Principles for determining mechanistic pathways from observable quantum control data

Hamiltonian encoding (HE) methods have been used to understand mechanism in computational studies of laser controlled quantum systems. This work studies the principles for extending such methods to extract control mechanisms from laboratory data. In an experimental setting, observables replace the utilization of wavefunctions in computational HE. With laboratory data, HE gives rise to a set of quadratic equations for the interfering transition amplitudes, and the solution to the equations reveals the mechanistic pathways. The extraction of the mechanism from the system of quadratic equations raises questions of uniqueness and solvability, even in the ideal case without noise. Symmetries are shown to exist in the quadratic system of equations, which is generally overdetermined. Therefore, the mechanism is likely to be unique up to these symmetries. Numerical simulations demonstrate the concepts on simple model systems.     

A catalytic, asymmetric formal synthesis of (+)-hamigeran B

A concise asymmetric, formal synthesis of (+)-hamigeran B is reported. A Pd-catalyzed, decarboxylative allylic alkylation, employing a trifluoromethylated derivative of t-BuPHOX, is utilized as the enantioselective step to form the critical quaternary carbon center in excellent yield and enantioselectivity. The product is converted in three steps to a late-stage intermediate previously used in the synthesis of hamigeran B.     

Control of nitromethane photoionization efficiency with shaped femtosecond pulses

The applicability of adaptive femtosecond pulse shaping is studied for achieving selectivity in the photoionization of low-density polyatomic targets. In particular, optimal dynamic discrimination (ODD) techniques exploit intermediate molecular electronic resonances that allow a significant increase in the photoionization efficiency of nitromethane with shaped near-infrared femtosecond pulses. The intensity bias typical of high-photon number, nonresonant ionization is accounted for by reference to a strictly intensity-dependent process. Closed-loop adaptive learning is then able to discover a pulse form that increases the ionization efficiency of nitromethane by ～150%. The optimally induced molecular dynamics result from entry into a region of parameter space inaccessible with intensity-only control. Finally, the discovered pulse shape is demonstrated to interact with the molecular system in a coherent fashion as assessed from the asymmetry between the response to the optimal field and its time-reversed counterpart.     

Why is chemical synthesis and property optimization easier than expected?

Identifying optimal conditions for chemical and material synthesis as well as optimizing the properties of the products is often much easier than simple reasoning would predict. The potential search space is infinite in principle and enormous in practice, yet optimal molecules, materials, and synthesis conditions for many objectives can often be found by performing a reasonable number of distinct experiments. Considering the goal of chemical synthesis or property identification as optimal control problems provides insight into this good fortune. Both of these goals may be described by a fitness function J that depends on a suitable set of variables (e.g., reactant concentrations, components of a material, processing conditions, etc.). The relationship between J and the variables specifies the fitness landscape for the target objective. Upon making simple physical assumptions, this work demonstrates that the fitness landscape for chemical optimization contains no local sub-optimal maxima that may hinder attainment of the absolute best value of J. This feature provides a basis to explain the many reported efficient optimizations of synthesis conditions and molecular or material properties. We refer to this development as OptiChem theory. The predicted characteristics of chemical fitness landscapes are assessed through a broad examination of the recent literature, which shows ample evidence of trap-free landscapes for many objectives. The fundamental and practical implications of OptiChem theory for chemistry are discussed.     

General formulation of HDMR component functions with independent and correlated variables

The High Dimensional Model Representation (HDMR) technique decomposes an n-variate function f (x) into a finite hierarchical expansion of component functions in terms of the input variables x = (x ₁, x ₂, . . . , x _n ). The uniqueness of the HDMR component functions is crucial for performing global sensitivity analysis and other applications. When x ₁, x ₂, . . . , x _n are independent variables, the HDMR component functions are uniquely defined under a specific so called vanishing condition. A new formulation for the HDMR component functions is presented including cases when x contains correlated variables. Under a relaxed vanishing condition, a general formulation for the component functions is derived providing a unique HDMR decomposition of f (x) for independent and/or correlated variables. The component functions with independent variables are special limiting cases of the general formulation. A novel numerical method is developed to efficiently and accurately determine the component functions. Thus, a unified framework for the HDMR decomposition of an n-variate function f (x) with independent and/or correlated variables is established. A simple three variable model with a correlated normal distribution of the variables is used to illustrate this new treatment.     

Optimal control of molecular motion: Nonlinear field effects

This paper is concerned with some of the consequences of strong optical fields and corresponding nonlinear field effects upon the optimal control of molecular motion. It is shown that the presence of nonlinear interactions can give rise to the existence of multiple field solutions to the problem of optimally controlling molecular motion where each of the fields produces exactly the same physical effects on the molecule. Secondly, it is argued that nonlinear field interactions may either act as a constraint on the control of molecular motion or an enhancement of that process depending on the circumstances. These variation phenomena are illustrated through consideration of control over the motion of harmonic molecules.     

