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The electronic structure of XeF6 and associated molecules were studied based on quantum chemical computations at a state-of-the-art level. All-electron computations were performed including electron correlation at the MP2 level. Also, computations for the valence-electrons in an effective core potential were conducted including relativistic effects. Findings revealed that the XeF6-like XF6 compounds with light central atoms or ions prefer the structure of a regular octahedron. The same is true for KrF6.

High-resolution solid-state magic angle spinning NMR spectroscopy helps evaluate the principal elements of the 31P nuclear magnetic shielding tensors of various substituted iminophosphines. Spectral data and results of IGLO calculations help derive the orientation of the shielding tensor in the molecular network. Experimental and theoretical studies help analyze the influence of electronic structure and configuration of double bond on chemical shielding.

Individual gauge for localized orbitals method is employed to determine the magnetic susceptibilities of benzene and related compounds, along with the shielding tensors for 13C and 1H chemical shifts. In-plane and out-of-plane susceptibilities for these molecules are measured and compared. Analysis of pi-electron system reveals the presence of ring current in benzene and less mobile pi-systems in cyclohexatriene.

The ab initio SCF computations of H NMR chemical shifts and the deprotonation energies reveal intrinsic acidity in catalytically active sites and gas-phase molecules, some of which are models of surface hydroxyl groups. There is no property-reactivity relation between the chemical shift of the hydroxyl proton and its acidity, as previously assumed. This is because the chemical shift is influenced by the lone pairs of oxygen and the X-O bond, which have non-constant and non-negligible effects.

A new approach to density cumulant functional theory is developed that derives density cumulant N-representability conditions from an approximate Fock space unitary transformation. We present explicit equations for the third- and fourth-order two-particle cumulant N-representability, as well as the second-order contributions that depend on the connected three-particle density cumulant. These conditions are used to formulate the ODC-13 method and the non-iterative (λ3) correction that employ an incomplete description of the fourth-order two-particle cumulant N-representability and the second-order three-particle correlation effects, respectively. We perform an analysis of the ODC-13 N-representability description for the dissociation of H2 and apply the ODC-13 method and the (λ3) correction to diatomic molecules with multiple bond character and the symmetry-breaking tetraoxygen cation (O+4). For the O+4 molecule, the vibrational frequencies of the ODC-13(λ3) method do not exhibit spatial symmetry breaking and are in a good agreement with the recent infrared photodissociation experiment. We report the O+4 equilibrium structure, harmonic frequencies, and dissociation energy computed using ODC-13(λ3) with a diffuse, core-correlated aug-cc-pCVTZ basis set. [ABSTRACT FROM AUTHOR]

Multiple system atrophy (MSA) is a rare and fatal neurodegenerative disease with limited symptomatic treatment options. Aggregation of α‐synuclein in oligodendrocytes is believed to be a central mechanism of the neurodegenerative process. PD01A and PD03A are 2 novel therapeutic vaccine candidates containing short peptides as antigenic moieties that are designed to induce a sustained antibody response, specifically targeting pathogenic assemblies of α‐synuclein. The objectives of the current study were to evaluate primarily the safety and tolerability of PD01A and PD03A in patients with early MSA. Thirty patients (11 women) were randomized to receive 5 subcutaneous injections of either PD01A (n = 12), PD03A (n = 12), or placebo (n = 6) in this patient‐ and examiner‐blinded, placebo‐controlled, 52‐week phase 1 clinical trial (ClinicalTrial.gov identifier: NCT02270489). Immunogenicity and clinical scores were assessed as secondary objectives. Twenty‐nine patients reported a total of 595 treatment‐emergent adverse events (mild or moderate, n = 555; severe, n = 40). Treatment‐related adverse events included 190 injection‐site reactions typically observed in vaccination trials with similar per‐subject incidence in the treatment groups over time. Sustained IgG titers were observed in the PD01A‐treated group, and 89% of treated patients developed a PD01‐specific antibody response after receiving all injections. Induced antibodies displayed clear reactivity to the α‐synuclein target epitope. Titers and antibody responder rate (58%) were lower in the PD03A‐treated group. In conclusion, both PD01A and PD03A were safe and well tolerated. PD01A triggered a rapid and long‐lasting antibody response that specifically targeted the α‐synuclein epitope. © 2020 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society. [ABSTRACT FROM AUTHOR]

Density cumulant functional theory [W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006)] is implemented for the first time. Benchmark results are provided for atoms and diatomic molecules, demonstrating the performance of DCFT-06 for both nonbonded and bonded interactions. The results show that DCFT-06 appears to perform similarly to coupled cluster theory with single and double excitations (CCSD) in describing dispersion. For covalently bound systems, the physical properties predicted by DCFT-06 appear to be at least of CCSD quality around equilibrium geometries. The computational scaling of both DCFT-06 and CCSD is O(N6), but the former has reduced nonlinearities among the variables and a Hermitian energy functional, making it an attractive alternative. [ABSTRACT FROM AUTHOR]

