for the H9O4+ system. For the larger H(H2O)21+ water cluster, the mean absolute error is on the order of a 0.1 kcal/mol, when compared with full MP2 calculations for 84 different geometries, at a fraction of the computational cost. Ab initio dynamics calculations were performed for H9O4+ and H13O6+, and the energy conservation was found to be of the order of 0.01 kcal/mol for short trajectories (on the order of a picosecond). The trajectories were kept short because our algorithm does not currently include dynamical fragmentation, which will be considered in future publications. Nevertheless, the velocity autocorrelation functions and their Fourier transforms computed from the fragment-based AIMD approaches were found to be in excellent agreement with those computed using the respective higher level of theory from the chosen hybrid calculation.

Using ab initio molecular dynamics (AIMD) simulations that facilitate the treatment of rare events, we probe the active site participation in the rate-determining hydrogen transfer step in the catalytic oxidation of linoleic acid by soybean lipoxygenase-1 (SLO-1). The role of two different active site components is probed. (a) On the hydrogen atom acceptor side of the active site, the hydrogen bonding propensity between the acceptor side hydroxyl group, which is bound to the iron cofactor, and the backbone carboxyl group of isoleucine (residue number 839) is studied toward its role in promoting the hydrogen transfer event. Primary and secondary (H/D) isotope effects are also probed and a definite correlation with subtle secondary H/D isotope effects is found. With increasing average nuclear kinetic energy, the increase in transfer probability is enhanced due to the presence of the hydrogen bond between the backbone carbonyl of I839 and the acceptor oxygen. Further increase in average nuclear kinetic energy reduces the strength of this secondary hydrogen bond which leads to a deterioration in hydrogen transfer rates and finally embrances an Arrhenius-like behavior. (b) On the hydrogen atom donor side, the coupling between vibrational modes predominantly localized on the donor-side linoleic acid group and the reactive mode is probed. There appears to be a qualitative difference in the coupling between modes that belong to linoleic acid and the hydrogen transfer mode, for hydrogen and deuterium transfer. For example, the donor side secondary hydrogen atom is much more labile (by nearly a factor of 5) during deuterium transfer as compared to the case for hydrogen transfer. This appears to indicate a greater coupling between the modes belonging to the linoleic acid scaffold and the deuterium transfer mode and also provides a new rationalization for the abnormal (nonclassical) secondary isotope effect results obtained by Knapp, Rickert, and Klinman in J. Am. Chem. Soc., 2002, 124, 3865. To substantiate our findings noted in point a above, we have suggested an I839 → A839 or I839 → V839 mutation. This will modify the bulkiness of hydrogen the bonding residue, allowing greater flexibility in the secondary hydrogen bond formation highlighted above and adversely affecting the reaction rate.

We present an hierarchical scheme where the propagator in quantum dynamics is represented using a multiwavelet basis. The approach allows for a recursive refinement methodology, where the representation in momentum space can be adaptively improved through additional, decoupled layers of basis functions. The method is developed within the constructs of quantum-wavepacket ab initio molecular dynamics (QWAIMD), which is a quantum-classical method and involves the synergy between a time-dependent quantum wavepacket description and ab initio molecular dynamics. Specifically, the current development is embedded within an “on-the-fly” multireference electronic structural generalization of QWAIMD. The multiwavelet treatment is used to study the dynamics and spectroscopy in a small hydrogen bonded cluster. The results are in agreement with previous calculations and with experiment. The studies also allow an interpretation of the shared proton dynamics as one that can be modeled through the dynamics of dressed states.

We discuss a multiconfigurational treatment of the “on-the-fly” electronic structure within the quantum wavepacket ab initio molecular dynamics (QWAIMD) method for coupled treatment of quantum nuclear effects with electronic structural effects. Here, multiple single-particle electronic density matrices are simultaneously propagated with a quantum nuclear wavepacket and other classical nuclear degrees of freedom. The multiple density matrices are coupled through a nonorthogonal configuration interaction (NOCI) procedure to construct the instantaneous potential surface. An adaptive-mesh-guided set of basis functions composed of Gaussian primitives are used to simplify the electronic structure calculations. Specifically, with the replacement of the atom-centered basis functions positioned on the centers of the quantum-mechanically treated nuclei by a mesh-guided band of basis functions, the two-electron integrals used to compute the electronic structure potential surface become independent of the quantum nuclear variable and hence reusable along the entire Cartesian grid representing the quantum nuclear coordinates. This reduces the computational complexity involved in obtaining a potential surface and facilitates the interpretation of the individual density matrices as representative diabatic states. The parametric nuclear position dependence of the diabatic states is evaluated at the initial time-step using a Shannon-entropy-based sampling function that depends on an approximation to the quantum nuclear wavepacket and the potential surface. This development is meant as a precursor to an on-the-fly fully multireference electronic structure procedure embedded, on-the-fly, within a quantum nuclear dynamics formalism. We benchmark the current development by computing structural, dynamic, and spectroscopic features for a series of bihalide hydrogen-bonded systems: FHF–, ClHCl–, BrHBr–, and BrHCl–. We find that the donor–acceptor structural features are in good agreement with experiments. Spectroscopic features are computed using a unified velocity/flux autocorrelation function and include vibrational fundamentals and combination bands. These agree well with experiments and other theories.

