Quantum Control of Photoelectron Circular Dichroism.

We demonstrate coherent control over the photoelectron circular dichroism in randomly oriented chiral molecules, based on quantum interference between multiple photoionization pathways. To significantly enhance the chiral signature, we use a finite manifold of indistinguishable (1+1^{'}) resonantly enhanced multiphoton ionization pathways interfering at a common photoelectron energy but probing different intermediate states. We show that this coherent control mechanism maximizes the number of molecular states that constructively contribute to the dichroism at an optimal photoelectron energy and thus outperforms other schemes, including interference between opposite-parity pathways driven by bichromatic (ω, 2ω) fields as well as sequential pump-probe ionization.

Perfect control of photoelectron anisotropy for randomly oriented ensembles of molecules by XUV REMPI and polarization shaping.

We report two schemes to generate perfect anisotropy in the photoelectron angular distribution of a randomly oriented ensemble of polyatomic molecules. In order to exert full control over the anisotropy of photoelectron emission, we exploit interferences between single-photon pathways and a manifold of resonantly enhanced two-photon pathways. These are shown to outperform nonsequential (ω, 2ω) bichromatic phase control for the example of CHFClBr molecules. We are able to optimize pulses that yield anisotropic photoelectron emission thanks to a very efficient calculation of photoelectron momentum distributions. This is accomplished by combining elements of quantum chemistry, variational scattering theory, and time-dependent perturbation theory.

Ultrafast photodissociation dynamics and nonadiabatic coupling between excited electronic states of methanol probed by time-resolved photoelectron spectroscopy.

The electronic and nuclear dynamics in methanol, following 156 nm photoexcitation, are investigated by combining a detailed analysis of time-resolved photoelectron spectroscopy experiments with electronic structure calculations. The photoexcitation pump pulse is followed by a delayed 260 nm photoionization probe pulse to produce photoelectrons that are analyzed by velocity map imaging. The yields of mass-resolved ions, measured with similar experimental conditions, are found to exhibit the same time-dependence as specific photoelectron spectral features. Energy-resolved signal onset and decay times are extracted from the measured photoelectron spectra to achieve high temporal resolution, beyond the 20 fs pump and probe pulse durations. When combined with ab initio calculations of selected cuts through the excited state potential energy surfaces, this information allows the dynamics of the transient excited molecule, which exhibits multiple nuclear and electronic degrees of freedom, to be tracked on its intrinsic few-femtosecond time scale. Within 15 fs of photoexcitation, we observe nuclear motion on the initially bound photoexcited 21A″ (S2) electronic state, through a conical intersection with the 11A' (S3) state, which reveals paths to photodissociation following C-O stretch and C-O-H angle opening.

Ab initio calculation of molecular aggregation effects: a Coumarin-343 case study.

We present time-dependent density functional theory (TDDFT) calculations for single and dimerized Coumarin-343 molecules to investigate the quantum mechanical effects of chromophore aggregation in extended systems designed to function as a new generation of sensors and light-harvesting devices. Using the single-chromophore results, we describe the construction of effective Hamiltonians to predict the excitonic properties of aggregate systems. We compare the electronic coupling properties predicted by such effective Hamiltonians to those obtained from TDDFT calculations of dimers and to the coupling predicted by the transition density cube (TDC) method. We determine the accuracy of the dipole-dipole approximation and TDC with respect to the separation distance and orientation of the dimers. In particular, we investigate the effects of including Coulomb coupling terms ignored in the typical tight-binding effective Hamiltonian. We also examine effects of orbital relaxation which cannot be captured by either of these models.

Pump-probe spectroscopy of chiral vibrational dynamics.

A planar molecule may become chiral upon excitation of an out-of-plane vibration, changing its handedness during half a vibrational period. When exciting such a vibration in an ensemble of randomly oriented molecules with an infrared laser, half of the molecules will undergo the vibration phase-shifted by π compared to the other half, and no net chiral signal is observed. This symmetry can be broken by exciting the vibrational motion with a Raman transition in the presence of a static electric field. Subsequent ionization of the vibrating molecules by an extreme ultraviolet pulse probes the time-dependent net handedness via the photoelectron circular dichroism. Our proposal for pump-probe spectroscopy of molecular chirality, based on quantum-chemical theory and discussed for the example of the carbonyl chlorofluoride molecule, is feasible with current experimental technology.

