Adiabatic approximation of time-dependent density matrix functional response theory

Time-dependent density matrix functional theory can be formulated in terms of coupled-perturbed response equations, in which a coupling matrix K(omega) features, analogous to the well-known time-dependent density functional theory (TDDFT) case. An adiabatic approximation is needed to solve these equations, but the adiabatic approximation is much more critical since there is not a good "zero order" as in TDDFT, in which the virtual-occupied Kohn-Sham orbital energy differences serve this purpose. We discuss a simple approximation proposed earlier which uses only results from static calculations, called the static approximation (SA), and show that it is deficient, since it leads to zero response of the natural orbital occupation numbers. This leads to wrong behavior in the omega-->0 limit. An improved adiabatic approximation (AA) is formulated. The two-electron system affords a derivation of exact coupled-perturbed equations for the density matrix response, permitting analytical comparison of the adiabatic approximation with the exact equations. For the two-electron system also, the exact density matrix functional (2-matrix in terms of 1-matrix) is known, enabling testing of the static and adiabatic approximations unobscured by approximations in the functional. The two-electron HeH(+) molecule shows that at the equilibrium distance, SA consistently underestimates the frequency-dependent polarizability alpha(omega), the adiabatic TDDFT overestimates alpha(omega), while AA improves upon SA and, indeed, AA produces the correct alpha(0). For stretched HeH(+), adiabatic density matrix functional theory corrects the too low first excitation energy and overpolarization of adiabatic TDDFT methods and exhibits excellent agreement with high-quality CCSD ("exact") results over a large omega range.     

On the optimal mixing of the exchange energy and the electron-electron interaction part of the exchange-correlation energy

The optimal mixing coefficient C of the exchange energy E_x and the electron-electron interaction part of the exchange-correlation energy W¹_xc in the formula for the total exchange-correlation energy E_xc was expressed through the ratio of the kinetic T_c and potential W_c contributions to the correlation energy E_c. This expression can be derived from a Heavyside step function model of the dependence of W^λ_xc on the coupling parameter of the electron interaction λ. Values of T_c and W_c obtained from ab initio wave functions were used to estimate C for a number of atoms and molecules. A strong dependence of T_c, W_c, and C on the bond distance was demonstrated for the case of the H₂ molecule. T_c and C approach zero in the bond-dissociation limit; so for an electron-pair bond, the admixing of exact exchange to obtain an accurate E_xc is strongly dependent on the bond length and has to disappear for weak interaction/large bond distances. The potential of the exchange-correlation hole constructed for H₂ from an ab initio second-order density matrix was compared with its generalized gradient approximation (GGA). © 1996 John Wiley & Sons, Inc.     

Pulse radiolysis study of reactions of alkyl and alkylperoxy radicals originating from methyl tert-butyl ether in the gas phase

UV spectra and kinetics for the reactions of alkyl and alkylperoxy radicals from methyl tert-butyl ether (MTBE) were studied in 1 atm of SF₆ by the pulse radiolysis-UV absorption technique. UV spectra for the radical mixtures were quantified from 215 to 340 nm. At 240 nm. σ_R = (2.6 ± 0.4) × 10⁻¹⁸ cm² molecule⁻¹ and σ_RO2 = (4.1 ± 0.6) × 10⁻¹⁸ cm² molecule⁻¹ (base e). The rate constant for the self-reaction of the alkyl radicals is (2.5 ± 1.1) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹. The rate constants for reaction of the alkyl radicals with molecular oxygen and the alkylperoxy radicals with NO and NO₂ are (9.1 ± 1.5) × 10⁻¹³, (4.3 ± 1.6) × 10⁻¹² and (1.2 ± 0.3) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹, respectively. The rate constants given above refer to reaction at the tert-butyl side of the molecule.     

Spatial sign preprocessing: a simple way to impart moderate robustness to multivariate estimators

The spatial sign is a multivariate extension of the concept of sign. Recently multivariate estimators of covariance structures based on spatial signs have been examined by various authors. These new estimators are found to be robust to outlying observations. From a computational point of view, estimators based on spatial sign are very easy to implement as they boil down to a transformation of the data to their spatial signs, from which the classical estimator is then computed. Hence, one can also consider the transformation to spatial signs to be a preprocessing technique, which ensures that the calibration procedure as a whole is robust. In this paper, we examine the special case of spatial sign preprocessing in combination with partial least squares regression as the latter technique is frequently applied in the context of chemical data analysis. In a simulation study, we compare the performance of the spatial sign transformation to nontransformed data as well as to two robust counterparts of partial least squares regression. It turns out that the spatial sign transform is fairly efficient but has some undesirable bias properties. The method is applied to a recently published data set in the field of quantitative structure-activity relationships, where it is seen to perform equally well as the previously described best linear model for these data.     

Assessment of a simple correction for the long-range charge-transfer problem in time-dependent density-functional theory

The failure of the time-dependent density-functional theory to describe long-range charge-transfer (CT) excitations correctly is a serious problem for calculations of electronic transitions in large systems, especially if they are composed of several weakly interacting units. The problem is particularly severe for molecules in solution, either modeled by periodic boundary calculations with large box sizes or by cluster calculations employing extended solvent shells. In the present study we describe the implementation and assessment of a simple physically motivated correction to the exchange-correlation kernel suggested in a previous study [O. Gritsenko and E. J. Baerends J. Chem. Phys. 121, 655 (2004)]. It introduces the required divergence in the kernel when the transition density goes to zero due to a large spatial distance between the "electron" (in the virtual orbital) and the "hole" (in the occupied orbital). A major benefit arises for solvated molecules, for which many CT excitations occur from solvent to solute or vice versa. In these cases, the correction of the exchange-correlation kernel can be used to automatically "clean up" the spectrum and significantly reduce the computational effort to determine low-lying transitions of the solute. This correction uses a phenomenological parameter, which is needed to identify a CT excitation in terms of the orbital density overlap of the occupied and virtual orbitals involved. Another quantity needed in this approach is the magnitude of the correction in the asymptotic limit. Although this can, in principle, be calculated rigorously for a given CT transition, we assess a simple approximation to it that can automatically be applied to a number of low-energy CT excitations without additional computational effort. We show that the method is robust and correctly shifts long-range CT excitations, while other excitations remain unaffected. We discuss problems arising from a strong delocalization of orbitals, which leads to a breakdown of the correction criterion.     