We describe how complex concepts in macroscopic chemistry, namely, thermodynamics and kinetics, can be taught at considerable depth both at the first-year undergraduate as well as upper levels. We begin with a careful treatment of PV diagrams, and by pictorially integrating the appropriate area in a PV diagram, we introduce work. This starting point allows us to elucidate the concept of state functions and nonstate functions. The students readily appreciate that for a given transition, the area enclosed by the PV curve (work) depends on the path taken. It is then argued that heat, within this chosen framework, is a consequence of energy conservation and the fact that work is not a state function. This leads to a visual introduction of all the components involved in the first law of thermodynamics. The PV diagrams are then used to introduce entropy as being related to the maximum possible work to be done by the system. This macroscopic description of entropy is then related to the usual microscopic view of Boltzmann. This equivalence connects the area inside the PV diagram (work from a specific kind of pathway) and the number of microstates involved in the Boltzmann expression. The connection between the macroscopic and microscopic description of entropy also illuminates the exponential dependence of the number of microstates (or probability) on an energy, known as free energy. The Arrhenius picture of chemical kinetics then readily follows from the exponential dependence stated above, and finally, a reactive event is viewed as a statistically rare event, to further clarify the appearance of entropy in the rate expression.Keywords: Curriculum; First-Year Undergraduate/General; Interdisciplinary/Multidisciplinary; Kinetics; Mathematics/Symbolic Mathematics; Physical Chemistry; Rate Law; Thermodynamics; Upper-Division Undergraduate;

A first-year undergraduate course that introduces students to chemistry through a conceptually detailed description of quantum mechanics is outlined. Quantization as arising from the confinement of a particle is presented and these ideas are used to introduce the reasons behind resonance, molecular orbital theory, degeneracy of electronic states, quantum mechanical tunneling, and band structure in solids and quantum dots.Keywords: Atomic Properties/Structure; Covalent Bonding; Curriculum; First-Year Undergraduate/General; MO Theory; Nuclear/Radiochemistry; Physical Chemistry; Quantum Chemistry; Resonance Theory;

A method of analysis is introduced to probe the spectral features obtained from ab initio molecular dynamics simulations. Here, the instantaneous mass-weighted velocities are projected onto irreducible representations constructed from discrete time translation groups comprising operations that invoke the time-domain symmetries (or periodic phase space orbits) reflected in the spectra. The projected velocities are decomposed using singular value decomposition (SVD) to construct a set of “modes” pertaining to a given frequency domain. These modes now include all anharmonicities, as sampled during the dynamics simulations. In this approach, the underlying motions are probed in a manner invariant with respect to coordinate transformations, operations being performed along the time axis rather than coordinate axes, making the analysis independent of choice of reference frame. The method is used to probe the underlying motions responsible for the doublet at ∼1000 cm–1 in the vibrational spectrum of the H5O2+, Zundel cation. The associated analysis results are confirmed by projecting the Fourier transformed velocities onto the harmonic normal mode coordinates and a set of mass-weighted, symmetrized Jacobi coordinates. It is found that the two peaks of the doublet are described and differentiated by their respective contributions from the proton transfer, water–water stretch, and water wag coordinates, as these are defined. Temperature dependent effects are also briefly noted.

The effect of water on the stability and vibrational states of a hydroxy-isoprene adduct is probed through the introduction of 1–15 water molecules. It is found that when a static nuclear harmonic approximation is invoked there is a substantial red-shift of the alcohol O–H stretch (of the order of 800 cm–1) as a result of introduction of water. When potential energy surface sampling and associated anharmonicities are introduced through finite temperature ab initio dynamics, this hydroxy-isoprene OH stretch strongly couples with all the water vibrational modes as well as the hydroxy-isoprene OH bend modes. A new computational technique is introduced to probe the coupling between these modes. The method involves a two-dimensional, time-frequency analysis of the finite temperature vibrational properties. Such an analysis not only provides information about the modes that are coupled as a result of finite-temperature analysis, but also the temporal evolution of such coupling.