Decoherence in attosecond photoionization.

The creation of superpositions of hole states via single-photon ionization using attosecond extreme-ultraviolet pulses is studied with the time-dependent configuration-interaction singles (TDCIS) method. Specifically, the degree of coherence between hole states in atomic xenon is investigated. We find that interchannel coupling not only affects the hole populations, but it also enhances the entanglement between the photoelectron and the remaining ion, thereby reducing the coherence within the ion. As a consequence, even if the spectral bandwidth of the ionizing pulse exceeds the energy splittings among the hole states involved, perfectly coherent hole wave packets cannot be formed. For sufficiently large spectral bandwidth, the coherence can only be increased by increasing the mean photon energy.

Strong correlation in acene sheets from the active-space variational two-electron reduced density matrix method: effects of symmetry and size.

Polyaromatic hydrocarbons (PAHs) are a class of organic molecules with importance in several branches of science, including medicine, combustion chemistry, and materials science. The delocalized π-orbital systems in PAHs require highly accurate electronic structure methods to capture strong electron correlation. Treating correlation in PAHs has been challenging because (i) traditional wave function methods for strong correlation have not been applicable since they scale exponentially in the number of strongly correlated orbitals, and (ii) alternative methods such as the density-matrix renormalization group and variational two-electron reduced density matrix (2-RDM) methods have not been applied beyond linear acene chains. In this paper we extend the earlier results from active-space variational 2-RDM theory [Gidofalvi, G.; Mazziotti, D. A. J. Chem. Phys. 2008, 129, 134108] to the more general two-dimensional arrangement of rings--acene sheets--to study the relationship between geometry and electron correlation in PAHs. The acene-sheet calculations, if performed with conventional wave function methods, would require wave function expansions with as many as 1.5 × 10(17) configuration state functions. To measure electron correlation, we employ several RDM-based metrics: (i) natural-orbital occupation numbers, (ii) the 1-RDM von Neumann entropy, (iii) the correlation energy per carbon atom, and (iv) the squared Frobenius norm of the cumulant 2-RDM. The results confirm a trend of increasing polyradical character with increasing molecular size previously observed in linear PAHs and reveal a corresponding trend in two-dimensional (arch-shaped) PAHs. Furthermore, in PAHs of similar size they show significant variations in correlation with geometry. PAHs with the strictly linear geometry (chains) exhibit more electron correlation than PAHs with nonlinear geometries (sheets).

Balancing single- and multi-reference correlation in the chemiluminescent reaction of dioxetanone using the anti-Hermitian contracted Schrödinger equation.

Direct computation of energies and two-electron reduced density matrices (2-RDMs) from the anti-Hermitian contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)], it is shown, recovers both single- and multi-reference electron correlation in the chemiluminescent reaction of dioxetanone especially in the vicinity of the conical intersection where strong correlation is important. Dioxetanone, the light-producing moiety of firefly luciferin, efficiently converts chemical energy into light by accessing its excited-state surface via a conical intersection. Our previous active-space 2-RDM study of dioxetanone [L. Greenman and D. A. Mazziotti, J. Chem. Phys. 133, 164110 (2010)] concluded that correlating 16 electrons in 13 (active) orbitals is required for realistic surfaces without correlating the remaining (inactive) orbitals. In this paper we pursue two complementary goals: (i) to correlate the inactive orbitals in 2-RDMs along dioxetanone's reaction coordinate and compare these results with those from multireference second-order perturbation theory (MRPT2) and (ii) to assess the size of the active space-the number of correlated electrons and orbitals-required by both MRPT2 and ACSE for accurate energies and surfaces. While MRPT2 recovers very different amounts of correlation with (4,4) and (16,13) active spaces, the ACSE obtains a similar amount of correlation energy with either active space. Nevertheless, subtle differences in excitation energies near the conical intersection suggest that the (16,13) active space is necessary to determine both energetic details and properties. Strong electron correlation is further assessed through several RDM-based metrics including (i) total and relative energies, (ii) the von Neumann entropy based on the 1-electron RDM, as well as the (iii) infinity and (iv) squared Frobenius norms based on the cumulant 2-RDM.

