Ab initio potential energy surface for linear H3

Repartitioning the Hamiltonian in many-body second-order Brillouin-Wigner perturbation theory: Uncovering new size-consistent models

Second-order Møller-Plesset perturbation theory is well-known as a computationally inexpensive approach to the electron correlation problem that is size-consistent with a size-consistent reference but fails to be regular. On the other hand, the less well-known many-body version of Brillouin-Wigner perturbation theory has the reverse properties: it is regular but fails to be size-consistent when used with the standard MP partitioning. Consequently, its widespread use remains limited. In this work, we analyze the ways in which it is possible to use alternative non-MP partitions of the Hamiltonian to yield variants of BW2 that are size-consistent as well as regular. We show that there is a vast space of such BW2 theories and also show that it is possible to define a repartitioned BW2 theory from the ground state density alone, which regenerates the exact correlation energy. We also provide a general recipe for deriving regular, size-consistent, and size-extensive partitions from physically meaningful components, and we apply the result to small model systems. The scope of these results appears to further set the stage for a revival of BW2 in quantum chemistry.

Emergence of Linnett's "double quartets" from a model of "Lewis dots"

Chemists routinely explicate molecular structures and chemical reactions in terms of the propensities of semiclassical valence electrons (aka "Lewis dots"). Typically, the electrons are viewed as forming spin pairs and recent efforts to translate this concise and intuitive qualitative picture into an efficient and relatable quantitative model have made good progress. But electrons are not always paired and advanced quantum calculations have shown that this is so even in small diamagnetic species such as dicarbon and benzene. Here we show that the latest semiclassical model for paired electrons can clarify the limitations on pairing simply by dissecting the elements of the interparticle potentials. Although not trained to do so, these elements produce a Linnett-like benzene, with three valence electrons in each CC bond, when the electrons are free to move singly. At the same time, sustaining higher order bonds with independently mobile electrons requires adjustments in the details of the model potentials at short distances. This is addressed with new training data and new forms for the contributions from Coulomb integrals. Although trained on hydrogen and carbon species separately, the combination applied to ethyne predicts the pairing of spins in the CH bonds and the dispersion of spins in the CC bond that is found in ab initio calculations. This adjusted force field is named LINNETT, in appreciation of Linnett's insightful double quartet interpretation of the Lewis octet.

Crossed Molecular Beam Study of the H + HD → H2 + D Reaction at 0.60 and 1.26 eV Using the Near-Threshold Ionization Velocity Map Ion Imaging

By using the 1 + 1' near-threshold ionization velocity map ion imaging technique, state-to-state reactive differential cross sections have been measured for the H + HD → H₂ + D reaction. High-resolution images of the D products, with the rotational states of the H₂ co-products clearly resolved, were acquired at the collision energies of 0.60 and 1.26 eV, respectively. It is found that the angular distribution is predominantly backward-scattering at the collision energy of 0.60 eV. However, at 1.26 eV, where the collision energy is higher, the angular distribution becomes forward-backward-scattering. Notably, at both collision energies, the main peaks of backward-scattered products gradually shift from backward toward sideways direction as the rotational quantum number of H₂ increases. Moreover, in the forward direction, fast angular oscillations, which are induced by specific partial waves have also been observed at 1.26 eV. These features show a strong correlation between the product states and angular distributions and also indicate the unique role of partial waves in quantum reactive scattering.

How the Donor/Acceptor Spin States Affect the Electronic Couplings in Molecular Charge-Transfer Processes?

The electronic coupling matrix element H_AB is an essential ingredient of most electron-transfer theories. H_AB depends on the overlap between donor and acceptor wave functions and is affected by the involved states’ spin. We classify the spin-state effects into three categories: orbital occupation, spin-dependent electron density, and density delocalization. The orbital occupancy reflects the diverse chemical nature and reactivity of the spin states of interest. The effect of spin-dependent density is related to a more compact electron density cloud at lower spin states due to decreased exchange interactions between electrons. Density delocalization is strongly connected with the covalency concept that increases the spatial extent of the diabatic state’s electron density in specific directions. We illustrate these effects with high-level ab initio calculations on model direct donor–acceptor systems relevant to metal oxide materials and biological electron transfer. Obtained results can be used to benchmark existing methods for H_AB calculations in complicated cases such as spin-crossover materials or antiferromagnetically coupled systems.