The calculation of NMR parameters from relativistic quantum theory in a Gaussian basis expansion requires some care. While in the absence of a magnetic field the expansion in a kinetically balanced basis converges for the wave function in the mean and for the energy with any desired accuracy, this is not necessarily the case for magnetic properties. The results for the magnetizability or the nuclear magnetic shielding are not even correct in the nonrelativistic limit (nrl) if one expands the original Dirac equation in a kinetically balanced Gaussian basis. This defect disappears if one starts from the unitary transformed Dirac equation as suggested by Kutzelnigg [Phys. Rev. A 67, 032109 (2003)]. However, a new difficulty can arise instead if one applies the transformation in the presence of the magnetic field of a point nucleus. If one decomposes certain contributions, the individual terms may diverge, although their sum is regular. A controlled cancellation may become difficult and numerical instabilities can arise. Various ways exist to avoid these singularities and at the same time get the correct nrl. There are essentially three approaches intermediate between the transformed and the untransformed formulation, namely, the bispinor decomposition, the decomposition of the lower component, and the hybrid unitary transformation partially at operator and partially at matrix level. All three possibilities were first considered by Xiao et al. [J. Chem. Phys. 126, 214101 (2007)] in a different context and in a different nomenclature. Their analysis and classification in a more general context are given here for the first time. Use of an extended balanced basis has no advantages and has other drawbacks and is not competitive, while the use of a restricted magnetic balance basis can be justified. [ABSTRACT FROM AUTHOR]

It is shown that the exact relativistic wave function of the ground state of H-like ions can be expanded in a kinetically balanced even-tempered Gaussian basis. The error of the overlap integral between exact and approximate wave function depends as [formula], with [formula], on the size n of the basis, both for the large and the small components. Even the error of the energy has essentially the same dependence on n and decays only slightly slower than its nonrelativistic counterpart, which goes as ∼n3/2 exp[-π3n/2]. [ABSTRACT FROM AUTHOR]

The Dirac operator in a matrix representation in a kinetically balanced basis is transformed to the matrix representation of a quasirelativistic Hamiltonian that has the same electronic eigenstates as the original Dirac matrix (but no positronic eigenstates). This transformation involves a matrix X, for which an exact identity is derived and which can be constructed either in a noniterative way or by various iteration schemes, not requiring an expansion parameter. Both linearly convergent and quadratically convergent iteration schemes are discussed and compared numerically. The authors present three rather different schemes, for each of which even in unfavorable cases convergence is reached within three or four iterations, for all electronic eigenstates of the Dirac operator. The authors present the theory both in terms of a non-Hermitian and a Hermitian quasirelativistic Hamiltonian. Quasirelativistic approaches at the matrix level known from the literature are critically analyzed in the frame of the general theory. [ABSTRACT FROM AUTHOR]

Starting point is the energy expectation value as a functional of the one-particle density matrix γ and the two-particle density cumulant λ2. We decompose γ into a best idempotent approximation κ and a correction τ, that is entirely expressible in terms of λ2. So we get the energy E as a functional of κ and λ2, which can be varied independently. Approximate n-representability conditions, derived by perturbation theory are imposed on the variation of λ2. A nonlinear system of equations satisfied by λ2 is derived, the linearized version of which turns out to be equivalent to the coupled electron-pair approximation, variant zero. The start for κ is Hartree-Fock, but κ is then updated to become the best idempotent approximation of γ. Relations to density matrix functional theory and Kohn-Sham type density functional theory are discussed. [ABSTRACT FROM AUTHOR]

The Dirac operator in a matrix representation in a kinetically balanced basis is transformed to a quasirelativistic Hamiltonian matrix, that has the same electronic eigenstates as the original Dirac matrix. This transformation involves a matrix X, for which an exact identity is derived, and which can be constructed either in a noniterative way or by various iteration schemes, without requiring an expansion parameter. The convergence behavior of five different iteration schemes is studied numerically, with very promising results. [ABSTRACT FROM AUTHOR]

