Correlation effects in externally perturbed many-electron systems

Different methods for the calculation of the electron correlation contribution to atomic and molecular properties are analyzed and evaluated. The methods based on the self-consistent solution of the external perturbation problem are shown to offer several formal and computational advantages. The analysis of the correlation perturbation series for properties of many-electron systems indicates the importance of the appropriate treatment of unlinked diagrammatic contributions. In particular, the standard limited configuration interaction scheme based on single and double substitutions in the reference function may significantly suffer from the erratic treatment of unlinked clusters and needs to be corrected appropriately. The basis set choice for the calculation of highly accurate values of properties is also discussed. In order to circumvent the dimensionality problem the use of basis sets with explicit dependence on the external perturbation strength is recommended and methods for their choice and optimization are presented. A particular attention is paid to the many-body perturbation theory involving singly and doubly substituted intermediate states and based on the coupled Hartree–Fock solution for the one-electron perturbation problem. Different computational aspects of this method are discussed and compared with other techniques currently in use.     

Two-photon ionization of an inner shell electron of the Cl atom

We have calculated, using second order perturbation theory, the two photon ionization cross section of a K-shell electron of chlorine forE=1.6 keV incident photons. Two classes of intermediate states must be considered, those in which a 1s electron moves to an emptyp-orbital, and those in which an electron from an occupiedp-orbital moves into the continuum. The first class of intermediate states is followed by the ejection of ap-electron into the continuum. The second class of intermediate states is followed by the transfer of a 1s electron into an emptyp-state. The largest contribution comes from 3p →d-continuum followed by 1s → 3p transition. Our result is σ⁽²⁾/I=2.06×10⁴¹ cm⁴/W where σ⁽²⁾ is the two photon ionization cross-section andI is the light intensity.     

A stable intermediate wetting state after a water drop contacts the bottom of a microchannel or is placed on a single corner

It is considered that, after a water drop contacts the base of a roughness groove, water should immediately fill this roughness groove. Subsequently, Cassie-Baxter wetting state is transited to that of Wenzel. Accordingly, one of the criteria used to judge the transition from Cassie-Baxter to Wenzel states is whether a water drop has contact with the base of a roughness groove. In this work, through theoretical and experimental investigations, we show that this transition criterion does not always hold true in the case of microchannels. We first theoretically prove that, when an angle criterion is satisfied, there may exist an intermediate wetting state inside a microchannel after a water drop contacts the bottom of the microchannel. In this wetting state, water does not completely fill the microchannel, and air pockets still exist in its bottom corners. Also, the wetting state is stable in the sense that its energy state is lower than that of the Wenzel model. According to the angle criterion, such intermediate states may exist, for example, in microchannels with vertical sidewalls, when contact angles on the inner surfaces of these microchannels are larger than 135°. In addition to microchannels, the aforementioned intermediate state may also exist on a single corner (which is formed by a horizontal plate and an inclined plate), when the angle criterion is met. After theoretical modeling, we then conduct four types of tests on single corners and microchannels to validate the angle criterion. In these tests, once the angle criterion is met, stable intermediate states are observed on the corresponding samples. In addition, it is found from the two types of tests conducted on microchannels that, once Laplace pressure inside a water drop is gradually reduced, such an intermediate wetting state may be transited back to the original Cassie-Baxter state. On the other hand, the Wenzel state may not have such a reversal transition unless an additional force is applied to overcome energy barrier between Wenzel and Cassie-Baxter states.     

Ab initio investigation of the stability of Si3C3 clusters and their structural and bonding features

Various structural possibilities for Si₃C₃ clusters are investigated by ab initio calculations employing basis sets of double- and triple-zeta quality augmented by d polarization functions. Correlation effects are included by a second-order Moeller Plesset perturbation treatment. For the two lowest-lying structures higher-order correlation corrections and multi-reference effects are also included. Bonding features are investigated by two different types of population analyses to obtain insight into the nature of chemical bonding. A total of 17 stationary points were investigated, 14 of which correspond to local minima and three being transition states. The energetically lowest-lying structures are: A “pyramidlike” structure with various multicenter bonds, followed by a C_s symmetric isomer closely related to the ground state Si₆ structure. Planar structures, favoured in small carbon clusters, lie higher in energy and are transition states. The lowest-lying triplet system is found to be the linear nonsymmetric Si-C-C-C-Si-Si structure, which is calculated to lie about 38 kcal/mole above the singlet ground state. A building-up principle based on bonding criteria is suggested for the occurence of the various structural possibilities.     