Effect of Reagent Vibration and Rotation on the State-to-State Dynamics of the Hydrogen Exchange Reaction, H + H2 → H2 + H

State-to-state dynamics of the benchmark hydrogen exchange reaction H + H₂ (v = 0-4, j = 0-3) → H₂ (v', j') + H is investigated with the aid of the real wave packet approach of Gray and Balint-Kurti (J. Chem. Phys. 1998, 108, 950-962) and electronic ground BKMP2 potential energy surface of Boothroyd et al. (J. Chem. Phys. 1996, 104, 7139-7152). Initial state-selected and product state-resolved reaction probabilities, integral cross section, and product diatom vibrational and rotational level populations at a few collision energies are reported to elucidate the energy disposal mechanism. State-specific thermal rate constants are also calculated and compared with the available literature results. Coriolis coupling terms of the nuclear Hamiltonian are included, and calculations are parallelized over the helicity quantum number, Ω'. Attempts are made, in particular, to study the effect of reagent vibrational and rotational excitations on the dynamical attributes. It is found that the calculations become computationally expensive with reagent vibrational and rotational excitation. Reagent vibrational excitation is found to enhance the reactivity and has significant impact on the energy disposal to the vibrational and rotational degrees of freedom of the product. The interplay of reagent translational and vibrational energy on the product vibrational distribution unfolds an important aspect of the energy disposal mechanism. The effect of reagent rotation on the state-to-state dynamics is found not to be very significant, and the weak effect turns out to be specific to v'.

Prediction of a Feshbach Resonance in the Below-the-Barrier Reactive Scattering of Vibrationally Excited HD with H

Quantum reactive scattering calculations on the vibrational quenching of HD due to collisions with H were carried out employing an accurate potential energy surface. The state-to-state cross sections for the chemical reaction HD(v = 1, j = 0) + H → D + H₂(v' = 0, j') at collision energies between 1 and 10 000 cm^-1 are presented, and a Feshbach resonance in the low-energy regime, below the reaction barrier, is observed for the first time. The resonance is attributed to coupling with the vibrationally adiabatic potential correlating to the v = 1, j = 1 level of the HD molecule, and it is dominated by the contribution from a single partial wave. The properties of the resonance, such as its dynamic behavior, phase behavior, and lifetime, are discussed.

Interplay between the Gentlest Ascent Dynamics Method and Conjugate Directions to Locate Transition States

An algorithm to locate transition states on a potential energy surface (PES) is proposed and described. The technique is based on the GAD method where the gradient of the PES is projected into a given direction and also perpendicular to it. In the proposed method, named GAD-CD, the projection is not only applied to the gradient but also to the Hessian matrix. Then, the resulting Hessian matrix is block diagonal. The direction is updated according to the GAD method. Furthermore, to ensure stability and to avoid a high computational cost, a trust region technique is incorporated and the Hessian matrix is updated at each iteration. The performance of the algorithm in comparison with the standard ascent dynamics is discussed for a simple two dimensional model PES. Its efficiency for describing the reaction mechanisms involving small and medium size molecular systems is demonstrated for five molecular systems of interest.

Improving the Efficiency of the Multireference Driven Similarity Renormalization Group via Sequential Transformation, Density Fitting, and the Noninteracting Virtual Orbital Approximation

This study examines several techniques to improve the efficiency of the linearized multireference driven similarity renormalization group truncated to one- and two-body operators [MR-LDSRG(2)]. We propose a sequential MR-LDSRG(2) [sq-MR-LDSRG(2)] scheme, in which one-body substitutions are folded exactly into the Hamiltonian. This new approach is combined with density fitting (DF) to reduce the storage cost of two-electron integrals. To further avoid storage of large four-index intermediates, we propose a noninteracting virtual orbital (NIVO) approximation of the Baker-Campbell-Hausdorff series that neglects commutators terms with three and four virtual indices. The NIVO approximation reduces the computational prefactor of the MR-LDSRG(2), bringing it closer to that of coupled cluster with singles and doubles (CCSD). We test the effect of the DF and NIVO approximations on the MR-LDSRG(2) and sq-MR-LDSRG(2) methods by computing properties of eight diatomic molecules. The diatomic constants obtained by DF-sq-MR-LDSRG(2)+NIVO are found to be as accurate as those from the original MR-LDSRG(2) and coupled cluster theory with singles, doubles, and perturbative triples. Finally, we demonstrate that the DF-sq-MR-LDSRG(2)+NIVO scheme can be applied to chemical systems with more than 550 basis functions by computing the automerization energy of cyclobutadiene with a quintuple-ζ basis set. The predicted automerization energy is found to be similar to the value computed with Mukherjee's state-specific multireference coupled cluster theory with singles and doubles.

Beyond energies: geometry predictions with the XYG3 type of doubly hybrid density functionals

The scaled mean absolute deviations (s-MADs) of the optimized geometric parameters for covalent bondings (the CCse set), nonbonded interactions (the S22G30 set) and the transition state structures (the TSG36 set), with Tot referring to the averaged s-MAD for general performances.

