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In a previous publication [S. E. Schrader et al., J. Chem. Phys. 161, 044105 (2024)], it has been shown that Rothe's method can be used to solve the time-dependent Schrödinger equation for the hydrogen atom in a strong laser field using time-dependent Gaussian wave packets. Here, we generalize these results, showing that Rothe's method can propagate arbitrary numbers of thawed, complex-valued, Explicitly Correlated Gaussian (ECGs) functions with dense correlation matrices for systems with varying dimensionality. We consider the multidimensional Hénon-Heiles potential and show that the dynamics can be quantitatively reproduced using only 30 Gaussians in 2D and that accurate spectra can be obtained using 20 Gaussians in 2D and 30-40 Gaussians in 3D and 4D. Therefore, the relevant multidimensional dynamics can be described at high quality using only a small number of ECGs that give a very compact representation of the wave function. This efficient representation, along with the demonstrated ability of Rothe's method to propagate Gaussian wave packets in strong fields and ECGs in complex potentials, paves the way for accurate molecular dynamics calculations beyond the Born-Oppenheimer approximation in strong fields., (© 2025 Author(s). Published under an exclusive license by AIP Publishing.)

Laser-induced molecular alignment is well understood within the framework of the Born–Oppenheimer (BO) approximation. Without the BO approximation, however, the concept of molecular structure is lost, making it hard to precisely define alignment. In this work, we demonstrate the emergence of alignment from the first-ever non-BO quantum dynamics simulations, using the HD molecule exposed to ultrashort laser pulses as a few-body test case. We extract the degree of alignment from the non-BO wave function by means of an operator expressed in terms of pseudo-proton coordinates that mimics the BO-based definition of alignment. The only essential approximation, in addition to the semiclassical electric-dipole approximation for the matter–field interaction, is the choice of time-independent explicitly correlated Gaussian basis functions. We use a variational, electric-field-dependent basis-set construction procedure, which allows us to keep the basis-set dimension low while capturing the main effects of electric polarization on the nuclear and electronic degrees of freedom. The basis-set construction procedure is validated by comparing with virtually exact grid-based simulations for two one-dimensional model systems: laser-driven electron dynamics in a soft attractive Coulomb potential and nuclear rovibrational dynamics in a Morse potential. [ABSTRACT FROM AUTHOR]

Recent advances in attosecond science have made it increasingly important to develop stable, reliable, and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in attosecond science is high-harmonic generation, which is challenging to model with fixed Gaussian basis sets, as it produces high-energy electrons, with a resulting rapidly varying and highly oscillatory wave function that extends over dozens of ångström. Recently, Rothe's method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schrödinger equation. Here, we apply Rothe's method to the hydrogen wave function and demonstrate that thawed, complex-valued Gaussian wave packets with time-dependent width, center, and momentum parameters are able to reproduce spectra obtained from essentially exact grid calculations for high-harmonic generation with only 50-181 Gaussians for field strengths up to 5 × 1014 W/cm2. This paves the way for the inclusion of continuum contributions into real-time, time-dependent electronic-structure theory with Gaussian basis sets for strong fields and eventually accurate simulations of the time evolution of molecules without the Born-Oppenheimer approximation., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wave packets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this Article, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential, we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.

We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the S -diagnostic. We provide a derivation of the S -diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the S -diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl 4 ] 2- , [Cu(NH 3 ) 4 ] 2+ , and [Cu(H 2 O) 4 ] 2+ . Throughout the numerical investigations, the S -diagnostic is compared to other SRCC diagnostic procedures, that is, the T 1 , D 1 , max T 2 , and D 2 diagnostics as well as different indices of multideterminantal and multireference character in coupled-cluster theory. Our numerical investigations show that the S -diagnostic outperforms the T 1 , D 1 , max T 2 and D 2 diagnostics and is comparable to the indices of multideterminantal and multireference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the S -diagnostic for geometry optimizations using SRCC reveal that the S -diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the S -diagnostic for electronic correlation simulations show that the S -diagnostic correctly predicts strong multireference regimes. The S -diagnostic, moreover, correctly detects the successful SRCC computations for [CuCl 4 ] 2- , [Cu(NH 3 ) 4 ] 2+ , and [Cu(H 2 O) 4 ] 2+ , which have been known to be misdiagnosed by T 1 and D 1 diagnostics in the past. This shows that the S -diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.

