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The definition of a consistent evolution equation for statistical hybrid quantum-classical systems is still an open problem. In this paper we analyze the case of Ehrenfest dynamics on systems defined by a probability density and identify the relations of the non-linearity of the dynamics with the obstructions to define a consistent dynamics for the first quantum moment of the distribution. This first quantum moment represents the physical states as a family of classically-parametrized density matrices $\hat \rho(\xi)$, for $\xi$ a classical point; and it is the most common representation of hybrid systems in the literature. Due to this obstruction, we consider higher order quantum moments, and argue that only a finite number of them are physically measurable. Because of this, we propose an effective solution for the hybrid dynamics problem based on approximating the distribution by those moments and representing the states by them., Comment: 21 pages. Minor correction in the list of affiliations

We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by a classical metric tensor field over a spatial hypersurface and its associated momentum. Thus, in our approach there is no non-dynamic background structure, apart from the manifold of events, and the gravitational and quantum degrees of freedom have their dynamics inextricably coupled. Given the Hamiltonian natureof the framework, we work with the generators of hypersurface deformations over the manifold of quantum states. The construction relies heavily on the differential geometry of a fibration of the set of quantum states over the set of gravitational variables. An important feature of this work is the use of Gaussian measures over the space of matter fields and of Hida distributions to define a common superspace to all possible Hilbert spaces with different measures, to properly characterize the Schrodinger wave functional picture of QFT in curved spacetime. This allows us to relate states within different Hilbert spaces in the case of vacuum states or measures that depend on the gravitational degrees of freedom, as the ones associated to Ashtekar's complex structure. This is achieved through the inclusion of a quantum Hermitian connection for the fibration, which will have profound physical implications. The most remarkable physical features of the construction are norm conservation of the quantum state (even if the total dynamics are non-unitary), the clear identification of the hybrid conserved quantities and the description of a dynamical backreaction of quantum matter on geometry and vice versa, which shall modify the physical properties the gravitational field would have in the absence of backreaction.

This letter is about confinement in QCD. At the moment we have pictures of confinement to complete our understanding of the physics of strongly interacting particles, interaction which asks for confinement. As it is said in [1] : " In principle it should be possible to derive the confinement hypothesis from the QCD Lagrangian. At this time, no rigorous derivation exists, so it is not absolutely clear that the confinement hypothesis is a bone fide prediction of QCD" . In this letter we show that a sufficient (of course not necessary) condition for confinement is that topological structure of vacuum in Nature does not correspond to the $\theta$-vacuum. Therefore, if different vacua with nontrivial winding number cannot be connected by tunneling, we obtain confinement as a consequence., Comment: 10 pages

In recent times, large organic molecules of exceptional complexity have been found in diverse regions of the interstellar medium. In this context, we aim to provide accurate frequencies of the ground vibrational state of two key aliphatic aldehydes, n-butanal and its branched-chain isomer, i-butanal, to enable their eventual detection in the interstellar medium. We employ a frequency modulation millimeter-wave absorption spectrometer to measure the rotational features of n- and i-butanal. We use the spectral line survey ReMoCA performed with the Atacama Large Millimeter/submillimeter Array to search for n- and i-butanal toward the star-forming region Sgr B2(N). We also search for both aldehydes toward the molecular cloud G+0.693-0.027 with IRAM 30 m and Yebes 40 m observations. Several thousand rotational transitions belonging to the lowest-energy conformers have been assigned in the laboratory spectra up to 325 GHz. A precise set of the relevant rotational spectroscopic constants has been determined for each structure. We report non-detections of n- and i-butanal toward both sources, Sgr B2(N1S) and G+0.693-0.027. We find that n- and i-butanal are at least 2-6 and 6-18 times less abundant than acetaldehyde toward Sgr B2(N1S), respectively, and that n-butanal is at least 63 times less abundant than acetaldehyde toward G+0.693-0.027. Comparison with astrochemical models indicates good agreement between observed and simulated abundances (where available). Grain-surface chemistry appears sufficient to reproduce aldehyde ratios in G+0.693-0.027; gas-phase production may play a more active role in Sgr B2(N1S). Our astronomical results indicate that the family of interstellar aldehydes in the Galactic center region is characterized by a drop of one order of magnitude in abundance at each incrementation in the level of molecular complexity.