Isotopes and analogs of hydrogen--from fundamental investigations to practical applications

Hydrogen has a central role in the story of the universe itself and also in the story of our efforts to understand it. This paper retells the story of the part played by hydrogen and its stable isotope deuterium in the primordial synthesis of the elements, then goes on to describe how the spectrum of atomic hydrogen led to insights into the laws governing matter at the most fundamental level, from the quantum mechanics of Schrödinger and Heisenberg, through quantum electrodynamics, to the most recent work investigating the underlying structure of the proton itself. Atomic hydrogen is unique among the elements in that the concept of isotopy--atoms having the same nuclear charge but different masses--is stretched to its limit in the isotopes of hydrogen, ranging from the well-known isotopes deuterium and tritium to exotic species such as muonium, muonic helium, and positronium. These atoms, or atom-like objects, have much to tell us about fundamental aspects of the universe. In recent years the idea of utilizing hydrogen either as an energy source (through nuclear fusion) or as an energy storage medium (bound in hydrides or other materials) has attracted much attention as a possible avenue to a post-oil energy future. Some of the more interesting recent developments are described here. Dedicated to the memory of Brian C. Webster (1939-2008).

The classical Wigner method with an effective quantum force: application to the collinear H + H2 reaction

To improve the classical Wigner (CW) model, we recently proposed the classical Wigner model with an effective quantum force (CWEQF). The results of the CWEQF model are more accurate than those of the CW model. Still the simplicity of the CW model is retained. The quantum force was obtained by defining a characteristic distance η(0) between two Feynman paths that enter the expression for the flux-flux correlation function. η(0) was considered independent of the position along the reaction path. The CWEQF leads to a lowering of the effective potential barrier. Here we develop the method to use position dependent η(0) values. The method is also generalized to two dimensions. Applications are carried out on one-dimensional model problems and the two-dimensional H + H(2) collinear reaction.

Tersoff-Type Potentials for Carbon, Hydrogen and Oxygen

The application of Tersoff-type potentials are illustrated for examples from three distinct classes of chemical systems: a covalently-bonded solid (carbon), a gas-phase few-body reactive system (H3), and a molecular solid (oxygen). For carbon, the potential energy expression yields stable planar graphite layers as well as a stable diamond phase, both with correct densities and binding energies. The potential also predicts the π-bonded chain structure to be the energetically-preferred reconstruction on the {111} surface of diamond, in agreement with ab initio studies. For hydrogen the potential provides a quantitative description of accurate ab initio energies. The oxygen potential describes both the O2 and O3 molecules, and qualitatively describes intramolecular bonding in the condensed phase.

Valence bond perturbation theory. A valence bond method that incorporates perturbation theory

A post-VBSCF method, called valence bond second-order perturbation theory (VBPT2), is developed in this paper and is shown to be (i) economical and (ii) at par with more sophisticated VB and MO-based methods. The VBPT2 method starts with VBSCF using a minimal structure set. Subsequently, the Møller-Plesset (MP) partition of the zeroth-order Hamiltonian is obtained by introducing a generalized Fock matrix constructed from the VBSCF density matrix. The first-order wave function is expressed in terms of singly and doubly excited VB structures, which are generated by replacing occupied orbitals by virtual orbitals, the latter being defined as orthogonal to the occupied orbitals. The VBPT2 method retains the simplicity of a VB presentation by condensing contributions from the excited structures into the minimal number of fundamental structures that are involved in the VBSCF calculation. The method is tested by calculating the bond energies of H(2), F(2), N(2), O(2), the barrier of identity hydrogen abstraction reaction, the atomization energy and a potential energy curve for the water molecule and the structural weights and covalent-ionic resonance energy of F(2). It is shown that the VBPT2 method gives results in good agreement with those of the VBCI method and molecular-orbital based methods such as MRPT and MRCI at the same truncation levels. However, the computational effort is greatly reduced, compared to that of VBCI. Future potential directions for the development of the VBPT2 method are outlined.

Three dimensional atom-diatom quantum reactive scattering calculations using absorbing potential: speed up of the propagation scheme

In this paper a new propagation scheme is proposed for atom-diatom reactive calculations using a negative imaginary potential (NIP) within a time independent approach. It is based on the calculation of a rotationally adiabatic basis set, the neglected coupling terms being re-added in the following step of the propagation. The results of this approach, which we call two steps rotationally adiabatic coupled states calculations (2-RACS), are compared to those obtained using the adiabatic DVR method (J. C. Light and Z. Bazic, J. Chem. Phys., 1987, 87, 4008; C. Leforestier, J. Chem. Phys., 1991, 94, 6388), to the NIP coupled states results of the team of Baer (D. M. Charutz, I. Last and M. Baer, J. Chem. Phys., 1997, 106, 7654) and to the exact results obtained by Zhang (J. Z. H. Zhang and W. H. Miller, J. Chem. Phys., 1989, 91, 1528) for the D + H(2) reaction. The example of implementation of our method of computation of the adiabatic basis will be given here in the coupled states approximation, as this method has proved to be very efficient in many cases and is quite fast.