Comparison of Variational and Perturbative Spin-Orbit Coupling within Two-Component CASSCF.

The modeling of spin-orbit coupling (SOC) remains a challenge in computational chemistry due to the high computational cost. With the rising popularity of spin-driven processes and f-block metals in chemistry and materials science, it is incumbent on the community to develop accurate multiconfigurational SOC methods that scale to large systems and understand the limits of different treatments of SOC. Herein, we introduce an implementation of perturbative SOC in scalar-relativistic two-component CASSCF (srX2C-CASSCF-SO). Perspectives on the limitations and accuracy of srX2C-CASSCF-SO are presented via benchmark calculations.

The variational quantum eigensolver self-consistent field method within a polarizable embedded framework.

We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the computational stress on the quantum device is only slightly increased in terms of gate counts compared to regular VQE-SCF. On the other hand, no increase in shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling of real chemical systems using a simulation of the reaction barrier of the Diels-Alder reaction between furan and ethene as an example.

Self-Consistent Field Approach for the Variational Quantum Eigensolver: Orbital Optimization Goes Adaptive.

We present a self-consistent field (SCF) approach within the adaptive derivative-assembled problem-tailored ansatz variational quantum eigensolver (ADAPT-VQE) framework for efficient quantum simulations of chemical systems on near-term quantum computers. To this end, our ADAPT-VQE-SCF approach combines the idea of generating an ansatz with a small number of parameters, resulting in shallow-depth quantum circuits with a direct minimization of an energy expression that is correct to second order with respect to changes in the molecular orbital basis. Our numerical analysis, including calculations for the transition-metal complex ferrocene [Fe (C5H5)2], indicates that convergence in the self-consistent orbital optimization loop can be reached without a considerable increase in the number of two-qubit gates in the quantum circuit by comparison to a VQE optimization in the initial molecular orbital basis. Moreover, the orbital optimization can be carried out simultaneously within each iteration of the ADAPT-VQE cycle. ADAPT-VQE-SCF thus allows us to implement a routine analogous to the complete active space SCF, a cornerstone of state-of-the-art computational chemistry, in a hardware-efficient manner on near-term quantum computers. Hence, ADAPT-VQE-SCF paves the way toward a paradigm shift for quantitative quantum-chemistry simulations on quantum computers by requiring fewer qubits and opening up for the use of large and flexible atomic orbital basis sets in contrast to earlier methods that are predominantly based on the idea of full active spaces with minimal basis sets.

Effort-based decision making and motivational deficits in stroke patients.

Motivational deficits in patients recovering from stroke are common and can reduce active participation in rehabilitation and thereby impede functional recovery. We investigated whether stroke patients with clinically reduced drive, initiation, and endurance during functional rehabilitative training (n = 30) display systematic alterations in effort-based decision making compared to age, sex, and severity-matched stroke patients (n = 30) whose drive appeared unaffected. Notably, the two groups did not differ in self-reported ratings of apathy and depression. However, on an effort-based decision-making task, stroke patients with clinically apparent drive impairment showed intact willingness to accept effort for reward, but were more likely to fail to execute the required effort compared to patients without apparent drive impairments. In other words, the decision behavioural assessment revealed that stroke patients that displayed reduced drive, initiation, and endurance during inpatient neurorehabilitation failed to persist in goal-directed effort production, even over very short periods. These findings indicate that reduced drive during rehabilitative therapy in post-stroke patients is not due to a diminished motivation to invest physical effort, but instead is related to a reduced persistence with effortful behaviour.

Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals.

Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.

Quantum Information-Assisted Complete Active Space Optimization (QICAS).

We propose an effective quantum information-assisted complete active space optimization scheme (QICAS). What sets QICAS apart from other correlation-based selection schemes is (i) the use of unique measures from quantum information that assess the correlation in electronic structures in an unambiguous and predictive manner and (ii) an orbital optimization step that minimizes the correlation discarded by the active space approximation. Equipped with these features, QICAS yields, for smaller correlated molecule, sets of optimized orbitals with respect to which the complete active space configuration interaction energy reaches the corresponding complete active space self-consistent field (CASSCF) energy within chemical accuracy. For more challenging systems such as the chromium dimer, QICAS offers an excellent starting point for CASSCF by greatly reducing the number of iterations required for numerical convergence. Accordingly, our study validates a profound empirical conjecture: the energetically optimal nonactive spaces are predominantly those that contain the least entanglement.

Correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field methods.

The fully correlated frequency-independent Dirac-Coulomb-Breit Hamiltonian provides the most accurate description of electron-electron interaction before going to a genuine relativistic quantum electrodynamics theory of many-electron systems. In this work, we introduce a correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field method within the frameworks of complete active space and density matrix renormalization group. In this approach, the Dirac-Coulomb-Breit Hamiltonian is included variationally in both the mean-field and correlated electron treatment. We also analyze the importance of the Breit operator in electron correlation and the rotation between the positive- and negative-orbital space in the no-virtual-pair approximation. Atomic fine-structure splittings and lanthanide contraction in diatomic fluorides are used as benchmark studies to understand the contribution from the Breit correlation.

[Slow demographic change and neurological rehabilitation-Part 2: what we can do]. / Schleichender demografischer Wandel und neurologische Rehabilitation ­ Teil 2: Handlungsmöglichkeiten.

In its current state the German healthcare system will not be able to adequately care for a growing proportion of older patients with a decreasing healthcare work force. This is particularly so in the postacute care of severely ill patients. In a second of two parts we discuss the perspectives and options at hand. A major conclusion is that substantial gains could be obtained by regulatory adjustments that better align acute care and rehabilitative measures.

[Slow demographic change and neurological rehabilitation-Part 1: state of affairs]. / Schleichender demografischer Wandel und neurologische Rehabilitation ­ Teil 1: Situationsbeschreibung.

In the next two decades the aging baby boomers in Germany will gradually be leaving the work force. They are being followed by the much less numerous, "baby bust" generation who now need to finance and staff healthcare for the growing number of old people in society. In order to care for more needy persons with a smaller working population, the healthcare system must be restructured; however, despite these worrisome prospects, the awareness of the problem is still low in many areas. Here we focus on the area in the healthcare system that is growing particularly rapidly and additionally has the greatest need of personnel per patient: the care of the critically ill and functionally impaired patients. The lack of coordination of hospitals, rehabilitation centers and nursing institution is historical in origin. It promotes the tendency to discharge functionally impaired patients to nursing facilities without giving them a chance for recovery of functional autonomy. As the demographic change progresses, this tendency threatens to increase. In a first of two parts, we attempt to describe the present situation.

Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple.

Based on self-consistent field (SCF) atomic mean-field (amf) quantities, we present two simple yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic and spin-orbit two-electron picture-change effects (PCEs) arising within an exact two-component (X2C) Hamiltonian framework. Both approaches, dubbed amfX2C and e(xtended)amfX2C, allow us to uniquely tailor PCE corrections to mean-field models, viz. Hartree-Fock or Kohn-Sham DFT, in the latter case also avoiding the need for a point-wise calculation of exchange-correlation PCE corrections. We assess the numerical performance of these PCE correction models on spinor energies of group 18 (closed-shell) and group 16 (open-shell) diatomic molecules, achieving a consistent ≈10-5 Hartree accuracy compared to reference four-component data. Additional tests include SCF calculations of molecular properties such as absolute contact density and contact density shifts in copernicium fluoride compounds (CnFn, n = 2,4,6), as well as equation-of-motion coupled-cluster calculations of x-ray core-ionization energies of 5d- and 6d-containing molecules, where we observe an excellent agreement with reference data. To conclude, we are confident that our (e)amfX2C PCE correction models constitute a fundamental milestone toward a universal and reliable relativistic two-component quantum-chemical approach, maintaining the accuracy of the parent four-component one at a fraction of its computational cost.

Stimulation-related modifications of evolving functional brain networks in unresponsive wakefulness.