Glycinamide is considered to be one of the possible precursors of the simplest amino acid glycine. Its only rotational spectrum reported so far has been in the cm-wave region. The aim of this work is to extend its laboratory spectrum into the mm wave region to support its searches in the ISM. Glycinamide was synthesised chemically and was studied with broadband rotational spectroscopy in the 90-329 GHz region. Tunneling across a low energy barrier between two symmetry equivalent configurations of the molecule resulted in splitting of each vibrational state and many perturbations in associated rotational energy levels, requiring careful coupled state fits for each vibrational doublet. We searched for emission of glycinamide in the imaging spectral line survey ReMoCA performed with ALMA toward Sgr B2(N). We report the first analysis of the mm-wave rotational spectrum of glycinamide, resulting in fitting to experimental measurement accuracy of over 1200 transition frequencies for the ground state tunneling doublet, of many lines for tunneling doublets for two singly excited vibrational states, and determination of precise vibrational separation in each doublet. We did not detect emission from glycinamide in the hot core Sgr B2(N1S). We found that glycinamide is at least seven times less abundant than aminoacetonitrile and 1.8 times less abundant than urea in this source. A comparison with results of astrochemical kinetics models for species related to glycinamide suggests that its abundance may be at least one order of magnitude below the upper limit obtained toward Sgr B2(N1S). This means that glycinamide emission in this source likely lies well below the spectral confusion limit in the frequency range covered by the ReMoCA survey. Targetting sources with a lower level of spectral confusion, such as the Galactic Center shocked region G+0.693-0.027, may be a promising avenue. [abridged], Comment: Accepted for publication in A&A

Molecular or condensed matter systems are often well approximated by hybrid quantum-classical models: the electrons retain their quantum character, whereas the ions are considered to be classical particles. We discuss various alternative approaches for the computation of equilibrium (canonical) ensemble averages for observables of these hybrid quantum-classical systems through the use of molecular dynamics (MD), i.e. by performing dynamics in the presence of a thermostat and computing time averages over the trajectories. Often, in classical or ab initio MD, the temperature of the electrons is ignored and they are assumed to remain at the instantaneous ground state given by each ionic configuration during the evolution. Here, however, we discuss the general case that considers both classical and quantum subsystems at finite temperature canonical equilibrium. Inspired by a recent formal derivation for the canonical ensemble for quantum classical hybrids, we discuss previous approaches found in the literature, and provide some new formulas., Comment: This is the version of the article before peer review or editing, as submitted by an author to New Journal of Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1367-2630/abf9b3

For all the amides detected in the interstellar medium (ISM), the corresponding nitriles or isonitriles have also been detected in the ISM, some of which have relatively high abundances. Among the abundant nitriles for which the corresponding amide has not yet been detected is cyanoacetylene (HCCCN), whose amide counterpart is propiolamide (HCCC(O)NH$_2$). With the aim of supporting searches for this amide in the ISM, we provide a complete rotational study of propiolamide from 6 GHz to 440 GHz using rotational spectroscopic techniques in the frequency and time domain. We identified and measured more than 5500 distinct frequency lines of propiolamide and obtained accurate sets of spectroscopic parameters for the ground state and the three low-lying excited vibrational states. We used the ReMoCA spectral line survey performed with the Atacama Large Millimeter/submillimeter Array toward the star-forming region Sgr B2(N) to search for propiolamide. We report the nondetection of propiolamide toward the hot cores Sgr B2(N1S) and Sgr B2(N2). We find that propiolamide is at least 50 and 13 times less abundant than acetamide in Sgr B2(N1S) and Sgr B2(N2), respectively, indicating that the abundance difference between both amides is more pronounced by at least a factor of 8 and 2, respectively, than for their corresponding nitriles. Although propiolamide has yet to be included in astrochemical modeling networks, the observed upper limit to the ratio of propiolamide to acetamide seems consistent with the ratios of related species as determined from past simulations., Comment: The article will be published as a regular paper in Astronomy and Astrophysics

Glycolamide is a glycine isomer and also one of the simplest derivatives of acetamide (e.g., one hydrogen atom is replaced with a hydroxyl group), which is a known interstellar molecule. Using a battery of state of the art rotational spectroscopic techniques in the frequency and time domain, around 1500 transitions have been newly assigned. Based on the reliable frequency predictions, we report a radioastronomical search for glycolamide in the well known high-mass star forming region Sgr B2(N) using the ALMA imaging spectral line survey ReMoCA. We also searched for glycolamide toward Sgr B2(N) with the Effelsberg radio telescope. We report the nondetection of glycolamide toward this source with an abundance at least six and five times lower than that of acetamide and glycolaldehyde, respectively. Our astrochemical model suggests that glycolamide may be present in this source at a level just below the upper limit, which was derived from the EMoCA survey. We could also not detect the molecule in the region's extended molecular envelope, which was probed with the Effelsberg telescope. We find an upper limit to its column density that is similar to the column densities obtained earlier for acetamide and glycolaldehyde with the Green Bank Telescope., Comment: The article will be published as a regular paper in Astronomy and Astrophysics (Forthcoming article since 19 May 2020)

