Jorge A. Morales

Valence-Bond/Coherent-States Approach to the Charge Equilibration Model I. Valence-Bond Models for Diatomic Molecules

A valence-bond (VB)/coherent-states (CS) approach to the charge equilibration (CE) model for diatomic molecules is presented in this work (VB part) and its sequel (CS part). By emphasizing theoretical aspects, this approach obtains the classical-electrostatics CE model from a quantum VB model in conjunction with the CS theory. For the VB part, a VB generalized CE (VB/GCE) model, which contains the CE model as a subcase, is derived from a two-electron, three-state VB model via the sequential application of seven approximations. Unlike its CE subcase, the VB/GCE model provides a satisfactory charge-transfer description at dissociation as illustrated with HF((g)) and other molecules. Through the previous derivation, CE charges and CE Coulomb interactions are elucidated in terms of VB Mulliken charges and VB atomic interactions, respectively. Modifications in the above derivation can generate a family of related VB/GCE models that includes the aforesaid VB/GCE model. Despite their classical appearance, all of the VB/GCE and CE models involve VB wave functions corresponding to ground and first-excited states. Moreover, all of the VB/GCE and CE energy and charge optimizations are proven to be equivalent to the variational eigenvector equation procedures of the underlying VB models. The quantum-mechanics/classical-electrostatics connection implicit in this work is further elaborated by means of VB CS sets in the sequel. The VB/CS treatment of polyatomic molecules and additional tests of the present approach will be reported in later papers in this series.

Dynamics of H+ + CO at ELab = 30 eV

The astrophysically relevant system H(+) + CO (v(i) = 0) → H(+) + CO (v(f)) at E(Lab) = 30 eV is studied with the simplest-level electron nuclear dynamics (SLEND) method. This investigation follows previous successful SLEND studies of H(+) + H(2) and H(+) + N(2) at E(Lab) = 30 eV [J. Morales, A. Diz, E. Deumens, and Y. Öhrn, J. Chem. Phys. 103(23), 9968 (1995); C. Stopera, B. Maiti, T. V. Grimes, P. M. McLaurin, and J. A. Morales, J. Chem. Phys. 134(22), 224308 (2011)]. SLEND is a direct, time-dependent, variational, and non-adiabatic method that adopts a classical-mechanics description for the nuclei and a single-determinantal wavefunction for the electrons. A canonical coherent-states (CS) procedure associated with SLEND reconstructs quantum vibrational properties from the SLEND classical dynamics. Present SLEND results include reactivity predictions, snapshots of the electron density evolution, average vibrational energy transfers, rainbow angle predictions, total and vibrationally resolved differential cross sections (DCS), and average vibrational excitation probabilities. SLEND results are compared with available data from experiments and vibrational close-coupling rotational infinite-order sudden (VCC-RIOS) approximation calculations. Present simulations employ four basis sets: STO-3G, 6-31G, 6-31G**, and cc-pVDZ to determine their effect on the results. SLEND simulations predict non-charge-transfer scattering and CO collision-induced dissociation as the main reactions. SLEND/6-31G, /6-31G**, and /cc-pVDZ predict rainbow angles and total DCS in excellent agreement with experiments and more accurate than their VCC-RIOS counterparts. SLEND/6-31G** and /cc-pVDZ predict vibrationally resolved DCS for v(f) = 0-2 in satisfactory experimental agreement, but less accurate than their comparable H(+) + CO VCC-RIOS and H(+) + H(2) and H(+) + N(2) SLEND results. SLEND∕6-31G** and ∕cc-pVDZ predict qualitatively correct average vibrational excitation probabilities, which are quantitatively correct for v(f) = 2, but under(over)estimated for v(f) = 0(1). Discrepancies in some H(+) + CO SLEND vibrational properties, not observed in H(+) + H(2) and H(+) + N(2) SLEND results, are attributed to the moderately overestimated SLEND vibrational energy through its effect upon the canonical CS probabilities. Correction of that energy to its experimental values produces a remarkable improvement in the average vibrational excitation probabilities. Ways to obtain more accurate vibrational properties with higher-level versions of electron nuclear dynamics are discussed.