Recent advances in neurophysiological brain network analysis have demonstrated novel potential for diagnosis and prognosis of disorders of consciousness. While most progress has been achieved on the population-sample level, time-economic and easy-to-apply personalized solutions are missing. This prospective controlled study combined EEG recordings, basal stimulation, and daily behavioral assessment as applied routinely during complex early rehabilitation treatment. We investigated global characteristics of EEG-derived evolving functional brain networks during the repeated (3-6 weeks apart) evaluation of brain dynamics at rest as well as during and after multisensory stimulation in ten patients who were diagnosed with an unresponsive wakefulness syndrome (UWS). The age-corrected average clustering coefficient C* allowed to discriminate between individual patients at first (three patients) and second assessment (all patients). Clinically, only two patients changed from UWS to minimally conscious state. Of note, most patients presented with significant changes of C* due to stimulations, along with treatment, and with an increasing temporal distance to injury. These changes tended towards the levels of nine healthy controls. Our approach allowed to monitor both, short-term effects of individual therapy sessions and possibly long-term recovery. Future studies will need to assess its full potential for disease monitoring and control of individualized treatment decisions.

Relativistic Kramers-Unrestricted Exact-Two-Component Density Matrix Renormalization Group.

In this work we develop a variational relativistic density matrix renormalization group (DMRG) approach within the exact-two-component (X2C) framework (X2C-DMRG), using spinor orbitals optimized with the two-component relativistic complete active space self-consistent field. We investigate fine-structure splittings of p- (Ga, In, Tl) and d-block (Sc, Y, La) atoms and excitation energies of monohydride molecules (GeH, SnH, and TlH) with X2C-DMRG calculations using an all-electron relativistic Hamiltonian in a Kramers-unrestricted basis. We find that X2C-DMRG yields accurate 2P and 2D splittings compared to multireference configuration interaction with singles and doubles (MRCISD). We also investigated the degree of symmetry breaking in the atomic multiplets and convergence of electron correlation in the total energies. Symmetry breaking can be large in some cases (∼30 meV); however, increasing the number of renormalized block states m for the DMRG optimization recovers the symmetry breaking by several orders of magnitude. Encouragingly, we find the convergence of electron correlation to be close to MRCISDTQ5 quality. Relativistic X2C-DMRG approaches are important for cases where spin-orbit coupling is significant and the underlying reference wave function requires a large determinantal space. We are able to obtain quantitatively correct fine-structure splittings for systems up to 1019 number of determinants with traditional CI approaches, which are currently unfeasible to converge for the field.

Simplified State Interaction for Matrix Product State Wave Functions.

We present an approximation to the state-interaction approach for matrix product state (MPS) wave functions (MPSSI) in a nonorthogonal molecular orbital basis, first presented by Knecht et al. [J. Chem. Theory Comput., 2016, 28, 5881], that allows for a significant reduction of the computational cost without significantly compromising its accuracy. The approximation is well-suited if the molecular orbital basis is close to orthogonality, and its reliability may be estimated a priori with a single numerical parameter. For an example of a platinum azide complex, our approximation offers up to 63-fold reduction in computational time compared to the original method for wave function overlaps and spin-orbit couplings, while still maintaining numerical accuracy.

Lesion Evidence for a Causal Role of the Insula in Aversion to Social Inequity.

Humans resist unequal distributions of goods in their social interactions, even if it requires foregoing personal gains. Functional neuroimaging studies implicate the insula in this aversion to social inequity and in fairness-related decisions, but a causal contribution has not yet been established. We compared the responses of 30 patients with lesions to the insula on a multiple-trial version of the one-shot Ultimatum Game, a neuroeconomic social exchange paradigm where a sum of money is split between two players, to those of 30 matched patients with brain injuries sparing the insula. Insula lesion patients accepted offers of an unequal disadvantageous split significantly more often than comparison lesion patients. Computational modeling confirmed that this difference in choice behavior was due to decreased aversion to disadvantageous inequity following insula damage, rather than due to increased decision noise or non-consideration of inequity. Our results provide novel evidence that the insula is causally involved in aversion to inequity and in value-based choices in the context of social interactions.