In this work we generalize and combine Gibbs and von Neumann approaches to build, for the first time, a rigorous definition of entropy for hybrid quantum-classical systems. The resulting function coincides with the two cases above when the suitable limits are considered. Then, we apply the MaxEnt principle for this hybrid entropy function and obtain the natural candidate for the Hybrid Canonical Ensemble (HCE). We prove that the suitable classical and quantum limits of the HCE coincide with the usual classical and quantum canonical ensembles since the whole scheme admits both limits, thus showing that the MaxEnt principle is applicable and consistent for hybrid systems., Comment: 7 pages. Final preprint corresponding to the published version of the manuscript

The three cosmological conjectures to which our work refers are: the phenomenon called geodesic incompleteness, the physical gravitational $\theta_G$-term that would characterize the 1-parameter family of inequivalent vacua of quantum gravidynamics, and the hypothesis of multiversality, more specifically, a zero-energy multiverse. The known cosmological phenomenology leads under plausible assumptions to theorems which establish that the universe is past incomplete. Here, starting from Wilczek's definition of multiverse (a larger physical structure of which the universe forms part) and that spacetime is much larger than the observable universe, in a new sense suggested by these theorems, we place the observable universe, labelled by $U_{\theta_G^{(1)}}$, within a multiverse ensemble, $\{U_{\theta_G}\}$. Its topological $\theta_G^{(1)}$-term would characterize the observable universe from the Planck epoch until the present time, and it could have physical effects in, for example, black-hole physics. Our proposal is therefore a possible framework for a multiverse quantum cosmology, in which the temporal parameters (see figures in the main text) start from a "timeless multiverse big bang" (TLMBB), where all members of the multiverse ensemble, $\{U_{\theta_G}\}$, disappear, together with their corresponding classical spacetimes. Since quantum cosmology can be viewed as one attempt among many to face with the question of finding a gravitational quantum theory, if the TLMBB were the appropriate ground to define the physical or mathematical underlying structure of quantum cosmology, then multiversality could come to have a predictive power within our observable universe., Comment: 7 pages, 2 figures. Final version accepted for publication in CQG

In this letter we show that it is possible to unravel both the physical origin of the Landau's consistence criterion and the specific and subtle meaning of interpenetration of the "two fluids" if one takes into account that in the hydrodynamic regime one needs a coarse-graining in time to bring the system into local equilibrium. That is, the fuzziness in time is relevant for the phenomenological Landau's consistency criterion and the meaning of interpenetration. Note also that we are not questioning the validity of the "Two-Fluid" Model., Comment: 8 pages, affiliation added, typos corrected, final version published in Eur. Phys. J. B

In previous works, we introduced a geometric route to define our Ehrenfest Statistical Dynamics (ESD) and we proved that, for a simple toy-model, the resulting ESD does not preserve purity. We now take a step further: we investigate decoherence and pointer basis in the ESD model by considering some uncertainty in the degrees of freedom of a simple but realistic molecular model, consisting of two classical cores and one quantum electron. The Ehrenfest model is sometimes discarded as a valid approximation to non-adiabatic coupled quantum-classical dynamics because it does not describe the decoherence in the quantum subsystem. However, any rigorous statistical analysis of the Ehrenfest dynamics, such as the described ESD formalism, proves that decoherence exists. In this article, decoherence in ESD is studied by measuring the change in the quantum subsystem purity and by analysing the appearance of the pointer basis to which the system decoheres, which for our example is composed by the eigenstates of the electronic Hamiltonian., Comment: 21 pages, 9 figures. Accepted for publication in the Journal of Chemical Theory and Computation

We present a proof of concept on the coupling of radio astronomical receivers and spectrometers with chemical reactorsand the performances of the resulting setup for spectroscopy and chemical simulations in laboratory astrophysics. Several experiments including cold plasma generation and UV photochemistry were performed in a 40\,cm long gas cell placed in the beam path of the Aries 40\,m radio telescope receivers operating in the 41-49 GHz frequency range interfaced with fast Fourier transform spectrometers providing 2 GHz bandwidth and 38 kHz resolution. The impedance matching of the cell windows has been studied using different materials. The choice of the material and its thickness was critical to obtain a sensitivity identical to that of standard radio astronomical observations. Spectroscopic signals arising from very low partial pressures of CH3OH, CH3CH2OH, HCOOH, OCS,CS, SO2 (<1E-03 mbar) were detected in a few seconds. Fast data acquisition was achieved allowing for kinetic measurements in fragmentation experiments using electron impact or UV irradiation. Time evolution of chemical reactions involving OCS, O2 and CS2 was also observed demonstrating that reactive species, such as CS, can be maintained with high abundance in the gas phase during these experiments., Comment: Accepted for publication in Astronomy and Astrophysics in September 21, 2017. 16 pages, 18 figures