Dynamics of H+ + N2 at ELab = 30 eV

The H(+) + N(2) system at E(Lab) = 30 eV, relevant in astrophysics, is investigated with the simplest-level electron nuclear dynamics (SLEND) method. SLEND is a time-dependent, direct, variational, non-adiabatic method that employs a classical-mechanics description for the nuclei and a single-determinantal wavefunction for the electrons. A canonical coherent-states procedure, intrinsic to SLEND, is used to reconstruct quantum vibrational properties from the SLEND classical mechanics. Present simulations employ three basis sets: STO-3G, 6-31G, and 6-31G∗∗, to determine their effect on the results, which include reaction visualizations, product predictions, and scattering properties. Present simulations predict non-charge-transfer scattering and N(2) collision-induced dissociation as the main reactions. Average vibrational energy transfer, H(+) energy-loss spectra, rainbow angle, and elastic vibrational differential cross sections at the SLEND∕6-31G∗∗ level agree well with available experimental data. SLEND∕6-31G∗∗ results are comparable to those calculated with the vibrational close-coupling rotational infinite-order sudden approximation and the quasi-classical trajectory method.

Some coherent-states aspects of the electron nuclear dynamics theory: past and present

Past and present coherent-states (CS) efforts with the electron nuclear dynamics (END) theory at its simplest level (SL-END) are reviewed. END is a time-dependent, variational, non-adiabatic, direct-dynamics method that describes simultaneously the nuclei and electrons of a molecular system. Within that characterization, SL-END adopts a classical-mechanics description for the nuclei and a quantum single-determinantal representation for the electrons. From its very inception, SL-END has been associated with the CS theory. CS sets are continuous and over-complete sets that satisfy the resolution of identity with a positive measure. Different CS sets can play an astonishing number of roles within SL-END that have several practical consequences. Originally, SL-END utilized the canonical and Thouless CS sets to correctly represent the nuclear and electronic parts of the SL-END wavefunction, respectively, thus defining a proper phase space for the SL-END dynamical equations. Later, canonical and rotational CS sets were used for reconstructing quantum vibrational and quantum rotational descriptions from the SL-END classical nuclear dynamics. That development proved essential to calculate state-resolved properties in ion-molecule and atom-molecule collisions with SL-END. Present CS efforts include a time-dependent Kohn-Sham density-functional-theory direct-dynamic method in the END framework and a CS approach to the charge-equilibration model inter alia.

Massively parallel implementations of coupled-cluster methods for electron spin resonance spectra. I. Isotropic hyperfine coupling tensors in large radicals

Coupled cluster (CC) methods provide highly accurate predictions of molecular properties, but their high computational cost has precluded their routine application to large systems. Fortunately, recent computational developments in the ACES III program by the Bartlett group [the OED∕ERD atomic integral package, the super instruction processor, and the super instruction architecture language] permit overcoming that limitation by providing a framework for massively parallel CC implementations. In that scheme, we are further extending those parallel CC efforts to systematically predict the three main electron spin resonance (ESR) tensors (A-, g-, and D-tensors) to be reported in a series of papers. In this paper inaugurating that series, we report our new ACES III parallel capabilities that calculate isotropic hyperfine coupling constants in 38 neutral, cationic, and anionic radicals that include the (11)B, (17)O, (9)Be, (19)F, (1)H, (13)C, (35)Cl, (33)S,(14)N, (31)P, and (67)Zn nuclei. Present parallel calculations are conducted at the Hartree-Fock (HF), second-order many-body perturbation theory [MBPT(2)], CC singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] levels using Roos augmented double- and triple-zeta atomic natural orbitals basis sets. HF results consistently overestimate isotropic hyperfine coupling constants. However, inclusion of electron correlation effects in the simplest way via MBPT(2) provides significant improvements in the predictions, but not without occasional failures. In contrast, CCSD results are consistently in very good agreement with experimental results. Inclusion of perturbative triples to CCSD via CCSD(T) leads to small improvements in the predictions, which might not compensate for the extra computational effort at a non-iterative N(7)-scaling in CCSD(T). The importance of these accurate computations of isotropic hyperfine coupling constants to elucidate experimental ESR spectra, to interpret spin-density distributions, and to characterize and identify radical species is illustrated with our results from large organic radicals. Those include species relevant for organic chemistry, petroleum industry, and biochemistry, such as the cyclo-hexyl, 1-adamatyl, and Zn-porphycene anion radicals, inter alia.