Charge-Transfer-Induced Predissociation in Rydberg States of Molecular Cations: MgAr.

Very little is known about the Rydberg states of molecular cations, i.e., Rydberg states having a doubly charged ion core. With the example of MgAr+, we present general features of the structure and dynamics of the Rydberg states of molecular cations, which we find are subject to the process of charge-transfer-induced predissociation. Our study focuses on the spectrum of low-n Rydberg states with potential-energy functions associated with the Mg+(3d and 4s) + Ar(1S0) dissociation asymptotes. In particular, we have recorded spectra of the 3dπΩ' (Ω' = 1/2, 3/2) Rydberg states, extending from the lowest (v' = 0) vibrational levels to their dissociation limits. This spectral range encompasses the region where the onset of predissociation by interaction with the mostly repulsive 2Σ and 2Π charge-transfer states associated with the Mg(3s2) + Ar+(2P1/2,3/2) dissociation asymptotes is observed. This interaction leads to very strong perturbations of the 3dπ Rydberg states of MgAr+, revealed by vibrational progressions exhibiting large and rapid variations of the vibrational intervals, line widths, and spin-orbit splittings. We attribute the anomalous sign and magnitude of the spin-orbit coupling constant of the 3dπ state to the interaction with a 2Π Rydberg state correlating to the Mg+(4p) + Ar(1S0) dissociation limit. To analyze our spectra and elucidate the underlying process of charge-transfer-induced predissociation, we implemented a model that allowed us to derive the potential-energy functions of the charge-transfer states and to quantitatively reproduce the experimental results. This analysis characterizes the main features of the dynamics of the Rydberg series converging to the ground state of MgAr2+. We expect that the results and analysis reported here are qualitatively valid for a broader range of singly charged molecular cations, which are inherently prone to charge-transfer interactions.

A decision-neuroscientific intervention to improve cognitive recovery after stroke.

Functional recovery after stroke is dose-dependent on the amount of rehabilitative training. However, rehabilitative training is subject to motivational hurdles. Decision neuroscience formalizes drivers and dampers of behaviour and provides strategies for tipping motivational trade-offs and behaviour change. Here, we used one such strategy, upfront voluntary choice restriction ('precommitment'), and tested if it can increase the amount of self-directed rehabilitative training in severely impaired stroke patients. In this randomized controlled study, stroke patients with working memory deficits (n = 83) were prescribed daily self-directed gamified cognitive training as an add-on to standard therapy during post-acute inpatient neurorehabilitation. Patients allocated to the precommitment intervention could choose to restrict competing options to self-directed training, specifically the possibility to meet visitors. This upfront choice restriction was opted for by all patients in the intervention group and highly effective. Patients in the precommitment group performed the prescribed self-directed gamified cognitive training twice as often as control group patients who were not offered precommitment [on 50% versus 21% of days, Pcorr = 0.004, d = 0.87, 95% confidence interval (CI95%) = 0.31 to 1.42], and, as a consequence, reached a 3-fold higher total training dose (90.21 versus 33.60 min, Pcorr = 0.004, d = 0.83, CI95% = 0.27 to 1.38). Moreover, add-on self-directed cognitive training was associated with stronger improvements in visuospatial and verbal working memory performance (Pcorr = 0.002, d = 0.72 and Pcorr = 0.036, d = 0.62). Our neuroscientific decision add-on intervention strongly increased the amount of effective cognitive training performed by severely impaired stroke patients. These results warrant a full clinical trial to link decision-based neuroscientific interventions directly with clinical outcome.

Frequency and nature of pain in patients undergoing neurorehabilitation.