We report on the tentative detection of $trans$ Ethyl Methyl Ether (tEME), $t-CH_3CH_2OCH_3$, through the identification of a large number of rotational lines from each one of the spin states of the molecule towards Orion KL. We also search for $gauche$-$trans$-n-propanol, $Gt-n-CH_3CH_2CH_2OH$, an isomer of tEME in the same source. We have identified lines of both species in the IRAM 30m line survey and in the ALMA Science Verification data. We have obtained ALMA maps to establish the spatial distribution of these species. Whereas tEME mainly arises from the compact ridge component of Orion, Gt-n-propanol appears at the emission peak of ethanol (south hot core). The derived column densities of these species at the location of their emission peaks are $\leq(4.0\pm0.8)\times10^{15} cm^{-2}$ and $\leq(1.0\pm0.2)\times10^{15} cm^{-2}$ for tEME and Gt-n-propanol, respectively. The rotational temperature is $\sim100 K$ for both molecules. We also provide maps of $CH_3OCOH$, $CH_3CH_2OCOH$, $CH_3OCH_3$, $CH_3OH$, and $CH_3CH_2OH$ to compare the distribution of these organic saturated O-bearing species containing methyl and ethyl groups in this region. Abundance ratios of related species and upper limits to the abundances of non-detected ethers are provided. We derive an abundance ratio $N(CH_3OCH_3)/N(tEME)\geq150$ in the compact ridge of Orion., Comment: Accepted in A&A Letters

New laboratory data of CH$_2$CHCN (vinyl cyanide) in its ground and vibrationally excited states at the microwave to THz domain allow searching for these excited state transitions in the Orion-KL line survey. Frequency-modulated spectrometers combined into a single broadband 50-1900 GHz spectrum provided measurements of CH$_2$CHCN covering a spectral range of 18-1893 GHz, whose assignments was confirmed by Stark modulation spectra in the 18-40 GHz region and by ab-initio anharmonic force field calculations. For analyzing the emission lines of CH$_2$CHCN species detected in Orion-KL we used the excitation and radiative transfer code (MADEX) at LTE conditions. The rotational transitions of the ground state of this molecule emerge from four cloud components of hot core nature which trace the physical and chemical conditions of high mass star forming regions in the Orion-KL Nebula. The total column density of CH$_2$CHCN in the ground state is (3.0$\pm$0.9)x10$^{15}$ cm$^{-2}$. We report on the first interstellar detection of transitions in the v10=1/(v11=1,v15=1) dyad in space, and in the v11=2 and v11=3 states in Orion-KL. The lowest energy vibrationally excited states of vinyl cyanide such as v11=1 (at 328.5 K), v15=1 (at 478.6 K), v11=2 (at 657.8 K), the v10=1/(v11=1,v15=1) dyad (at 806.4/809.9 K), and v11=3 (at 987.9 K) are populated under warm and dense conditions, so they probe the hottest parts of the Orion-KL source. Column density and rotational and vibrational temperatures for CH$_2$CHCN in their ground and excited states, as well as for the isotopologues, have been constrained by means of a sample of more than 1000 lines in this survey. Moreover, we present the detection of methyl isocyanide (CH$_3$NC) for the first time in Orion-KL and a tentative detection of vinyl isocyanide (CH$_2$CHNC) and give column density ratios between the cyanide and isocyanide isomers., Comment: 46 pages, 22 figures, 14 tables, 9 online tables

Schr\"odinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schr\"odinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions, and we prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schr\"odinger's idea can not be used to construct an appropriate quantum equilibrium thermodynamics., Comment: 32 pages, revtex 4.1 preprint style, 5 figures. Published version with several changes with respect to v2 in text and references

New laboratory data of ethyl mercaptan, CH$_{3}$CH$_{2}$SH, in the millimeter and submillimeter-wave domains (up to 880 GHz) provided very precise values of the spectroscopic constants that allowed the detection of $gauche$-CH$_3$CH$_2$SH towards Orion KL. 77 unblended or slightly blended lines plus no missing transitions in the range 80-280 GHz support this identification. A detection of methyl mercaptan, CH$_{3}$SH, in the spectral survey of Orion KL is reported as well. Our column density results indicate that methyl mercaptan is $\simeq$ 5 times more abundant than ethyl mercaptan in the hot core of Orion KL., Comment: Accepted for publication in ApJL (30 January 2014)/ submitted (8 January 2014)