Chapter Three - Some Recent Developments in the Simplest-Level Electron Nuclear Dynamics Method: Theory, Code Implementation, and Applications to Chemical Dynamics

Abstract Electron nuclear dynamics (END) is a time-dependent, variational, direct, and nonadiabatic dynamics method that treats nuclei and electrons simultaneously. While admitting a hierarchy of realizations, the simplest-level END (SLEND), which adopts nuclear classical dynamics and an electronic Thouless single-determinantal state, is the most utilized END version due to its feasibility. SLEND was successfully applied to various gas-phase reactions at intermediate and high energies. However, the SLEND reliance on nuclear classical dynamics alone and/or its lack of dynamical electron correlation inter alia impedes its reliable utilization for more challenging systems. With higher level END realizations overcoming those shortcomings at high computational cost, we advocate solutions that retain SLENDs feasibility due to classical dynamics and the single-determinantal representation. Thus, we advance a novel SLEND/density functional theory (DFT) method wherein electron correlation is included within a feasible single-determinantal representation through DFT procedures. Additionally, we extend a coherent states (CS) quantum reconstruction procedure (CSQRP) to recover some quantum effects from the nuclear classical dynamics; CSQRP now features harmonic, Morse, rotational, and electronic CS. Finally, we improve the SLEND performance by incorporating effective core potentials and implementing our models in our cutting-edge code PACE. The latter features parallel programming and an environment for rapid method development. The new SLEND developments are applied to various gas-phase systems at intermediate and high energies including proton–molecule collisions and Diels–Alder, SN2, and proton cancer therapy reactions.

Exploring water radiolysis in proton cancer therapy: Time-dependent, non-adiabatic simulations of H+ + (H2O)1-6

To elucidate microscopic details of proton cancer therapy (PCT), we apply the simplest-level electron nuclear dynamics (SLEND) method to H+ + (H2O)1-6 at ELab = 100 keV. These systems are computationally tractable prototypes to simulate water radiolysis reactions—i.e. the PCT processes that generate the DNA-damaging species against cancerous cells. To capture incipient bulk-water effects, ten (H2O)1-6 isomers are considered, ranging from quasi-planar/multiplanar (H2O)1-6 to “smallest-drop” prism and cage (H2O)6 structures. SLEND is a time-dependent, variational, non-adiabatic and direct method that adopts a nuclear classical-mechanics description and an electronic single-determinantal wavefunction in the Thouless representation. Short-time SLEND/6-31G* (n = 1–6) and /6-31G** (n = 1–5) simulations render cluster-to-projectile 1-electron-transfer (1-ET) total integral cross sections (ICSs) and 1-ET probabilities. In absolute quantitative terms, SLEND/6-31G* 1-ET ICS compares satisfactorily with alternative experimental and theoretical results only available for n = 1 and exhibits almost the same accuracy of the best alternative theoretical result. SLEND/6-31G** overestimates 1-ET ICS for n = 1, but a comparable overestimation is also observed with another theoretical method. An investigation on H+ + H indicates that electron direct ionization (DI) becomes significant with the large virtual-space quasi-continuum in large basis sets; thus, SLEND/6-31G** 1-ET ICS is overestimated by DI contributions. The solution to this problem is discussed. In relative quantitative terms, both SLEND/6-31* and /6-31G** 1-ET ICSs precisely fit into physically justified scaling formulae as a function of the cluster size; this indicates SLEND’s suitability for predicting properties of water clusters with varying size. Long-time SLEND/6-31G* (n = 1–4) simulations predict the formation of the DNA-damaging radicals H, OH, O and H3O. While “smallest-drop” isomers are included, no early manifestations of bulk water PCT properties are observed and simulations with larger water clusters will be needed to capture those effects. This study is the largest SLEND investigation on water radiolysis to date.