Three fully variational formulations of the complete-active space coupled-cluster method are derived. The formulations include the ability to approximate the model vectors by smooth manifolds, thereby opening up the possibility for overcoming the exponential wall of scaling for model spaces of complete-active space type. In particular, model vectors of matrix-product states are considered, and it is argued that the present variational formulation allows not only favorably scaling multireference coupled-cluster calculations but also systematic correction of tailored coupled-cluster calculations and of quantum chemical density-matrix renormalization group methods, which are fast and polynomial scaling but lack the ability to properly resolve dynamical correlation at chemical accuracy. The extension of the variational formulations to the time domain is also discussed, with derivations of abstract evolution equations., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Real-time simulations of laser-driven electron dynamics contain information about molecular optical properties through all orders in response theory. These properties can be extracted by assuming convergence of the power series expansion of induced electric and magnetic multipole moments. However, the accuracy relative to analytical results from response theory quickly deteriorates for higher-order responses due to the presence of high-frequency oscillations in the induced multipole moment in the time domain. This problem has been ascribed to missing higher-order corrections. We here demonstrate that the deviations are caused by nonadiabatic effects arising from the finite-time ramping from zero to full strength of the external laser field. Three different approaches, two using a ramped wave and one using a pulsed wave, for extracting electrical properties from real-time time-dependent electronic-structure simulations are investigated. The standard linear ramp is compared to a quadratic ramp, which is found to yield highly accurate results for polarizabilities, and first and second hyperpolarizabilities, at roughly half the computational cost. Results for the third hyperpolarizability are presented along with a simple, computable measure of reliability., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

The coupled cluster method is considered a gold standard in quantum chemistry, reliably giving energies that are exact within chemical accuracy (1.6 mhartree). However, even in the coupled cluster single-double (CCSD) approximation, where the cluster operator is truncated to include only single and double excitations, the method scales as O(N 6 ) in the number of electrons, and the cluster operator needs to be solved for iteratively, increasing the computation time. Inspired by eigenvector continuation, we present here an algorithm making use of the Gaussian processes that provides an improved initial guess for the coupled cluster amplitudes. The cluster operator is written as a linear combination of sample cluster operators that are obtained at particular sample geometries. By reusing the cluster operators from previous calculations in that way, it is possible to obtain a start guess for the amplitudes that surpasses both MP2 guesses and "previous geometry"-guesses in terms of the number of necessary iterations. As this improved guess is very close to the exact cluster operator, it can be used directly to calculate the CCSD energy to chemical accuracy, giving approximate CCSD energies scaling as O(N 5 ).

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

We present a derivation of real-time (RT) time-dependent orbital-optimized Møller-Plesset (TDOMP2) theory and its biorthogonal companion, time-dependent non-orthogonal OMP2 theory, starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in the time-independent molecular electronic structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from RT simulations, comparing the results with those obtained from conventional time-dependent coupled-cluster singles and doubles (TDCCSD) simulations and from its second-order approximation, TDCC2. We also compare our results with those from CCSD and CC2 linear and quadratic response theories. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, including core excitations where optimized orbitals might be particularly important, frequency-dependent polarizabilities and hyperpolarizabilities from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations.

A cornerstone of current-density functional theory (CDFT) in its paramagnetic formulation is proven. After a brief outline of the mathematical structure of CDFT, the lower semicontinuity and expectation-valuedness of the CDFT constrained-search functional is proven, meaning that there is always a minimizing density matrix in the CDFT constrained-search universal density functional. These results place the mathematical framework of CDFT on the same footing as that of standard DFT.