In spite of the relevance of the proposal introduced in the recent work A. Abedi, N. T. Maitra and E. K. U. Gross, J. Chem. Phys. 137, 22A530, 2012, there is an important ingredient which is missing. Namely, the proof that the norms of the electronic and nuclear wavefunctions which are the solutions to the nonlinear equations of motion are preserved by the evolution. To prove the conservation of these norms is precisely the objective of this Comment., Comment: 2 pages, published version

At non-zero temperature and when a system has low-lying excited electronic states, the ground-state Born--Oppenheimer approximation breaks down and the low-lying electronic states are involved in any chemical process. In this work, we use a temperature-dependent effective potential for the nuclei which can accomodate the influence of an arbitrary number of electronic states in a simple way, while at the same time producing the correct Boltzmann equibrium distribution for the electronic part. With the help of this effective potential, we show that thermally-activated low-lying electronic states can have a significant effect in molecular properties for which electronic excitations are oftentimes ignored. We study the thermal expansion of the Manganese dimer, Mn$_2$, where we find that the average bond length experiences a change larger than the present experimental accuracy upon the inclusion of the excited states into the picture. We also show that, when these states are taken into account, reaction rate constants are modified. In particular, we study the opening of the ozone molecule, O$_3$, and show that in this case the rate is modified as much as a 20% with respect to the ground-state Born--Oppenheimer prediction., Comment: 9 pages, 6 figures

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Ref. 1. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space $D$, and on the number of classical trajectories $N$ of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics., Comment: Revtex 4-1, 14 pages, 2 figures. Final published version

Quantum dynamics (i.e., the Schr\"odinger equation) and classical dynamics (i.e., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. In this paper we first show that the hybrid quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. Once we know the canonical distribution of a Ehrenfest system, it is straightforward to extend the formalism of Nos\'e (invented to do constant temperature Molecular Dynamics by a non-stochastic method) to our Ehrenfest formalism. This work also provides the basis for extending stochastic methods to Ehrenfest dynamics., Comment: 28 pages, 1 figure. Published version. arXiv admin note: substantial text overlap with arXiv:1010.1494

In principle, we should not need the time-dependent extension of density-functional theory (TDDFT) for excitations, and in particular not for Molecular Dynamics (MD) studies: the theorem by Hohenberg and Kohn teaches us that for any observable that we wish to look at (including dynamical properties or observables dependent on excited states) there is a corresponding functional of the ground-state density. Yet the unavailability of such magic functionals in many cases (the theorem is a non-constructive existence result) demands the development and use of the alternative exact reformulation of quantum mechanics provided by TDDFT. This theory defines a convenient route to electronic excitations and to the dynamics of a many-electron system subject to an arbitrary time-dependent perturbation. This is, in fact, the main purpose of inscribing TDDFT in a MD framework -the inclusion of the effect of electronic excited states in the dynamics. However, as we will show in this review, it may not be the only use of TDDFT in this context. In this manuscript, we review two recent proposals: In Section 1.2, we show how TDDFT can be used to design efficient gsBOMD algorithms -even if the electronic excited states are in this case not relevant. The work described in Section 1.3 addresses the problem of mixed quantum-classical systems at thermal equilibrium., Comment: 10 pages, 1 figure, to be published in the book "Time Dependent Density Functional Theory" by Springer Verlag

Quantum dynamics (e.g., the Schr\"odinger equation) and classical dynamics (e.g., Hamilton equations) can both be formulated in equal geometric terms: a Poisson bracket defined on a manifold. The difference between both worlds is due to the presence of extra structure in the quantum case, that leads to the appearance of the probabilistic nature of the measurements and the indetermination and superposition principles. In this paper we first show that the quantum-classical dynamics prescribed by the Ehrenfest equations can also be formulated within this general framework, what has been used in the literature to construct propagation schemes for Ehrenfest dynamics. Then, the existence of a well defined Poisson bracket allows to arrive to a Liouville equation for a statistical ensemble of Ehrenfest systems. The study of a generic toy model shows that the evolution produced by Ehrenfest dynamics is ergodic and therefore the only constants of motion are functions of the Hamiltonian. The emergence of the canonical ensemble characterized by the Boltzmann's distribution follows after an appropriate application of the principle of equal a priori probabilities to this case. This work provides the basis for extending stochastic methods to Ehrenfest dynamics., Comment: LaTeX(RevTeX 4.1), 14 pages, 1 figure. Submitted for publication

In this work, we introduce an algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system (i.e., constraints in which the hard coordinates are fixed to configuration-dependent values). The presented scheme is exact, it does not contain any tunable parameter, and it only requires the calculation and inversion of a sub-block of the Hessian matrix of second derivatives of the function through which the constraints are defined. We also present a practical application to the case in which the sought observables are the Euclidean coordinates of complex molecular systems, and the function whose minimization defines the constraints is the potential energy. Finally, and in order to validate the method, which, as far as we are aware, is the first of its kind in the literature, we compare it to the natural and straightforward finite-differences approach in three molecules of biological relevance: methanol, N-methyl-acetamide and a tri-glycine peptide, Comment: 13 pages, 8 figures, published version