In honour of N. Yngve Öhrn: surveying proton cancer therapy reactions with Öhrn's electron nuclear dynamics method. Aqueous clusters radiolysis and DNA-base damage by proton collisions

Proton cancer therapy (PCT) utilises high-energy H+ projectiles to cure cancer. PCT healing arises from its DNA damage in cancerous cells, which is mostly inflicted by the products from PCT water radiolysis reactions. While clinically established, a complete microscopic understanding of PCT remains elusive. To help in the microscopic elucidation of PCT, Professor Öhrns simplest-level electron nuclear dynamics (SLEND) method is herein applied to H+ + (H2O)3–4 and H+ + DNA-bases at ELab = 1.0 keV. These are two types of computationally feasible prototypes to study water radiolysis reactions and H+-induced DNA damage, respectively. SLEND is a time-dependent, variational, non-adiabatic and direct-dynamics method that adopts a nuclear classical-mechanics description and an electronic single-determinantal wavefunction. Additionally, our SLEND + effective-core-potential method is herein employed to simulate some computationally demanding PCT reactions. Due to these attributes, SLEND proves appropriate for the simulation of various types of PCT reactions accurately and feasibly. H+ + (H2O)3–4 simulations reveal two main processes: H+ projectile scattering and the simultaneous formation of H and OH fragments; the latter process is quantified through total integrals cross sections. H+ + DNA-base simulations reveal atoms and groups displacements, ring openings and base-to-proton electron transfers as predominant damage processes.

New massively parallel linear-response coupled-cluster module in ACES III: application to static polarisabilities of closed-shell molecules and oligomers and of open-shell radicals

ABSTRACT Stemming from our implementation of parallel coupled-cluster (CC) capabilities for electron spin resonance properties [J. Chem. Phys. 139, 174103 (2013)], we present a new massively parallel linear response CC module within ACES III. Unlike alternative parallel CC modules, this general purpose module evaluates any type of first- and second-order CC properties of both closed- and open-shell molecules employing restricted, unrestricted and restricted-open-shell Hartree–Fock (HF) references. We demonstrate the accuracy and usefulness of this module through the calculation of static polarisabilities of large molecules. Closed-shell calculations are performed at the following levels: second-order many-body perturbation theory [MBPT(2)], CC with single- and double-excitations (CCSD), coupled-perturbed HF and density functional theory (DFT), and open-shell calculations at the unrestricted CCSD (UCSSD) one. Applications involve eight closed-shell organic-chemistry molecules (Set I), the first four members of the closed-shell thiophene oligomer series (Set II), and five open-shell radicals (Set III). In Set I, all calculated average polarisabilities agree reasonably well with experimental data. In Set II, all calculated average polarisabilities vs. the number of monomers show comparable values and saturation patterns and demonstrate that experimental polarisabilities may be inaccurate. In Set III, UCCSD perpendicular polarisabilities show a reasonable agreement with previous UCCSD(T) and restricted-open-shell-MBPT(2) values.

Benchmark coupled-cluster g-tensor calculations with full inclusion of the two-particle spin-orbit contributions

We present a parallel implementation to compute electron spin resonance g-tensors at the coupled-cluster singles and doubles (CCSD) level which employs the ACES III domain-specific software tools for scalable parallel programming, i.e., the super instruction architecture language and processor (SIAL and SIP), respectively. A unique feature of the present implementation is the exact (not approximated) inclusion of the five one- and two-particle contributions to the g-tensor [i.e., the mass correction, one- and two-particle paramagnetic spin-orbit, and one- and two-particle diamagnetic spin-orbit terms]. Like in a previous implementation with effective one-electron operators [J. Gauss et al., J. Phys. Chem. A 113, 11541-11549 (2009)], our implementation utilizes analytic CC second derivatives and, therefore, classifies as a true CC linear-response treatment. Therefore, our implementation can unambiguously appraise the accuracy of less costly effective one-particle schemes and provide a rationale for their widespread use. We have considered a large selection of radicals used previously for benchmarking purposes including those studied in earlier work and conclude that at the CCSD level, the effective one-particle scheme satisfactorily captures the two-particle effects less costly than the rigorous two-particle scheme. With respect to the performance of density functional theory (DFT), we note that results obtained with the B3LYP functional exhibit the best agreement with our CCSD results. However, in general, the CCSD results agree better with the experimental data than the best DFT/B3LYP results, although in most cases within the rather large experimental error bars.