Time-resolved “pump–probe” ab initio molecular dynamics studies are constructed to probe the stability of reaction intermediates, the mechanism of energy transfer, and energy repartitioning, for moieties involved during the interaction of volatile organic compunds with hydroxyl radical. These systems are of prime importance in the atmosphere. Specifically, the stability of reaction intermediates of hydroxyl radical adducts to isoprene and butadiene molecules is used as a case study to develop novel computational techniques involving “pump–probe” ab initio molecular dynamics. Starting with the various possible hydroxyl radical adducts to isoprene and butadiene, select vibrational modes of each of the adducts are populated with excess energy to mimic the initial conditions of an experiment. The flow of energy into the remaining modes is then probed by subjecting the excited adducts to ab initio molecular dynamics simulations. It is found that the stability of the adducts arises directly due to the anhormonically driven coupling of the modes to facilitate repartitioning of the excess vibrational energy. This kind of vibrational repartitioning has a critical influence on the energy density.

We present a computational methodology to sample rare events in large biological enzymes that may involve electronically polarizing, reactive processes. The approach includes simultaneous dynamical treatment of electronic and nuclear degrees of freedom, where contributions from the electronic portion are computed using hybrid density functional theory and the computational costs are reduced through a hybrid quantum mechanics/molecular mechanics (QM/MM) treatment. Thus, the paper involves a QM/MM dynamical treatment of rare events. The method is applied to probe the effect of the active site elements on the critical hydrogen transfer step in the soybean lipoxygenase-1 (SLO-1) catalyzed oxidation of linoleic acid. It is found that the dynamical fluctuations and associated flexibility of the active site are critical toward maintaining the electrostatics in the regime where the reactive process can occur smoothly. Physical constraints enforced to limit the active site flexibility are akin to mutations and, in the cases studied, have a detrimental effect on the electrostatic fluctuations, thus adversely affecting the hydrogen transfer process.

A new set of time-dependent deterministic sampling (TDDS) measures, based on local Shannon entropy, are presented to adaptively gauge the importance of various regions on a potential energy surface and to be employed in “on-the-fly” quantum dynamics. Shannon sampling and Shannon entropy are known constructs that have been used to analyze the information content in functions: for example, time-series data and discrete data sets such as amino acid sequences in a protein structure. Here the Shannon entropy, when combined with dynamical parameters such as the instantaneous potential, gradient and wavepacket density provides a reliable probe on active regions of a quantum mechanical potential surface. Numerical benchmarks indicate that the methods proposed are highly effective in locating regions of the potential that are both classically allowed as well as those that are classically forbidden, such as regions beyond the classical turning points which may be sampled during a quantum mechanical tunneling process. The approaches described here are utilized to improve computational efficiency in two different settings: (a) It is shown that the number of potential energy calculations required to be performed during on-the-fly quantum dynamics is fewer when the Shannon entropy based sampling functions are used. (b) Shannon entropy based TDDS functions are utilized to define a new family of grid-based electronic structure basis functions that reduce the computational complexity while maintaining accuracy. The role of both results for on-the-fly quantum/classical dynamics of electrons and nuclei is discussed.

In this paper, we introduce a symmetry-adapted quantum nuclear propagation technique that utilizes distributed approximating functionals for quantum wavepacket dynamics in extended condensed-phase systems. The approach is developed with a goal for implementation in quantum−classical methods such as the recently developed quantum wavepacket ab intio molecular dynamics (QWAIMD) to facilitate the study of extended systems. The method has been numerically benchmarked for extended electronic systems as well as protonic conducting systems that benefit from quantum nuclear treatment. Vibrational properties are computed for the case of the protonic systems through use of a novel velocity−flux correlation function. The treatment is found to be numerically accurate and efficient.

We build on our earlier quantum wavepacket study of hydrogen transfer in the biological enzyme soybean lipoxygenase-1 by using von Neumann quantum measurement theory to gain qualitative insights into the transfer event. We treat the enzyme active site as a measurement device which acts on the tunneling hydrogen nucleus via the potential it exerts at each configuration. A series of changing active site geometries during the tunneling process effects a sequential projection of the initial, reactant state onto the final, product state. We study this process using several different kinds of von Neumann measurements and show how a discrete sequence of such measurements not only progressively increases the projection of the hydrogen nuclear wavepacket onto the product side but also favors proton over deuteron transfer. Several qualitative features of the hydrogen tunneling problem found in wavepacket dynamics studies are also recovered here. These include the shift in the “transition state” toward the reactant as a result of nuclear quantization, greater participation of excited states in the case of deuterium, and the presence of critical points along the reaction coordinate that facilitate hydrogen and deuterium transfer and coincide with surface crossings. To further “tailor” the dynamics, we construct a perturbation to the sequence of measurements, that is a perturbation to the dynamical sequence of active site geometry evolution, which leads us to insight on the existence of sensitive regions of the reaction profile where subtle changes to the dynamics of the active site can have an effect on the hydrogen and deuterium transfer process.