OBJECTIVE: This prospective study investigated the extent to which patients undergoing neurorehabilitation reported pain, how this pain developed during inpatient stay and whether patients were treated accordingly (using pain medication). METHODS: The extent of pain, performance in daily activities, with a focus on possible impairment from pain, and pain medication were assessed at the beginning and the end of neurorehabilitation treatment. Overall 584 patients, with various neurological diagnoses, such as stroke, intracerebral hemorrhage, polyneuropathy, etc. were classified into four groups based on whether they reported having "no pain," "mild pain," "moderate pain," or "severe pain." All patients received conventional neurorehabilitation therapy in the Mauritius Hospital, Germany. RESULTS: A total of 149 patients had clinically relevant pain at the beginning of their inpatient stay, at a group level this did not change significantly during the treatment period. At the end of inpatient stay, a slight increase was noted in patients reporting pain. Overall 164 patients suffered from moderate or severe pain, operationalized of pain scores >3 on the visual analog scale. A total of 145 patients who had pain at the end of inpatient stay, did not receive pain medication. There was a weak negative association between pain at baseline and activities of daily living at the end of the treatment period, such that, patients with higher pain levels tended to showed lower Barthel Index scores at the end. CONCLUSION: In our study, about one-third of patients suffered from clinically relevant pain during neurorehabilitation treatment and most of them did not receive any pain medication.

[Acute care interventions in inpatient neurorehabilitation]. / Krankenhausmedizinische Interventionen in der neurologischen Anschlussrehabilitation.

Treatment in hospitals differs from treatment in rehabilitation centers from a legal perspective because German law mandates that in hospitals physicians and other qualified personnel must be on duty at all times. This is not required for inpatient rehabilitation centers. Since this Act was passed more than 30 years ago, more acute medical interventions are now carried out and the number of older people in the population has increased. As a result patients are nowadays older, more multimorbid and therefore have a greater risk for medical complications. This is especially true for postacute neurological care. For this reason, the original legal framework for neurological rehabilitation treatment has become questionable. Therefore, we prospectively tested how often patients in inpatient neurorehabilitation suffer from complications that require immediate attention by qualified personnel. In 759 patients observed over a period of 6 months we found 602 complications requiring immediate interventions by physicians (e.g. falls, urinary tract infections, other forms of fever, diarrhea associated with Clostridium difficile, pneumonia, respiratory insufficiency, sepsis, epileptic seizures and arrhythmia). On average at least three acute care interventions occurred per day at the facility examined. We conclude that neurological inpatient rehabilitation has outgrown its legal foundations and now incorporates hospital care.

Complete characterization of the 3p Rydberg complex of a molecular ion: MgAr+. I. Observation of the Mg(3pσ)Ar+ B+ state and determination of its structure and dynamics.

We report on the experimental observation of the B+ 2Σ+ state of MgAr+ located below the Mg+(3p 2P3/2) + Ar(1S0) dissociation asymptote. Using the technique of isolated-core multiphoton Rydberg-dissociation spectroscopy, we have recorded rotationally resolved spectra of the B+ 2Σ+(v') ← X+ 2Σ+(v″ = 7) transitions, which extend from the vibrational ground state (v' = 0) to the dissociation continuum above the Mg+(3p 2P3/2) + Ar(1S0) dissociation threshold. The analysis of the rotational structure reveals a transition from Hund's angular-momentum-coupling case (b) at low v' values to case (c) at high v' values caused by the spin-orbit interaction. Measurements of the kinetic-energy release and the angular distribution of the Mg+ fragments detected in the experiments enabled the characterization of the dissociation mechanisms. The vibrational levels of the B+ state above v' = 6 are subject to predissociation into the Mg+(3p 2P1/2) + Ar(1S0) continuum, and the fragment angular distributions exhibit anisotropy ß parameters around 0.5, whereas direct dissociation into the continuum above the Mg+(3p 2P3/2) + Ar(1S0) asymptote is characterized by ß parameters approaching 2. Molecular ions excited to the B+ state with v' = 0-6 efficiently absorb a second photon to the repulsive part of the 2Σ+ state associated with the Mg+(3d 2D3/2,5/2) + Ar(1S0) continua. The interpretation of the data is validated by the results of ab initio calculations of the low-lying electronic states of MgAr+, which provided initial evidence for the existence of bound vibrational levels of the B+ state and for the photodissociation mechanisms of its low vibrational levels.