Finite-field many-body perturbation theory II. SD-MBPT study of the nuclear charge dependence of the electron correlation contribution to the dipole polarizability of 10-electron atomic systems

The finite-field many-body perturbation theory limited to intermediate states involving single and double substitutions in the reference HF determinant is applied to the calculation of dipole polarizabilities of 10-electron atomic systems. The nuclear charge dependence of the convergence of the SD-MBPT series for correlation corrections to the dipole polarizability is investigated. It is concluded that the fourth-order SD-MBPT scheme is quite appropriate for neutral and positively charged species. For negatively charged systems the convergence of the SD-MBPT series becomes much poorer and including higher-order substitutions may be necessary. The role of the renormalization contributions to the SD-CI polarizability results is also considered. It follows that the corresponding data need to be corrected for the erratic treatment of unlinked clusters. The size inconsistency effects make quite important contributions to the SD-CI values of the correlation corrections to dipole polarizabilities.     

Origin of the enhancement of the second hyperpolarizability of singlet diradical systems with intermediate diradical character

The origin of the diradical character dependence of the second hyperpolarizability (gamma) of neutral singlet diradical systems is clarified based on the perturbation formula of gamma using the simplest diradical molecular model with different diradical characters, i.e., H2 under bond dissociation. The enhancement of gamma in the intermediate diradical character region turns out to originate from the increasing magnitude of the transition moment between the first and second excited states and the decrease of that between the ground and first excited states, respectively, with the increase in diradical character. This feature confirms that open-shell singlet conjugated molecules with intermediate diradical characters constitute a new class of third-order nonlinear optical systems, whose gamma values can be controlled by the diradical character in addition to the conjugation length.     

Total synthesis of the quinone epoxide dimer (+)-torreyanic acid: application of a biomimetic oxidation/electrocyclization/Diels-Alder dimerization cascade

An asymmetric synthesis of the quinone epoxide dimer (+)-torreyanic acid (48) has been accomplished employing [4 + 2] dimerization of diastereomeric 2H-pyran monomers. Synthesis of the related monomeric natural product (+)-ambuic acid (2) has also been achieved which establishes the biosynthetic relationship between these two natural products. A tartrate-mediated nucleophilic epoxidation involving hydroxyl group direction facilitated the asymmetric synthesis of a key chiral quinone monoepoxide intermediate. Thermolysis experiments have also been conducted on a model dimer based on the torreyanic acid core structure and facile retro Diels-Alder reaction processes and equilibration of diastereomeric 2H-pyrans have been observed. Theoretical calculations of Diels-Alder transition states have been performed to evaluate alternative transition states for Diels-Alder dimerization of 2H-pyran quinone epoxide monomers and provide insight into the stereocontrol elements for these reactions.     

Pulsed pressure perturbations, an extra dimension in NMR spectroscopy of proteins

The introduction of multidimensional NMR spectroscopy was a breakthrough in biological NMR methodology because it allowed the unequivocal correlation of different spin states of the system. The introduction of large pressure perturbations in the corresponding radio frequency (RF) pulse sequences adds an extra structural dimension into these experiments. We have developed a microprocessor-controlled pressure jump unit that is able to introduce fast, strong pressure changes at any point in the pulse sequences. Repetitive pressure changes of 80 MPa in the sample tube are thus feasible in less than 30 ms. Two general forms of these experiments are proposed here, the pressure perturbation transient state spectroscopy (PPTSS) and the pressure perturbation state correlation spectroscopy (PPSCS). PPTSS can be used to measure the rate constants and the activation energies and activation volumes for the transition between different conformational states including the folded and unfolded state of proteins, for polymerization-depolymerization processes, and for ligand binding at atomic resolution. PPSCS spectroscopy correlates the NMR parameters of different pressure-induced states of the system, thus allowing the measurement of properties of a given pressure induced state such as a folding intermediate in a different state, for example, the folded state. Selected examples for PPTSS and PPSCS spectroscopy are presented in this Article.     