Improving numerical integration through basis set expansion

Calculations are presented to assess a theorem presented by S.F. Boys [(1969) Proc. R. Soc. A. 309:195], regarding the accuracy of numerical integration in quantum chemical calculations. The theorem states that the error due to numerical integration can be made proportional to the error due to basis set truncation, and thus goes to zero in the limit of a complete basis. We test this theorem on the hydrogen atom, showing that with a solution-spanning basis, the numerically exact orbital energy can indeed be calculated with a small number of integration points. Moreover, tests for H and H₂⁺ demonstrate that even when only a near-complete basis is employed, Boys Theorem can significantly reduce integration error. However, for other systems, like the oxygen atom and the CO₂ molecule, the theorem yields no advantage for some occupied orbitals. It is concluded that the theorem would be most useful for calculations that demand large basis sets.     

Cu(bipy)2+/TEMPO-catalyzed oxidation of alcohols: radical or nonradical mechanism?

In the oxidation of alcohols with TEMPO as catalyst, the substrate has alternatively been postulated to be oxidized but uncoordinated TEMPO(+) (Semmelhack) or Cu-coordinated TEMPO(?) radical (Sheldon). The reaction with the Cu(bipy)(2+)/TEMPO cocatalyst system has recently been claimed, on the basis of DFT calculations, to not be a radical reaction but to be best viewed as electrophilic attack on the alcohol C-H(α) bond by coordinated TEMPO(+). This mechanism combines elements of the Semmelhack mechanism (oxidation of TEMPO to TEMPO(+)) and the Sheldon proposal ("in the coordination sphere of Cu"). The recent proposal has been challenged on the basis of DFT calculations with a different functional, which were reported to lead to a radical mechanism. We carefully examine the results for the two functionals and conclude from both the calculated energetics and from an electronic structure analysis that the results of the two DFT functionals are consistent and that both lead to the proposed mechanism with TEMPO not acting as radical but as (coordinated) positive ion.     

Counterpoise correction is not useful for short and Van der Waals distances but may be useful at long range

This article investigates the errors in supermolecule calculations for the helium dimer. In a full CI calculation, there are two errors. One is the basis set superposition error (BSSE), the other is the basis set convergence error (BSCE). Both of the errors arise from the incompleteness of the basis set. These two errors make opposite contributions to the interaction energies. The BSCE is by far the largest error in the short range and larger than (but much closer to) BSSE around the Van der Waals minimum. Only at the long range, the BSSE becomes the larger error. The BSCE and BSSE largely cancel each other over the Van der Waals well. Accordingly, it may be recommended to not include the BSSE for the calculation of the potential energy curve from short distance till well beyond the Van der Waals minimum, but it may be recommended to include the BSSE correction if an accurate tail behavior is required. Only if the calculation has used a very large basis set, one can refrain from including the counterpoise correction in the full potential range. These results are based on full CI calculations with the aug-cc-pVXZ (X = D, T, Q, 5) basis sets.     

Hydrolysis of glycosides with microgel catalysts

A dormant macromolecular catalyst was prepared by polymerization of an aqueous styrene-butyl acrylate miniemulsion in the presence of a new polymerizable pentadentate ligand. The catalyst was activated by binding Cu(II) ions to the ligand site and then explored for its ability to hydrolyze glycosidic bonds in alkaline solution. The performance was correlated to the catalytic activity shown by low molecular weight analogs. A turnover rate of up to 43 × 10(-4) min(-1) was previously observed for cleavage of the glycosidic bond in selected p-nitrophenylglycosides with a binuclear, low molecular weight catalyst; by contrast, the same reaction is more than 1 order of magnitude faster and has a turnover rate of up to 380 × 10(-4) min(-1) when using the prepared macromolecular catalyst. The catalyzed hydrolysis is about 10(5)-fold accelerated over the uncatalyzed background reaction under the provided conditions, while a significant discrimination of the α- and β-glycosidic bond or of the galacto- and gluco-configuration in the sugar moiety in the glycoside substrates is not observed.     

Dynamic Interplay between Defective UiO-66 and Protic Solvents in Activated Processes

UiO-66, composed by Zr-oxide inorganic bricks [Zr₆(μ₃-O)₄(μ₃-OH)₄] and organic terephthalate linkers, is one of the most studied metal–organic frameworks (MOFs) due to its exceptional thermal, chemical, and mechanical stability. Thanks to its high connectivity, the material can withstand structural deformations during activation processes such as linker exchange, dehydration, and defect formation. These processes do alter the zirconium coordination number in a dynamic way, creating open metal sites for catalysis and thus are able to tune the catalytic properties. In this work, it is shown, by means of first-principle molecular-dynamics simulations at operating conditions, how protic solvents may facilitate such changes in the metal coordination. Solvent can induce structural rearrangements in the material that can lead to undercoordinated but also overcoordinated metal sites. This is demonstrated by simulating activation processes along well-chosen collective variables. Such enhanced MD simulations are able to track the intrinsic dynamics of the framework at realistic conditions.