Comment on: "Estimating the Hartree-Fock limit from finite basis set calculations" [Jensen F (2005) Theor Chem Acc 113:267]

We demonstrate that a minor modification of the extrapolation proposed by Jensen [(2005): Theor Chem Acc 113:267] yields very reliable estimates of the Hartree-Fock limit in conjunction with correlation consistent basis sets. Specifically, a two-point extrapolation of the form $E_{HF,L}=E_{HF,\infty}+A(L+1)\exp(-9\sqrt{L})$ yields HF limits $E_{HF,\infty}$ with an RMS error of 0.1 millihartree using aug-cc-pVQZ and aug-cc-pV5Z basis sets, and of 0.01 millihartree using aug-cc-pV5Z and aug-cc-pV6Z basis sets.Comment: Theoretical Chemistry Accounts, in pres

Scanning-probe spectroscopy of semiconductor donor molecules

Semiconductor devices continue to press into the nanoscale regime, and new applications have emerged for which the quantum properties of dopant atoms act as the functional part of the device, underscoring the necessity to probe the quantum structure of small numbers of dopant atoms in semiconductors[1-3]. Although dopant properties are well-understood with respect to bulk semiconductors, new questions arise in nanosystems. For example, the quantum energy levels of dopants will be affected by the proximity of nanometer-scale electrodes. Moreover, because shallow donors and acceptors are analogous to hydrogen atoms, experiments on small numbers of dopants have the potential to be a testing ground for fundamental questions of atomic and molecular physics, such as the maximum negative ionization of a molecule with a given number of positive ions[4,5]. Electron tunneling spectroscopy through isolated dopants has been observed in transport studies[6,7]. In addition, Geim and coworkers identified resonances due to two closely spaced donors, effectively forming donor molecules[8]. Here we present capacitance spectroscopy measurements of silicon donors in a gallium-arsenide heterostructure using a scanning probe technique[9,10]. In contrast to the work of Geim et al., our data show discernible peaks attributed to successive electrons entering the molecules. Hence this work represents the first addition spectrum measurement of dopant molecules. More generally, to the best of our knowledge, this study is the first example of single-electron capacitance spectroscopy performed directly with a scanning probe tip[9].Comment: In press, Nature Physics. Original manuscript posted here; 16 pages, 3 figures, 5 supplementary figure

Does Al4H14— cluster anion exist? High-level ab initio study

A comprehensive ab initio investigation using coupled cluster theory with the aug-cc-pVnZ, n = D,T basis sets is carried out to identify distinct structures of the Al4H14— cluster anion and to evaluate its fragmentation stability. Both thermodynamic and mechanistic aspects of the fragmentation reactions are studied. The observation of this so far the most hydrogenated aluminum tetramer was reported in the recent mass spectrometry study of Li et al. (2010) J Chem Phys 132:241103–241104. The four Al4H14— anion structures found are chain-like with the multiple-coordinate Al center and can be viewed approximately as comprising Al2H7— and Al2H7 moieties. Locating computationally some of the Al4H14— minima on the correlated ab initio potential energy surfaces required the triple-zeta quality basis set to describe adequately the Al multi-coordinate bonding. For the two most stable Al4H14— isomers, the mechanism of their low-barrier interconversion is described. The dissociation of Al4H14— into the Al2H7— and Al2H7 units is predicted to require 20-22 (10-13) kcal mol-1 in terms of ΔH (ΔG) estimated at T = 298.15 K and p = 1 atm. However, Al4H14— is found to be a metastable species in the gas phase: the H2 loss from the radical moiety of its most favorable isomer is exothermic by 18 kcal mol-1 in terms of ΔH (298.15 K) and by 25 kcal mol-1 in terms of ΔG(298.15 K), with the enthalpic/free energy barrier involved being less than 1 kcal mol-1. By contrast with alane Al4H14—, only a weakly bound complex between Ga4H12— and H2 has been identified for the gallium analogue using the relativistic effective core potential

The Schwinger Variational Method

Variational methods have proven invaluable in theoretical physics and chemistry, both for bound state problems and for the study of collision phenomena. For collisional problems they can be grouped into two types: those based on the Schroedinger equation and those based on the Lippmann-Schwinger equation. The application of the Schwinger variational (SV) method to e-molecule collisions and photoionization has been reviewed previously. The present chapter discusses the implementation of the SV method as applied to e-molecule collisions

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

A computational study of the heterogeneous synthesis of hydrazine on Co3Mo3N

Periodic and molecular density functional theory calculations have been applied to elucidate the associative mechanism for hydrazine and ammonia synthesis in the gas phase and hydrazine formation on Co3Mo3N. We find that there are two activation barriers for the associative gas phase mechanism with barriers of 730 and 658 kJ/mol, corresponding to a hydrogenation step from N2 to NNH2 and H2NNH2 to H3NNH3, respectively. The second step of the mechanism is barrierless and an important intermediate, NNH2, can also readily form on Co3Mo3N surfaces via the Eley–Rideal chemisorption of H2 on a pre-adsorbed N2 at nitrogen vacancies. Based on this intermediate a new heterogeneous mechanism for hydrazine synthesis is studied. The highest relative barrier for this heterogeneous catalysed process is 213 kJ/mol for Co3Mo3N containing nitrogen vacancies, clearly pointing towards a low-energy process for the synthesis of hydrazine via a heterogeneous catalysis route

On the potential application of DFT methods in predicting the interaction-induced electric properties of molecular complexes. Molecular H-bonded chains as a case of study

A detailed analysis of the selected DFT functionals for the calculations of interaction-induced dipole moment, polarizability and first-order hyperpolarizability has been carried out. The hydrogen-bonded model chains consisting of HF, H2CO and H3N molecules have been chosen as a case study. The calculations of the components of the static electric properties using the diffuse Dunning’s basis set (aug-cc-pVDZ) have been performed employing different types of density functionals (B3LYP, LC-BLYP, PBE0, M06-2X and CAM-B3LYP). Obtained results have been compared with those gained at the CCSD(T) level of theory. The counterpoise correction scheme, namely site-site function counterpoise, has been applied in order to eliminate basis set superposition error. The performed tests allow to conclude that the DFT functionals can provide a useful tool for prediction of the interaction-induced electric properties, however a caution has to be urged to their decomposition to the two- and many-body terms