Time-dependence of wave functions and the calculation of transition intensities

The standard formalism of the perturbation theory for time-dependent perturbations follows from the assumption that the exact solution of the unperturbed time-independent problem is known. The consequences of this assumption are analyzed. Particular attention is given to the methods used for the evaluation of transition intensities. It is shown that the traditional intensity formula in most cases violates the assumptions underlying its derivation. It is shown that for the given ansatz concerning the form of the approximate wave function, the transition intensities should be determined from the variation treatment of the corresponding time-dependent problem. The wave functions of both states involved in the transition should be given the same amount of variation flexibility. This condition is satisfied if the transition intensity expression follows from the complete timedependent perturbation treatment of the perturbed system.     

Multiphoton association reaction He + H+ → HeH+ steered by ultra‐short laser pulse

The multiphoton association reaction He + H⁺ → HeH⁺ in the electronic ground state is investigated using the time‐dependent quantum wave packet method. It is shown that the collision pairs He + H⁺ in continuum state transfer into ν = 0 state and then produce stable molecules HeH⁺ through emission of two or three photons. The multiphoton transition takes place via intermediate states, and the transfer probability is determined by the collision energy and the intermediate states. The populations of the intermediate states and ν = 0 state can be controlled by the laser duration. The three‐photon transition is more efficient than the two‐photon transition for producing the molecule HeH⁺ in ν = 0 state. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Review of theories on ionization in fast ion-atom collisions with prospects for applications to hadron therapy

This work reviews quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The widely used distorted wave methods of the first- and second-order in the pertinent perturbation series expansions are compared with each other. This tests the presumed importance of double continuum intermediate states of two electrons. Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wave functions for double continuum intermediate states. This checks the correctness and usefulness of the eikonalized Coulomb waves when two electrons participate actively to the transition from the initial to the final state of the entire system. We also analyze the significance of the contributions from excited heliumlike states especially in comparison between theory and measurement. The overall goal of the present study is to determine how much of the unprecedented experience gained over several decades in studying high-energy theories of pure three-body charge exchange could be exported directly to four-body double-electron capture without much of additional and essential eleaborations, besides the naturally increased computational demand. In particular, we address the unexpected breakdown of the continuum distorted wave eikonal initial state approximation and the anticipated success of continuum distorted wave theory for double charge exchange in ion-atom collisions at high impact energies.     

On the contribution of higher-order excitations to correlation energies: The ground state of the water molecule

Using the results of a configuration interaction calculation reported by Rosenberg and Shavitt, we derive an approximation to the correlation energy which may be associated with the sum to infinite order of all linked diagrams involving singly- and doubly-excited states. This result is compared with that obtained by calculation of the energy through third-order. The fourth-order linked diagrams involving quadruply-excited states are computed. It is shown that there is a considerable degree of cancellation between the fourth-order linked diagram energy terms involving doubly-excited intermediate states only and those which contain quadruply-excited states.     

A comprehensive,self-contained derivation of the one-body density matrices from single-reference excited-state calculation methods using the equation-of-motion formalism

In this contribution, we review in a rigorous, yet comprehensive fashion the assessment of the one-body reduced density matrices derived from the most used single-reference excited-state calculation methods in the framework of the equation-of-motion formalism. Those methods are separated into two types: those which involve the coupling of a deexcitation operator to a single-excitation transition operator, and those which do not involve such a coupling. The case of many-body auxiliary wave functions for excited states is also addressed. For each of these approaches we were interested in deriving the elements of the one-body transition and difference density matrices, and to highlight their particular structure. This has been accomplished by applying a decomposition of integrals involving one-determinant quantum electronic states on which two or three pairs of second quantization operators can act. Such a decomposition has been done according to a corollary to Wick's theorem, which is brought in a comprehensive and detailed manner. A comment is also given about the consequences of using the equation-of-motion formulation in this context, and the two types of excited-state calculation methods (with and without coupling excitations to deexcitations) are finally compared from the point of view of the structure of their transition and difference density matrices.     

Energy shifts in the relative coordinates treatment of the collinear collision between an atom and an oscillator. Exponential repulsive potential

The treatment of the kinetic term which may be taken as the perturbation when the collision between an atom and an oscillator is described with relative coordinates is shown to require the use of energy shifted basis functions in the calculation of the transition probabilities. For an exponential repulsive potential, a simple analytical formula is obtained for one quantum jumps in the first order Born approximation, which has a simple relationship with the first order Born distorted wave expression, and which lead to better results than the other available analytical formulas.     