We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster (CC) theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion CC theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for He and Be atoms and for LiH, CH + , and LiF molecules show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by full configuration interaction (FCI) theory, provided that all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorates. Observing that populations computed from the linear response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations.

A state-specific multireference coupled-cluster (MRCC) method based on Arponen's bivariational principle is presented, the bivar-MRCC method. The method is based on single-reference theory and therefore has a relatively straightforward formulation and modest computational complexity. The main difference from established methods is the bivariational formulation, in which independent parameterizations of the wave function (ket) and its complex conjugate (bra) are made. Importantly, this allows manifest multiplicative separability of the state (exact in the extended bivar-MRECC version of the method and approximate otherwise), and additive separability of the energy, while preserving polynomial scaling of the working equations. A feature of the bivariational principle is that the formal bra and ket references can be included as bivariational parameters, which eliminates much of the bias toward the formal reference. A pilot implementation is described, and extensive benchmark calculations on several standard problems are performed. The results from the bivar-MRCC method are comparable to established state-specific multireference methods. Considering the relative affordability of the bivar-MRCC method, it may become a practical tool for non-experts.

We investigate the numerical stability of time-dependent coupled-cluster theory for many-electron dynamics in intense laser pulses, comparing two coupled-cluster formulations with full configuration interaction theory. Our numerical experiments show that orbital-adaptive time-dependent coupled-cluster doubles (OATDCCD) theory offers significantly improved stability compared with the conventional Hartree-Fock-based time-dependent coupled-cluster singles-and-doubles (TDCCSD) formulation. The improved stability stems from greatly reduced oscillations in the doubles amplitudes, which, in turn, can be traced to the dynamic biorthonormal reference determinants of OATDCCD theory. As long as these are good approximations to the Brueckner determinant, OATDCCD theory is numerically stable. We propose the reference weight as a diagnostic quantity to identify situations where the TDCCSD and OATDCCD theories become unstable.

Recent work has established Moreau-Yosida regularization as a mathematical tool to achieve rigorous functional differentiability in density-functional theory. In this article, we extend this tool to paramagnetic current-density-functional theory, the most common density-functional framework for magnetic field effects. The extension includes a well-defined Kohn-Sham iteration scheme with a partial convergence result. To this end, we rely on a formulation of Moreau-Yosida regularization for reflexive and strictly convex function spaces. The optimal L p -characterization of the paramagnetic current density L 1 ∩ L 3/2 is derived from the N-representability conditions. A crucial prerequisite for the convex formulation of paramagnetic current-density-functional theory, termed compatibility between function spaces for the particle density and the current density, is pointed out and analyzed. Several results about compatible function spaces are given, including their recursive construction. The regularized, exact functionals are calculated numerically for a Kohn-Sham iteration on a quantum ring, illustrating their performance for different regularization parameters.

The formulation of the time-dependent Schrödinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced, inducing physical interpretation of coupled-cluster states in the form of transition probabilities, autocorrelation functions, and explicitly real values for observables, solving interpretation issues which are present in time-dependent coupled-cluster theory and in ground-state calculations of molecular systems under the influence of external magnetic fields. The problem of the numerical integration of the equations of motion is considered, and a critical evaluation of the standard fourth-order Runge-Kutta scheme and the symplectic Gauss integrator of variable order are given, including several illustrative numerical experiments. While the Gauss integrator is stable even for laser pulses well above the perturbation limit, our experiments indicate that a system-dependent upper limit exists for the external field strengths. Above this limit, time-dependent coupled-cluster calculations become very challenging numerically, even in the full configuration interaction limit. The source of these numerical instabilities is shown to be rapid increases of the amplitudes as ultrashort high-intensity laser pulses pump the system out of the ground state into states that are virtually orthogonal to the static Hartree-Fock reference determinant.