We prove that for a combined system of classical and quantum particles, it is possible to write a dynamics for the classical particles that incorporates in a natural way the Boltzmann equilibrium population for the quantum subsystem. In addition, these molecular dynamics do not need to assume that the electrons immediately follow the nuclear motion (in contrast to any adiabatic approach), and do not present problems in the presence of crossing points between different potential energy surfaces (conical intersections or spin-crossings). A practical application of this molecular dynamics to study the effect of temperature in molecular systems presenting (nearly) degenerate states - such as the avoided crossing in the ring-closure process of ozone - is presented., Comment: published in New J. Phys

We present in detail the recently derived ab-initio molecular dynamics (AIMD) formalism [Phys. Rev. Lett. 101 096403 (2008)], which due to its numerical properties, is ideal for simulating the dynamics of systems containing thousands of atoms. A major drawback of traditional AIMD methods is the necessity to enforce the orthogonalization of the wave-functions, which can become the bottleneck for very large systems. Alternatively, one can handle the electron-ion dynamics within the Ehrenfest scheme where no explicit orthogonalization is necessary, however the time step is too small for practical applications. Here we preserve the desirable properties of Ehrenfest in a new scheme that allows for a considerable increase of the time step while keeping the system close to the Born-Oppenheimer surface. We show that the automatically enforced orthogonalization is of fundamental importance for large systems because not only it improves the scaling of the approach with the system size but it also allows for an additional very efficient parallelization level. In this work we provide the formal details of the new method, describe its implementation and present some applications to some test systems. Comparisons with the widely used Car-Parrinello molecular dynamics method are made, showing that the new approach is advantageous above a certain number of atoms in the system. The method is not tied to a particular wave-function representation, making it suitable for inclusion in any AIMD software package., Comment: 28 pages, 5 figures, published in a special issue of J. Chem. Theory Comp. in honour of John Perdew

A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schroedinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast to other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large scale AIMD simulations., Comment: 5 pages, 3 color figures, revtex4 package

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference., Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn packages

We present an exhaustive study of more than 250 ab initio potential energy surfaces (PESs) of the model dipeptide HCO-L-Ala-NH2. The model chemistries (MCs) used are constructed as homo- and heterolevels involving possibly different RHF and MP2 calculations for the geometry and the energy. The basis sets used belong to a sample of 39 selected representants from Pople's split-valence families, ranging from the small 3-21G to the large 6-311++G(2df,2pd). The reference PES to which the rest are compared is the MP2/6-311++G(2df,2pd) homolevel, which, as far as we are aware, is the more accurate PES of a dipeptide in the literature. The aim of the study presented is twofold: On the one hand, the evaluation of the influence of polarization and diffuse functions in the basis set, distinguishing between those placed at 1st-row atoms and those placed at hydrogens, as well as the effect of different contraction and valence splitting schemes. On the other hand, the investigation of the heterolevel assumption, which is defined here to be that which states that heterolevel MCs are more efficient than homolevel MCs. The heterolevel approximation is very commonly used in the literature, but it is seldom checked. As far as we know, the only tests for peptides or related systems, have been performed using a small number of conformers, and this is the first time that this potentially very economical approximation is tested in full PESs. In order to achieve these goals, all data sets have been compared and analyzed in a way which captures the nearness concept in the space of MCs., Comment: 54 pages, 16 figures, LaTeX, AMSTeX, Submitted to J. Comp. Chem

A general approach to the design of accurate classical potentials for protein folding is described. It includes the introduction of a meaningful statistical measure of the differences between approximations of the same potential energy, the definition of a set of Systematic and Approximately Separable and Modular Internal Coordinates (SASMIC), much convenient for the simulation of general branched molecules, and the imposition of constraints on the most rapidly oscillating degrees of freedom. All these tools are used to study the effects of constraints in the Conformational Equilibrium Distribution (CED) of the model dipeptide HCO-L-Ala-NH2. We use ab initio Quantum Mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of the correcting terms to the naive CED based in the Potential Energy Surface (PES) without any simplifying assumption. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function., Comment: 8 pages, 1 figure, LaTeX, aipproc style (included)