Upper and lower bounds on the control field and the quality of achieved optimally controlled quantum molecular motion

A large class of problems in optimally controlled quantum or classical molecular dynamics has multiple solutions for the control field amplitude. A denumerably infinite number of solutions may exist depending on the structure of the design cost functional. This fact has been recently proved with the aid of perturbation theory by considering the electric field as the perturbating agent. In carrying out this analysis, an eigenvalue (i.e., a spectral parameter) appears which gives the degree of deviation of the control objective from its desired value. In this work, we develop a scheme to construct upper and lower bounds for the field amplitude and spectral parameter for each member of the denumerably infinite set of control solutions. The bounds can be tightened if desired. The analysis here is primarily restricted to the weak field regime, although the bounds for the strong field nonlinear case are also presented.     

A strategy to derive new internal coordinates by partitioning the internal configuration space according to invariance properties

A method to derive optimally orthogonal curvilinear coordinates for N-body systems is proposed. The invariance of certain subspaces under groups of linear transformations is employed to partition the configuration subspace into internal and external components. The construction is initially carried out locally by orthogonalizing typical group invariant vector fields. Integration is performed subsequently by means of integrating factors. Simple examples of orthogonal invariants illustrate the discussion.     

Hyperfine structure measurements in the ground states5 F 5,5 F 4,5 F 3 and5F2 of99Ru and101Ru with the atomic beam magnetic resonance method

The hyperfine structure of the four lowest levels⁵ F _{5, 4, 3, 2} of the⁵ F ground state multiplet arising from the configuration 4d ⁷ 5s in⁹⁹Ru and¹⁰¹Ru has been studied by the atomic — beam magnetic — resonance technique. After applying corrections due to the effects of off-diagonal hyperfine mixing we obtain the following multipole interaction constants:⁹⁹Ru:A(⁵ F ₅)=?204.5514(33) MHzB(⁵ F ₅)=27.281 (62) MHzA ⁵ F ₄=?163.6845(36) MHzB(⁵ F ₄)=17.455(52) MHzA ⁵ F ₃=?135.0294(37) MHzB(⁵ F ₃)=10.164(50) MHzA(⁵ F ₂)=? 82.5325(27) MHzB(⁵ F ₂)=5.457(22) MHz¹⁰¹Ru:A(⁵ F ₅)=?229.2881(33) MHzB(⁵ F ₅)=158.934(62) MHzA(⁵ F ₄)=?183.4744(36) MHzB(⁵ F ₄)=101.799(52) MHzA(⁵ F ₃)=?151.3502(38) MHzB(⁵ F ₃)=59.323(50) MHzA(⁵ F ₂)=?92.4974(27) MHzB(⁵ F ₂)=31.869(23) MHz. The magnetic dipole and the electric quadrupole moments of the⁹⁹Ru and¹⁰¹Ru nuclear ground states as calculated from these constants are the following:μ _I (⁹⁹Ru)=?0.594(119) nmQ(⁹⁹Ru)=0.077 (15) barnsμ _I (¹⁰¹Ru)=?0.666(133)nmQ(¹⁰¹Ru)=0.45 (9) barns. From measurements of the Zeeman effect in the even isotope¹⁰²Ru we find the followingg _J -factors for the⁵ F ground multiplet:g _J (⁵ F ₅)=1.397741(20)g _J (⁵ F ₄)=1.347604(20)g _J (⁵ F ₃)=1.248988(20)g _J (⁵ F ₂)=1.001120(3).     

Principal component analysis of dipeptides

Principal component analysis applied to a set of dipeptides illustrates how changes in families of parameters act in concert to produce overall molecular structural changes. Principal component analysis is an eigenvalue–eigenvector analysis whereby the parametric sensitivity coefficient matrix is manipulated to produce weighted principal components, which reveal the variant and invariant directions in the parameter space. This analysis summarizes the sensitivity results by revealing interdependence among the parameter values with regard to their role in controlling the molecular structure. An analysis of the principal components reveals hidden relationships among the parameters. Thus, those parameters, which were thought to be of controlling significance with respect to the molecular structure, may, in fact, not be (or vice versa) due to cooperative parametric interactions; as a result, the parameters of significance in a sequence of dipeptides are identified. In general, for the dipeptides studied, there is mutual exclusion of dominant parameters between the sets of invariant and variant eigenvectors. © 1994 by John Wiley & Sons, Inc.