In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate formal properties of the used method, such as energy size consistency and the equivalence of linked and unlinked formulation. The existing mathematical analysis is here elaborated in a quantum chemical framework. In particular, we highlight the use of what we have defined as a complete active space-external space gap describing the basis splitting between the complete active space and the external part generalizing the concept of a HOMO-LUMO gap. Furthermore, the behavior of the energy error for an optimal basis splitting, i.e., an active space choice minimizing the density matrix renormalization group-tailored coupled-cluster singles doubles error, is discussed. We show numerical investigations on the robustness with respect to the bond dimensions of the single orbital entropy and the mutual information, which are quantities that are used to choose a complete active space. Moreover, the dependence of the ground-state energy error on the complete active space has been analyzed numerically in order to find an optimal split between the complete active space and external space by minimizing the density matrix renormalization group-tailored coupled-cluster error.

A detailed account of the Kohn-Sham (KS) algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy-Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows us to rigorously introduce, in contrast to the common unregularized approach, a well-defined KS iteration scheme. Convergence in a weak sense is then proven. This generalized formulation is applicable to a wide range of different density-functional theories and possibly even to models outside of quantum mechanics.

We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional density functional theory and Current-Density Functional Theory (CDFT). In the intermediate theory, which we term linear vector potential-DFT (LDFT), the basic variables are the density, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre-Fenchel transformations are constructed. Many theoretical issues in CDFT find simplified analogs in LDFT. We prove results concerning N-representability, Hohenberg-Kohn-like mappings, existence of minimizers in the constrained-search expression, and a restricted analog to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.

Children absconding from countries of conflict and war are often not able to document their age. When an age is given, it is frequently untraceable or poorly documented and therefore questioned by immigration authorities. Consequently many countries perform age estimations on these children. Provision of ethical practice during the age estimation investigation of unaccompanied minors is considered from different angles: (1) The UN convention on children’s rights, formulating specific rights, protection, support, healthcare and education for unaccompanied minors. (2) Since most age estimation investigations are based on medical examination, the four basic principles of biomedical ethics, namely autonomy, beneficence, non-malevolence, justice. (3) The use of medicine for non treatment purposes. (4) How age estimates with highest accuracy in age prediction can be obtained. Ethical practice in age estimation of unaccompanied minors is achieved when different but related aspects are searched, evaluated, weighted in importance and subsequently combined. However this is not always feasible and unanswered questions remain. [ABSTRACT FROM AUTHOR]

The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.

Objectives: Understanding human tooth structure fluorescence aids clinical and forensic dentistry, enabling tissue/material differentiation and the creation of esthetic restorative materials. Material manufacturers seek to replicate natural tooth fluorescence, necessitating the development of novel techniques to detect them. Procuring human teeth for research is challenging due to ethical and infection control standards, prompting a search for alternative models. Material and Methods: This study compares visible light‐induced fluorescence of porcine and human teeth to assess the value of porcine teeth as human analogs. Using a pulsed laser, an optimal fluorescence‐inducing wavelength was determined, followed by comparing fluorescence spectra between species. Results: Luminescence sensitivity and lifetimes were comparable between species, but spectral geometry differed. Conclusion: Porcine teeth, commonly used for dental material investigations, may not be suitable for dental fluorescence studies due to spectral differences. Accurately mimicking human tooth fluorescence remains complex. Further research is needed to develop reliable alternatives for dental fluorescence investigations that will advance clinical and forensic dentistry. [ABSTRACT FROM AUTHOR]

The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density-in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ((ε)E, (ε)F) that converge to (E, F) pointwise everywhere as ε → 0(+), and such that (ε)F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy (ε)E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ((ε)E, (ε)F). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of (ε)F, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.