If constraints are imposed on a macromolecule, two inequivalent classical models may be used: the stiff and the rigid one. This work studies the effects of such constraints on the Conformational Equilibrium Distribution (CED) of the model dipeptide HCO-L-Ala-NH2 without any simplifying assumption. We use ab initio Quantum Mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of all the correcting terms to the naive CED based in the Potential Energy Surface (PES) that appear when the constraints are considered. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function., Comment: 37 pages, 4 figures, LaTeX, BibTeX, AMSTeX

A set of rules is defined to systematically number the groups and the atoms of organic molecules and, particularly, of polypeptides in a modular manner. Supported by this numeration, a set of internal coordinates is defined. These coordinates (termed Systematic, Approximately Separable and Modular Internal Coordinates, SASMIC) are straightforwardly written in Z-matrix form and may be directly implemented in typical Quantum Chemistry packages. A number of Perl scripts that automatically generate the Z-matrix files for polypeptides are provided as supplementary material. The main difference with other Z-matrix-like coordinates normally used in the literature is that normal dihedral angles (``principal dihedrals'' in this work) are only used to fix the orientation of whole groups and a somewhat non-standard type of dihedrals, termed ``phase dihedrals'', are used to describe the covalent structure inside the groups. This physical approach allows to approximately separate soft and hard movements of the molecule using only topological information and to directly implement constraints. As an application, we use the coordinates defined and ab initio quantum mechanical calculations to assess the commonly assumed approximation of the free energy, obtained from ``integrating out'' the side chain degree of freedom chi, by the Potential Energy Surface (PES) in the protected dipeptide HCO-L-Ala-NH2. We also present a sub-box of the Hessian matrix in two different sets of coordinates to illustrate the approximate separation of soft and hard movements when the coordinates defined in this work are used., Comment: 27 pages, 10 figures, LaTeX, mcite package

In the study of the conformational behavior of complex systems, such as proteins, several related statistical measures are commonly used to compare two different potential energy functions. Among them, the Pearson's correlation coefficient r has no units and allows only semi-quantitative statements to be made. Those that do have units of energy and whose value may be compared to a physically relevant scale, such as the root mean square deviation (RMSD), the mean error of the energies (ER), the standard deviation of the error (SDER) or the mean absolute error (AER), overestimate the distance between potentials. Moreover, their precise statistical meaning is far from clear. In this article, a new measure of the distance between potential energy functions is defined which overcomes the aforementioned difficulties. In addition, its precise physical meaning is discussed, the important issue of its additivity is investigated and some possible applications are proposed. Finally, two of these applications are illustrated with practical examples: the study of the van der Waals energy, as implemented in CHARMM, in the Trp-Cage protein (PDB code 1L2Y) and the comparison of different levels of the theory in the ab initio study of the Ramachandran map of the model peptide HCO-L-Ala-NH2., Comment: 30 pages, 7 figures, LaTeX, BibTeX. v2: A misspelling in the author's name has been corrected. v3: A new application of the method has been added at the end of section 9 and minor modifications have also been made in other sections. v4: Journal reference and minor corrections added

The phase diagram of the simplest approximation to Double-Exchange systems, the bosonic Double-Exchange model with antiferromagnetic super-exchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions and Variational Mean-Field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segment like ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase-transition, only short-range ordering would be found in neutron-scattering. Researchers looking for a Quantum Critical Point in manganites should be wary of this possibility. Finite-Size Scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes., Comment: 17 pages, 14 figures

The phase diagram of the double perovskites of the type Sr_{2-x} La_x Fe Mo O_6 is analyzed, with and without disorder due to antisites. In addition to an homogeneous half metallic ferrimagnetic phase in the absence of doping and disorder, we find antiferromagnetic phases at large dopings, and other ferrimagnetic phases with lower saturation magnetization, in the presence of disorder., Comment: 4 pages, 3 postscript figures, some errata corrected

It is shown that, contrary to previous claims, a scalar tensor theory of Brans-Dicke type provides a relativistic generalization of Newtonian gravity in 2+1 dimensions. The theory is metric and test particles follow the space-time geodesics. The static isotropic solution is studied in vacuum and in regions filled with an incompressible perfect fluid. It is shown that the solutions can be consistently matched at the matter vacuum interface, and that the Newtonian behavior is recovered in the weak field regime., Comment: 6 pages, no figures, Revtex4. Some discussions on the physical nature of the interior solution and on the omega->infinity limit and some references added. Version to appear in Phys. Rev. D

Considering the disorder caused in manganites by the substitution of Mn by Fe or Ga, we accomplish a systematic study of doped manganites begun in previous papers. To this end, a disordered model is formulated and solved using the Variational Mean Field technique. The subtle interplay between double exchange, super-exchange, and disorder causes similar effects on the dependence of T_C on the percentage of Mn substitution in the cases considered. Yet, in La$_{2/3}$Ca$_{1/3}$Mn$_{1-y}$Ga$_y$O$_3$ our results suggest a quantum critical point (QCP) for $y\approx 0.1-0.2$, associated to the localization of the electronic states of the conduction band. In the case of La$_x$Ca$_x$Mn$_{1-y}$Fe$_y$O$_3$ (with $x=1/3,3/8$) no such QCP is expected., Comment: 6 pages + 3 postscript figures. Largely extended discussion