We analyze the structure and the solutions of the irreducible k-particle Brillouin conditions (IBCk) and the irreducible contracted Schrödinger equations (ICSEk) for an n-electron system without electron interaction. This exercise is very instructive in that it gives one both the perspective and the strategies to be followed in applying the IBC and ICSE to physically realistic systems with electron interaction. The IBC1 leads to a Liouville equation for the one-particle density matrix γ1=γ, consistent with our earlier analysis that the IBC1 holds both for a pure and an ensemble state. The IBC1 or the ICSE1 must be solved subject to the constraints imposed by the n-representability condition, which is particularly simple for γ. For a closed-shell state γ is idempotent, i.e., all natural spin orbitals (NSO’s) have occupation numbers 0 or 1, and all cumulants λk with k>=2 vanish. For open-shell states there are NSO’s with fractional occupation number, and at the same time nonvanishing elements of λ2, which are related to spin and symmetry coupling. It is often useful to describe an open-shell state by a totally symmetric ensemble state. If one wants to treat a one-particle perturbation by means of perturbation theory, this mainly as a run-up for the study of a two-particle perturbation, one is faced with the problem that the perturbation expansion of the Liouville equation gives information only on the nondiagonal elements (in a basis of the unperturbed states) of γ. There are essentially three possibilities to construct the diagonal elements of γ: (i) to consider the perturbation expansion of the characteristic polynomial of γ, especially the idempotency for closed-shell states, (ii) to rely on the ICSE1, which (at variance with the IBC1) also gives information on the diagonal elements, though not in a very efficient manner, and (iii) to formulate the perturbation theory in terms of a unitary transformation in Fock space. The latter is particularly powerful, especially, when one wishes to study realistic Hamiltonians with a two-body interaction. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The k-particle irreducible Brillouin conditions IBCk and the k-particle irreducible contracted Schrödinger equations ICSEk for a closed-shell state are analyzed in terms of a Møller–Plesset–type perturbation expansion. The zeroth order is Hartree–Fock. From the IBC2(1), i.e., from the two-particle IBC to first order in the perturbation parameter μ, one gets the leading correction λ2(1) to the two-particle cumulant λ2 correctly. However, in order to construct the second-order energy E2, one also needs the second-order diagonal correction γD(2) to the one-particle density matrix γ. This can be obtained: (i) from the idempotency of the n-particle density matrix, i.e., essentially from the requirement of n-representability; (ii) from the ICSE1(2); or (iii) by means of perturbation theory via a unitary transformation in Fock space. Method (ii) is very unsatisfactory, because one must first solve the ICSE3(2) to get λ3(2), which is needed in the ICSE2(2) to get λ2(2), which, in turn, is needed in the ICSE1(2) to get γ(2). Generally the (k+1)-particle approximation is needed to obtain Ek correctly. One gains something, if one replaces the standard hierarchy, in which one solves the ICSEk, ignoring λk+1 and λk+2, by a renormalized hierarchy, in which only λk+2 is ignored, and λk+1 is expressed in terms of the λp of lower particle rank via the partial trace relation for λk+2. Then the k-particle approximation is needed to obtain Ek correctly. This is still poorer than coupled-cluster theory, where the k-particle approximation yields Ek+1. We also study the possibility to use some simple necessary n-representability conditions, based on the non-negativity of γ(2) and two related matrices, in order to get estimates for γD(2) in terms of λ2(1). In general these estimates are rather weak, but they can become close to the best possible bounds in special situations characterized by a very sparse structure of λ2 in terms of a localized representation. The perturbative analysis does not encourage the use of a k-particle hierarchy based on the ICSEk (or on their reducible counterparts, the CSEk), it rather favors the approach in terms of the unitary transformation, where the k-particle approximation yields the energy correct up to E2k-1. The problems that arise are related to the unavoidable appearance of exclusion-principle violating cumulants. The good experience with perturbation theory in terms of a unitary transformation suggests that one should abandon a linearly convergent iteration scheme based on the ICSEk hierarchy, in favor of a quadratically convergent one based on successive unitary transformations. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Recently [W. Kutzelnigg and D. Mukherjee, Chem. Phys. Lett. 317, 567 (2000); D. Mukherjee and W. Kutzelnigg, J. Chem. Phys 114, 2047 (2001)] the irreducible k-particle Brillouin conditions IBC[sub k] and the irreducible k-particle contracted Schrödinger equations ICSE[sub k] were derived. These permit the definition of a hierarchy of k-particle approximations for the direct calculation of the cumulants λ[sub k] of the k-particle density matrices. Now, the spin-free form of these conditions, appropriate for a spin-free Hamiltonian, is given. This is particularly useful for open-shell states. The definition of the cumulants of the reduced densities has to be generalized for these anyway, making use of irreducible tensor operators with respect to SU[sub 2]. There are two alternative definitions of spin-free cumulants, of which the one in terms of spin-free reduced density matrices appears to be preferable. Alternatively to the straight spin-free formulation, we also present a theory in terms of spin-free operators adapted to the symmetric group. Partial trace relations that relate the elements of the cumulants of different particle rank are derived. There are partial trace relations for "exchange elements," which are determined by the total spin quantum number S. From these relations the individual exchange elements of A[sub 2] can be obtained in special cases. This allows a simple formulation of the stationarity conditions for open-shell states of any spin multiplicity. [ABSTRACT FROM AUTHOR]