Counting incremental lines in dental cementum is an accepted method for estimating age in many wild mammals. In human teeth such countings have given variable results, and the aim of the present investigation was to find out if one incremental line is formed per year in human teeth as well. Canines and single-rooted premolars were demineralized, paraffin wax-embedded, sectioned and stained, and the sections were viewed in a fluorescence microscope. Non-fluorescent lines, seen against a fluorescent background, were either counted directly or their number calculated by counting only some of them and computing this on the total width of the cementum. The correlation coefficient between tooth age and the number of lines for the whole material was =0.84 when counted and =0.73 when calculated. This coefficient was stronger in mandibular second premolars but lower in teeth extracted because of dental diseases. The coefficient was only significant in teeth from individuals below the age of 50 yr. The regression formula with tooth age as dependent variable indicated that only incremental lines formed in about every other year stained sufficiently to be counted. [ABSTRACT FROM AUTHOR]

Peritubular dentine is a mineralised deposit formed centripetally in the dentine tubules with advancing age, so that the tubular diameter is smaller in teeth from older persons. The aim of the present study was to investigate the relationship between age in humans and the amount of peritubular dentine and the extent of the consequent obliteration of the tubules, and to find out whether this relationship was strong enough to be used as a parameter for age estimation. Fifty mandibular central and lateral human incisors were ground on the lingual aspect of the root and examined in a scanning electron microscope (SEM). The number of open tubules was counted and the diameter of the tubules measured both before and after etching with 35% orthophosphoric acid. The difference in the number of tubules in unetched and etched specimens was taken to be the number of occluded tubules, and the difference in radii before and after etching to be the thickness of peritubular dentine. The results did not demonstrate a significant relationship between age and the reduction in the number of tubules. One explanation might be that a certain age has to be reached before obliterated dentine tubules can be observed. The correlation between age and the thickness of peritubular dentine was not significant in teeth extracted because of periodontal disease, so these teeth were excluded from the regression analysis with age as the dependent variable.(ABSTRACT TRUNCATED AT 250 WORDS) [ABSTRACT FROM AUTHOR]

The curse of dimensionality (COD) limits the current state-of-the-art ab initio propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schrödinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster, and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given.

Military combat can result in the need for comprehensive care related to both physical and psychological trauma, most commonly chronic pain and post-traumatic stress disorder (PTSD). These conditions tend to co-occur and result in high levels of distress and interference in everyday life. Thus, it is imperative to develop effective, time-efficient treatments for these conditions before they become chronic and resistant to change. We developed and pilot-tested the Pain and Trauma Intensive Outpatient Treatment (PATRIOT) Program, a brief, intensive (3 weeks, six sessions) integrated chronic pain and PTSD treatment. An overview and session-by-session outline of the PATRIOT Program is provided, followed by results from the first pilot evaluation of the PATRIOT Program's feasibility, acceptability, and preliminary efficacy in a sample of eight participating Veterans with comorbid chronic pain and PTSD. There were no treatment dropouts. At post-treatment, there were significant reductions in PTSD symptoms based on the Clinician-Administered Assessment of PTSD (CAPS). Pain and catastrophic thinking also decreased from pre- to post-treatment. With continued investigations and support, the PATRIOT Program may offer a brief, cost-effective, and more easily accessible treatment option for individuals who could benefit from learning skills to manage pain and PTSD more effectively. [ABSTRACT FROM AUTHOR]

Understanding the real-time evolution of many-electron quantum systems is essential for studying dynamical properties in condensed matter, quantum chemistry, and complex materials, yet it poses a significant theoretical and computational challenge. Our work introduces a variational approach for fermionic time-dependent wave functions, surpassing mean-field approximations by accurately capturing many-body correlations. We employ time-dependent Jastrow factors and backflow transformations, enhanced through neural networks parameterizations. To compute the optimal time-dependent parameters, we employ the time-dependent variational Monte Carlo technique and introduce a new method based on Taylor-root expansions of the propagator, enhancing the accuracy of our simulations. The approach is demonstrated in three distinct systems. In all cases, we show clear signatures of many-body correlations in the dynamics. The results showcase the ability of our variational approach to accurately describe the time evolution, providing insight into quantum dynamical effects in interacting electronic systems, beyond the capabilities of mean-field. Variational parameterization of many-body wavefunctions using neural network quantum states is a powerful technique for studying many-body quantum systems but has been limited to time-independent cases. Nys et al. extend this approach to real-time evolution, providing improved accuracy over traditional methods. [ABSTRACT FROM AUTHOR]