Review of theories on double electron capture in fast ion-atom collisions

This work reviews quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The widely used distorted wave methods of the first- and second-order in the pertinent perturbation series expansions are compared with each other. This tests the presumed importance of double continuum intermediate states of two electrons. Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wave functions for double continuum intermediate states. This checks the correctness and usefulness of the eikonalized Coulomb waves when two electrons participate actively to the transition from the initial to the final state of the entire system. We also analyze the significance of the contributions from excited heliumlike states especially in comparison between theory and measurement. The overall goal of the present study is to determine how much of the unprecedented experience gained over several decades in studying high-energy theories of pure three-body charge exchange could be exported directly to four-body double-electron capture without much of additional and essential eleaborations, besides the naturally increased computational demand. In particular, we address the unexpected breakdown of the continuum distorted wave eikonal initial state approximation and the anticipated success of continuum distorted wave theory for double charge exchange in ion-atom collisions at high impact energies.     

Multiconfigurational second-order perturbative methods: Overview and comparison of basic properties

Summary The multiconfigurational second-order perturbative treatments of molecular electronic calculations can be classified into four groups: i) quasi-degenerate perturbation theory (QDPT) in the basis of determinants, ii) non-degenerate perturbation theory applied to eigenvectors resulting from a truncated CI, ii) QDPT in a model space of non-interacting multiconfigurational functions, iv) intermediate Hamiltonians theory, and examined according to three criteria: i) risk of numerical instability due to intruder states, ii) ability to treat the effect of the outer-space on the model space component of the wavefunction, especially important for the treatment of weakly avoided crossings, iii) separability for (A* ... B) problems. None of the existing methods satisfies these three criteria, as shown both by model analysis and real ab initio calculations on LiF and CuF.     

Two-state and continuous phase transitions in lipid bilayers A time-resolved X-ray diffraction study

Structural changes associated with transition from one phase to another have been examined in several lipid-water systems using time-resolved X-ray diffraction methods. Two types of transition mechanism can be recognized on the basis of scattering originating from the packing of the hydrocarbon chains. Two-state transitions are characterized by coexistence of the wide-angle scattering patterns of the initial and final phases throughout the transition region. Continuous transitions, on the other hand, take place through a series of intermediate states that are believed to arise from deformation of the hydrocarbon chain lattice as one phase transforms into another. Two-state processes are observed as subgel to liquid crystal transitions, and continuous transformations are typical of subgel to gel phase transitions. Examples of these transition types are presented and other transitions that do not appear to conform to either of these mechanisms are described.     

Two-state and continuous phase transitions in lipid bilayers A time-resolved X-ray diffraction study

Structural changes associated with transition from one phase to another have been examined in several lipid-water systems using time-resolved X-ray diffraction methods. Two types of transition mechanism can be recognized on the basis of scattering originating from the packing of the hydrocarbon chains. Two-state transitions are characterized by coexistence of the wide-angle scattering patterns of the initial and final phases throughout the transition region. Continuous transitions, on the other hand, take place through a series of intermediate states that are believed to arise from deformation of the hydrocarbon chain lattice as one phase transforms into another. Two-state processes are observed as subgel to liquid crystal transitions, and continuous transformations are typical of subgel to gel phase transitions. Examples of these transition types are presented and other transitions that do not appear to conform to either of these mechanisms are described.     

Stable mechanistically-relevant aromatic-based carbenium ions in zeolite catalysts

The existence of carbenium ion species is assumed in many zeolite catalysis mechanisms. Using computational techniques that include environmental effects, a benzenium-type carbenium ion is identified in zeolite catalysts for the first time. Localization of nearby transition states indicate that this species may play an important role as an intermediate in the bimolecular m-xylene disproportionation reaction. The barrier to back-donation of the proton from the benzenium ion is at least 50 kJ/mol, meaning that this species may be spectroscopically observable. An additional carbenium ion intermediate, formed by abstraction of a hydride from m-xylene, is also predicted. The stability of this second new carbenium ion suggests that aromatic-based carbenium ions are likely to be intermediates in many zeolite-catalyzed reactions. Two types of fundamentally different fully periodic calculations support the stability predictions.