Energy barriers of vinylidene carbene reactions from the anti-hermitian contracted Schrödinger equation.

Computational studies of carbenes must take into account the possibility of multireference correlation because the highest occupied and lowest unoccupied molecular orbitals can be nearly energetically degenerate. We apply the anti-Hermitian contracted Schrodinger equation (ACSE) [Mazziotti, D. A. Phys. Rev. Lett. 2006, 97, 143002] to compute two-electron reduced density matrices (2-RDMs) and their energies for two carbene reactions: (i) the acetylene-vinylidene rearrangement and (ii) the rearrangement of pent-1-en-4-yn-3-one to acryloylvinylidene, which then cyclizes to cyclopenta-2,4-dienone. The ACSE has some unique advantages in the treatment of carbene reactions and more general families of reactions in which the importance of multireference correlation is not known a priori: (i) the ACSE is more reliable than single-reference methods for confirming the presence or absence of multireference correlation and (ii) in the absence of multireference correlation, unlike multireference second-order perturbation theory (MRPT2), the ACSE recovers more single-reference correlation energy than similarly scaling coupled-cluster methods. Because MRPT2 does not recover as much single-reference correlation as the coupled-cluster or ACSE methods, it tends to underestimate reaction barriers within the carbene reactions. For example, in the rearrangement of pent-1-en-4-yn-3-one, the ACSE and CCSD(T) methods produce cyclization barriers of 18.9 and 18.7 kcal/mol with the 6-31G(d) basis set, whereas MRPT2 predicts this barrier to be 12.1 kcal/mol; furthermore, both the ACSE and CCSD(T) determine the energy of the transition state for acryloylvinylidene formation to be 6.6-6.7 kcal/mol above that of the carbene, and yet, MRPT2 does not predict a transition state.

Strong electron correlation in the decomposition reaction of dioxetanone with implications for firefly bioluminescence.

Dioxetanone, a key component of the bioluminescence of firefly luciferin, is itself a chemiluminescent molecule due to two conical intersections on its decomposition reaction surface. While recent calculations of firefly luciferin have employed four electrons in four active orbitals [(4,4)] for the dioxetanone moiety, a study of dioxetanone [F. Liu et al., J. Am. Chem. Soc. 131, 6181 (2009)] indicates that a much larger active space is required. Using a variational calculation of the two-electron reduced-density-matrix (2-RDM) [D. A. Mazziotti, Acc. Chem. Res. 39, 207 (2006)], we present the ground-state potential energy surface as a function of active spaces from (4,4) to (20,17) to determine the number of molecular orbitals required for a correct treatment of the strong electron correlation near the conical intersections. Because the 2-RDM method replaces exponentially scaling diagonalizations with polynomially scaling semidefinite optimizations, we readily computed large (18,15) and (20,17) active spaces that are inaccessible to traditional wave function methods. Convergence of the electron correlation with active-space size was measured with complementary RDM-based metrics, the von Neumann entropy of the one-electron RDM as well as the Frobenius and infinity norms of the cumulant 2-RDM. Results show that the electron correlation is not correctly described until the (14,12) active space with small variations present through the (20,17) space. Specifically, for active spaces smaller than (14,12), we demonstrate that at the first conical intersection, the electron in the σ(∗) orbital of the oxygen-oxygen bond is substantially undercorrelated with the electron of the σ orbital and overcorrelated with the electron of the carbonyl oxygen's p orbital. Based on these results, we estimate that in contrast to previous treatments, an accurate calculation of the strong electron correlation in firefly luciferin requires an active space of 28 electrons in 25 orbitals, beyond the capacity of traditional multireference wave function methods.

Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method.