This paper is devoted to the numerical solution of constrained energy minimization problems arising in computational physics and chemistry such as the Gross–Pitaevskii and Kohn–Sham models. In particular, we introduce Riemannian Newton methods on the infinite-dimensional Stiefel and Grassmann manifolds. We study the geometry of these two manifolds, its impact on the Newton algorithms, and present expressions of the Riemannian Hessians in the infinite-dimensional setting, which are suitable for variational spatial discretizations. A series of numerical experiments illustrates the performance of the methods and demonstrates their supremacy compared to other well-established schemes such as the self-consistent field iteration and gradient descent schemes. [ABSTRACT FROM AUTHOR]

The clinical art of applying scientific knowledge to a patient's circumstances of suffering is especially challenging when practicing psychotherapy with people who are experiencing chronic pain. Health psychology has made substantial contributions by showing that psychosocial factors are essential in explaining the phenomenon of pain and, particularly, its chronic progression to debilitating degrees. In addition, clinical health psychology has developed empirically supported treatments that improve the lives of chronic pain sufferers across many dimensions. This article is not concerned with reviewing that evidence or the treatment programs, but with noting some issues pain management psychotherapists may face in using this knowledge effectively to improve the lives of their patients.

Rationale: Critics have called into question findings from double-blind placebo-controlled studies because subjects are given drug administration instructions informing them of a placebo condition. The assertion that these drug administration instructions bias estimates of effectiveness has undergone surprisingly little empirical investigation., Objectives: The primary objective of this study was to determine whether drug administration instructions informing subjects of a placebo condition affect the drug response and affect the saliva concentration of the stimulant., Methods: We assessed caffeine responses and levels of saliva concentration of caffeine in 52 subjects who were randomly assigned to receive one of two drug administration instructions: (a) placebo-informed instructions (i.e., individuals informed of the placebo) analogous to those used in double-blind studies and (b) placebo-uninformed instructions (i.e., individuals informed they are taking an active stimulant)., Results: On most measures (systolic blood pressure, heart rate, hand steadiness, reaction time, fatigue, and tension), drug administration instructions did not significantly influence caffeine response. Instructions also had no significant effect on saliva concentration of caffeine. However, only individuals who were uninformed of the placebo condition showed significant diastolic blood pressure and vigor increases with 125 mg caffeine, and significant hand steadiness impairment and vigor increases with 325 mg caffeine compared to placebo., Conclusions: These overall findings suggest that a limited bias is introduced by drug administration instructions. The results do not support any suggestion that information about the existence of a placebo condition dramatically influences conclusions drawn about drug responses in placebo-controlled trials.

This article summarizes data from three studies (Maré, Lynn, Kvaal, Segal, & Sivec, in press; Lynn, Maré, Kvaal, Segal, & Sivec, 1993) designed to extend research on the "hidden observer" to two phenomena of clinical relevance: hypnotic dreams and suggested age regression. Subjects received suggestions for a hypnotic dream or age regression and then received suggestions for a "hidden observer" (i.e., the subject possesses a part of the self that is aware of images and ideas that the conscious mind is unaware of) with respect to the dream or age-regression experience. Hidden reports contained more personally relevant information than the target suggestions (i.e., dream, age regression). Subjectives were also less likely to recall hidden reports. The high rate of hidden-observer responding (> 80%) was also evident in nonhypnotized simulating and relaxed subjects, although they did not exhibit as much primary process thinking in their dream reports as hypnotized subjects. Case studies of a trauma client and a forensic client are used to illustrate the clinical potential of hidden-observer suggestions.