We study the hydrogen tunneling problem in a model system that represents the active site of the biological enzyme, soybean lipoxygenase-1. Toward this, we utilize quantum wavepacket dynamics performed on potential surfaces obtained by using hybrid density functional theory under the influence of a dynamical active site. The kinetic isotope effect is computed by using the transmission amplitude of the wavepacket, and the experimental value is reproduced. By computing the hydrogen nuclear orbitals (eigenstates) along the reaction coordinate, we note that tunneling for both hydrogen and deuterium occurs through the existence of distorted, spherical s-type proton wave functions and p-type polarized proton wave functions for transfer along the donor−acceptor axis. In addition, there is also a significant population transfer through distorted p-type proton wave functions directed perpendicular to the donor−acceptor axis (via intervening π-type proton eigenstate interactions) which underlines the three-dimensional nature of the tunneling process. The quantum dynamical evolution indicates a significant contribution from tunneling processes both along the donor−acceptor axis and along directions perpendicular to the donor−acceptor axis. Furthermore, the tunneling process is facilitated by the occurrence of curve crossings and avoided crossings along the proton eigenstate adiabats.

The rate constants for the reaction of the OH radical with 1,3-butadiene and its deuterated isotopomer has been measured at 1−6 Torr total pressure over the temperature range of 263−423 K using the discharge flow system coupled with resonance fluorescence/laser-induced fluorescence detection of OH. The measured rate constants for the OH + 1,3-butadiene and OH + 1,3-butadiene-d6 reactions at room temperature were found to be (6.98 ± 0.28) × 10−11 and (6.94 ± 0.38) × 10−11 cm3 molecule−1 s−1, respectively, in good agreement with previous measurements at higher pressures. An Arrhenius expression for this reaction was determined to be k1II(T) = (7.23 ± 1.2) ×10−11exp[(664 ± 49)/T] cm3 molecule−1 s−1 at 263−423 K. The reaction was found to be independent of pressure between 1 and 6 Torr and over the temperature range of 262− 423 K, in contrast to previous results for the OH + isoprene reaction under similar conditions. To help interpret these results, ab initio molecular dynamics results are presented where the intramolecular energy redistribution is analyzed for the product adducts formed in the OH + isoprene and OH + butadiene reactions.

The ab initio atom-centered density matrix propagation (ADMP) method has been employed to study the dynamics of protonated water clusters of various sizes. An interesting result that hints at the possible amphiphilicity of the hydronium ion is detected. The hydrated proton tends to reside on the surface of the water clusters studied, with the lone pair on the protonated oxygen pointing “outwards” from the cluster. It is also noted that the hopping rate and average bonding topology in the local vicinity of the protonated species show a pronounced difference when treated with B3LYP and BLYP functionals. This is proposed to be on account of the potential for greater electronic exchange interactions in the vicinity of the positive charge.

We probe the structure, stability and vibrational properties of the fundamental C2H3+ carbocation that exists with preference in a bridged hydrogen conformation. Our computational study includes electronic structure treatment, incorporation of nuclear motion through classical and quantum paradigms, the effect of temperature, and the associated sampling of the potential surface, and the effect of single H/D isotopic substitution (i.e., C2H2D+). We find that while the non-classical, “Bridged” isomer is most stable, the “Classical” form does have a small presence under ambient conditions since the zero point level straddles the barrier between the Classical and Bridged isomers in a reduced dimensional analysis of the Bridged ↔ Classical transfer coordinate. But the probability of the classical structure is too low and hence may remain undetected from the vibrational properties of the system. For the deuterated counterpart, the deuterium preferentially occupies the terminal instead of bridge position, in the more stable bridged isomeric structure. This preference is noted from nuclear dynamics. In all cases, at higher temperatures, an orbiting phenomenon is observed where the hydrogen atom density is distributed as an oblate ellipsoid surrounding the carbon–carbon bond. This is not observed at lower temperatures and the orbiting phenomenon is probed here by computing two-dimensional, time–frequency vibrational spectra, which show the spectral evolution in time and temperature, and the development of the system from one kind of isomer to another. New experiments that may probe this isomeric multiplicity are suggested, and these involve a combination of infra-red multiple photon dissociation (IRMPD) and argon-tagged action spectroscopy.