The variational two-electron reduced-density-matrix (2-RDM) method, scaling polynomially with the size of the system, was applied to linear chains and three-dimensional clusters of atomic hydrogen as large as H(64). In the case of the 4x4x4 hydrogen lattice of 64 hydrogen atoms, a correct description of the dissociation requires about 10(18) equally weighted determinants in the wave function, which is too large for traditional multireference methods. The correct energy in the dissociation limit was obtained from the variational 2-RDM method in contrast to Hartree-Fock and single-reference methods. Analysis of the occupation numbers demonstrates that even for 1.0 A bond distances the presence of strong electron correlation requires a multireference method. Three-dimensional systems exhibit a marked increase in electron correlation from one-dimensional systems regardless of size. The metal-to-insulator transition upon expansion of the clusters was studied using the decay of the 1-RDM off-diagonal elements. The variational 2-RDM method was shown to capture the metal-to-insulator transition and dissociation behavior accurately for all systems.

Highly multireferenced arynes studied with large active spaces using two-electron reduced density matrices.

Using the active-space two-electron reduced density matrix (2-RDM) method, which scales polynomially with the size of the active space [G. Gidofalvi and D. A. Mazziotti, J. Chem. Phys. 129, 134108 (2008)], we were able to use active spaces as large as 24 electrons in 24 orbitals in computing the ground-state energies and properties of highly multireferenced arynes. Because the conventional complete-active-space self-consistent-field (CASSCF) method scales exponentially with the size of the active space, its application to arynes was mainly limited to active spaces of 12 electrons in 12 orbitals. For these smaller active spaces the active-space 2-RDM method accurately reproduces the results of CASSCF. However, we show that the larger active spaces are necessary for describing changes in energies and properties with aryne chain length such as the emergence of polyradical character. Furthermore, the addition of further electron correlation by multireference perturbation theory is demonstrated to be inadequate for removing the limitations of the smaller active spaces.

Molecular Mechanics Simulations and Improved Tight-Binding Hamiltonians for Artificial Light Harvesting Systems: Predicting Geometric Distributions, Disorder, and Spectroscopy of Chromophores in a Protein Environment.

We present molecular mechanics and spectroscopic calculations on prototype artificial light harvesting systems consisting of chromophores attached to a tobacco mosaic virus (TMV) protein scaffold. These systems have been synthesized and characterized spectroscopically, but information about the microscopic configurations and geometry of these TMV-templated chromophore assemblies is largely unknown. We use a Monte Carlo conformational search algorithm to determine the preferred positions and orientations of two chromophores, Coumarin 343 together with its linker and Oregon Green 488, when these are attached at two different sites (104 and 123) on the TMV protein. The resulting geometric information shows that the extent of disorder and aggregation properties and therefore the optical properties of the TMV-templated chromophore assembly are highly dependent on both the choice of chromophores and the protein site to which they are bound. We use the results of the conformational search as geometric parameters together with an improved tight-binding Hamiltonian to simulate the linear absorption spectra and compare with experimental spectral measurements. The ideal dipole approximation to the Hamiltonian is not valid because the distance between chromophores can be very small. We found that using the geometries from the conformational search is necessary to reproduce the features of the experimental spectral peaks.

Electronic excited-state energies from a linear response theory based on the ground-state two-electron reduced density matrix.

Ground-state two-particle reduced density matrices (2-RDMs) are used to calculate excited-state energy spectra. Solving the Schrodinger equation for excited states dominated by single excitations from the ground-state wavefunction requires the ground-state 2- and 3-RDMs. The excited states, however, can be obtained without a knowledge of the ground-state 3-RDM by two methods: (i) cumulant expansion methods which build the 3-RDM from the 2-RDM, and (ii) double commutator methods which eliminate the 3-RDM. Previous work [Mazziotti, Phys. Rev. A 68, 052501 (2003)] examined the accuracy of excited states extracted from ground-state 2-RDMs, which were calculated by full configuration interaction or the variational 2-RDM method. In this work we employ (i) advances in semidefinite programming to treat the excited states of water and hydrogen fluoride and chains of hydrogen atoms, and (ii) the addition of partial three-particle N-representability conditions to compute more accurate ground-state 2-RDMs. With the hydrogen chains we examine the metal-to-insulator transition as measured by the band gap (the difference between the ground-state and the first excited-state energies), which is difficult for excited-state methods to capture.