A number of studies have investigated the use of variability measures in the detection of submaximal or insincere efforts in strength testing. The underlying assumption of these approaches is that submaximal efforts will be more variable than maximal efforts. Previous studies have investigated the variability of torque production in isometric or isokinetic tasks with mixed results. The present study investigated the variability of torque production and velocity in isometric and isotonic leg extension tasks, respectively. Fifteen asymptomatic subjects participated in a within-subject counterbalanced design in which they were asked to perform maximally and submaximally in both isometric and isotonic leg extension tasks. Results indicated that both isometric and isotonic tasks showed greater variability (measured by coefficient of variation) in the submaximal effort condition. However, the sensitivity to detect submaximal efforts was much greater for the isotonic velocity variability condition. It was concluded that the isotonic approach showed promise for clinical application, but that the isometric task had unacceptably poor classification rates, consistent with previous research.

Dental radiographs have rarely been used in dental age estimation methods for adults and the aim of this investigation was to derive formulae for age calculation based on measurements of teeth and their radiographs. Age-related changes were studied in 452 extracted, unsectioned incisors, canines and premolars. The length of the apical translucent zone and extent of the periodontal retraction were measured on the teeth while the pulp length and width as well as root length and width were measured on the radiographs and the ratios between the root and pulp measurements calculated. For all types of teeth significant, negative Pearson's correlation coefficients were found between age and the ratios between the pulp and the root width. In this study also, the correlation between age and the length of the apical translucent zone was weaker than expected. The periodontal retraction was significantly correlated with age in maxillary premolars alone. Multiple regression analyses showed inclusion of the ratio between the measurements of the pulp and the root on the radiographs for all teeth; the length of the apical translucency in five types; and periodontal retraction in only three types of teeth. The correlation coefficients ranged from r = 0.48 to r = 0.90 between the chronological and the calculated age using the formulae from this multiple regression study. The strongest coefficients were for premolars. These formulae may be recommended for use in odontological age estimations in forensic and archaeological cases where teeth are loose or can be extracted and where it is important that the teeth are not sectioned.

In Study 1, virtuoso (n = 13; passed more than 10 suggestions on the Harvard Group Scale of Hypnotic Susceptibility, Form A [HGSHS:A] and Stanford Hypnotic Susceptibility Scale, Form C), high hypnotizable (n = 14; passed more than 8 suggestions on the HGSHS:A), and medium hypnotizable (n = 17; passed 4-8 suggestions on the HGSHS:A) Ss were administered a hypnotic dream suggestion followed by a "dream hidden observer" suggestion (i.e., access hidden part; have new thoughts and images pertinent to dream). The majority of Ss reported dreams (81.8%) and hidden observers (80%), with hidden reports being characterized by more personal content, less primary processes, and poorer recall than dream reports. Study 2 replicated major findings. Although hypnotized (n = 18) and low hypnotizable simulating Ss (n = 17) responded comparably on most measures, hypnotizable Ss' dreams contained more primary process than did simulating Ss, providing support for M. R. Nash's (1991) psychoanalytic model.

The purpose of this investigation was to examine the relationship between the root surface structure of human teeth and the age of the individual and also to evaluate whatever contribution this relationship might give to multiple regression methods for age estimation. The material, consisting of 1000 permanent teeth, excluding molars, was examined by means of a new scoring system (Surface Roughness Scores, SRS) for surface roughness, in addition to the scoring systems of Gustafson (RG) and Johanson (RJ) for root resorption. Statistical analyses using the SPSS package indicated a symmetric left/right distribution of root surface structure. The Pearson correlation between age and RJ varied from -0.02 for maxillary central incisors to 0.54 for mandibular central incisors and was approximately the same for RG. These two scoring systems seem to be of little value in methods for age estimation. Correlations between age and the new scoring systems SRS were significant for all teeth and varied from 0.44 for maxillary second premolars to 0.68 for mandibular first premolars. There was no detectable influence of gender or reason for extraction. However, the SRS could not be assessed with sufficient reproducibility, and the estimates were therefore too subjective to be used as the sole criterion for age estimation. This scoring system could, however contribute positively to a multiple regression method.