We study the phase diagram of the double exchange model, with antiferromagnetic interactions, in a cubic lattice both at zero and at finite temperature. There is a rich variety of magnetic phases, combined with regions where phase separation takes place. We identify phases, intrinsic to the cubic lattice, which are stable for realistic values of the interactions and dopings. Some of these phases break chiral symmetry, leading to unusual features., Comment: 8 pages, 6 postscript figures

It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first and second order transitions than previously anticipated, and that such transitions are consistent with the magnetic properties of manganites. Here we present a thorough discussion of the variational Mean Field approach that leads to the these results. We also show that the effect of the Berry phase turns out to be crucial to produce first order Paramagnetic-Ferromagnetic transitions near half filling with transition temperatures compatible with the experimental situation. The computation relies on two crucial facts: the use of a Mean Field ansatz that retains the complexity of a system of electrons with off-diagonal disorder, not fully taken into account by the Mean Field techniques, and the small but significant antiferromagnetic superexchange interaction between the localized spins., Comment: 13 pages, 11 postscript figures, revtex

The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a path-integral formulation of the problem, in $d+1$ Euclidean space-time. A perfect action formulation allows to work on the continuum euclidean time, without need for a Trotter-Suzuki extrapolation. To demonstrate the feasibility of the method we study the Double Exchange Model in three dimensions. The complexity of the algorithm grows only as the system volume, allowing to simulate in lattices as large as $16^3$ on a personal computer. We conclude that the second order paramagnetic-ferromagnetic phase transition of Double Exchange Materials close to half-filling belongs to the Universality Class of the three-dimensional classical Heisenberg model., Comment: 20 pages plus 4 postscript figures

It is shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a rich variety of first order transitions between phases with different electronic densities and/or magnetizations. For band fillings in the range $0.3 \le x \le 0.5$, and at finite temperatures, a discontinuous transition between phases with similar electronic densities but different magnetizations takes place. This sharp transition, which is not suppressed by electrostatic effects, and survives in the presence of an applied field, is consistent with the phenomenology of the doped manganites near the transition temperature., Comment: three more variational ansatzs considered

We present a way of protecting a Dirac fermion interacting with a scalar (Higgs) field from getting a mass from the vacuum. It is obtained through an implementation of translational symmetry when the theory is formulated with a momentum cutoff, which forbids the usual Yukawa term. We consider that this mechanism can help to understand the smallness of neutrino masses without a tuning of the Yukawa coupling. The prohibition of the Yukawa term for the neutrino forbids at the same time a gauge coupling between the right-handed electron and neutrino. We prove that this mechanism can be implemented on the lattice., Comment: LATTICE99(Higgs,Yukawa,SUSY), 3 pages

The phase diagram at zero temperature of a lattice SU(2) scalar-fermion model in (2+1) dimensions is studied numerically and with Mean-Field methods. Special attention is devoted to the strong coupling regime. We have developed a new method to adaptate the Hybrid Monte Carlo algorithm to the O(3) non-linear $\sigma$ model constraint. The charged excitations in the various phases are studied at the Mean-Field lev el. Bound states of two charged fermions are found in a strongly coupled {\it paramagnetic} phase. On the other hand, in the strongly coupled antiferromagnetic phase fermionic excitations around momenta $(\pm\frac{\pi}{2},\pm\frac{\pi}{2},\pm\frac{\pi}{2})$ emerge., Comment: 28 pages plus 7 postscript figures

We study the linear response to an external electric field of a system of fermions in a lattice at zero temperature. This allows to measure numerically the Euclidean conductivity which turns out to be compatible with an analytical calculation for free fermions. The numerical method is generalizable to systems with dynamical interactions where no analytical approach is possible., Comment: version to be published in Physics Letters B

We propose a way of protecting a Dirac fermion interacting with a scalar field from acquiring a mass from the vacuum. It is obtained through an implementation of translational symmetry when the theory is formulated with a momentum cutoff, which forbids the usual Yukawa term. We consider that this mechanism can help to understand the smallness of neutrino masses without a tuning of the Yukawa coupling. The prohibition of the Yukawa term for the neutrino forbids at the same time a gauge coupling between the right-handed electron and neutrino. We prove that this mechanism can be implemented on the lattice., Comment: 9 pages, LaTeX. Final version to appear in Modern Physics Letters