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Andreas M. Köster - One of the best experts on this subject based on the ideXlab platform.
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mixed second and third energy derivatives from auxiliary Density Perturbation theory
Molecular Physics, 2019Co-Authors: Rogelio Isaac Delgadovenegas, Patrizia Calaminici, Andreas M. KösterAbstract:AbstractThe working equations for the calculation of mixed second- and third-order energy derivatives in the framework of auxiliary Density functional theory are presented. The Perturbations with r...
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analytic second derivatives from auxiliary Density Perturbation theory
Journal of Chemical Physics, 2016Co-Authors: Rogelio Isaac Delgadovenegas, Roberto Floresmoreno, Daniel Mejiarodriguez, Patrizia Calaminici, Andreas M. KösterAbstract:The working equations for the calculation of analytic second energy derivatives in the framework of auxiliary Density functional theory (ADFT) are presented. The needed Perturbations are calculated with auxiliary Density Perturbation theory (ADPT) which is extended to Perturbation dependent basis and auxiliary functions sets. The obtained ADPT equation systems are solved with the Eirola-Nevanlinna algorithm. The newly developed analytic second ADFT energy derivative approach was implemented in deMon2k and validated with respect to the corresponding finite difference approach by calculating the harmonic frequencies of small molecules. Good agreement between these two methodologies is found. To analyze the scaling of the new analytic second ADFT energy derivatives with respect to the number of processors in parallel runs, the harmonic frequencies of the carbon fullerene C240 are calculated with varying numbers of processors. Fair scaling up to 720 processors was found. As showcase applications, symmetry unrestricted optimization and frequency analyses of icosahedral carbon fullerenes with up to 960 atoms are presented.
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robust and efficient auxiliary Density Perturbation theory calculations
Journal of Chemical Theory and Computation, 2015Co-Authors: Daniel Mejiarodriguez, Rogelio Isaac Delgado Venegas, Patrizia Calaminici, Andreas M. KösterAbstract:: A new iterative solver for the recently developed time-dependent auxiliary Density Perturbation theory is presented. It is based on the Eirola-Nevanlinna algorithm for large nonsymmetric linear equation systems. The new methodology is validated by static and dynamic polarizability calculations of small molecules. Comparison between the analytic and iterative solutions of the response equation system shows excellent agreement for the calculated static and dynamic polarizabilities. The new iterative solver reduces the formal scaling from [Symbol: see text](N(4)) to [Symbol: see text](N(3)). Furthermore, the observed computational scaling for linear alkane chains is N(1.6). This subquadratic behavior is possible in systems with a few hundred atoms because of the very small prefactors of the [Symbol: see text](N(3)) and [Symbol: see text](N(2)) steps remaining in the iterative solver. To demonstrate the potential of this new methodology, static polarizabilities of giant fullerenes up to C960, with more than 14,000 basis functions, are calculated.
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Calculation of hyperpolarizabilities with auxiliary Density Perturbation theory
2015Co-Authors: Roberto Flores-moreno, Javier Carmona-espíndola, Andreas M. KösterAbstract:A new approach for the calculation of static first hyperpolarizabilities within the auxiliary Density Perturbation theory is derived. It takes advantage of Wigner's 2n+1 rule. As a byproduct quadratic response equations are obtained. The final expressions are similar to those found in other approaches but present subtle differences related to the use of the auxiliary Density. Validation of our new approach with respect to finite field and literature results demonstrates its numerical stability and accuracy.
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static and dynamic first hyperpolarizabilities from time dependent auxiliary Density Perturbation theory
International Journal of Quantum Chemistry, 2012Co-Authors: Javier Carmonaespindola, Roberto Floresmoreno, Andreas M. KösterAbstract:A new approach for the calculation of static and dynamic hyperpolarizabilities in the framework of auxiliary Density Perturbation theory is derived. It takes advantage of the Wigner's 2n+1 rule. As a byproduct dynamic quadratic response equations are obtained. Even though the final equations are similar to other approaches they present subtle differences due to their rooting in auxiliary Density functional theory. The numerical stability and accuracy of the new approach is validated with respect to other theoretical and experimental results. © 2012 Wiley Periodicals, Inc.
David H. Lyth - One of the best experts on this subject based on the ideXlab platform.
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the primordial Density Perturbation cosmology inflation and the origin of structure
2009Co-Authors: David H. Lyth, Andrew R LiddleAbstract:1. Overview Part I. Relativity: 2. Special relativity 3. General relativity Part II. The Universe after the First Second: 4. The unperturbed Universe 5. The primordial Density Perturbation 6. Stochastic properties 7. Newtonian Perturbations 8. General relativistic Perturbations 9. The matter distribution 10. Cosmic microwave background anistropy 11. Boltzmann hierarchy and polarization 12. Isocurvature and tensor modes Part III. Field Theory: 13. Scalar fields and gravity 14. Internal symmetry 15. Quantum field theory 16. The Standard Model 17. Supersymmetry Part IV. Inflation and the Early Universe: 18. Slow-roll inflation 19. More inflation paradigms 20. Reheating and phase transitions 21. Baryon number, CDM and dark energy 22. Generating field Perturbations at horizon exit 23. Generating zeta at horizon exit 24. Generating zeta and Si after horizon exit 25. Slow-roll inflation and observation Appendixes Index.
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Primordial Density Perturbation in the curvaton scenario
Physical Review D, 2003Co-Authors: David H. Lyth, C. Ungarelli, David WandsAbstract:We analyze the primordial Density Perturbation when it is generated by a “curvaton” field different from the inflaton. In some cases this Perturbation may have large isocurvature components, fully correlated or anticorrelated with the adiabatic component. It may also have a significant non-Gaussian component. All of these effects are calculated in a form which will enable direct comparison with current and forthcoming observational data.
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particle physics models of inflation and the cosmological Density Perturbation
Physics Reports, 1999Co-Authors: David H. Lyth, Antonio RiottoAbstract:This is a review of particle-theory models of inflation, and of their predictions for the primordial Density Perturbation that is thought to be the origin of structure in the Universe. It contains mini-reviews of the relevant observational cosmology, of elementary field theory and of supersymmetry, that may be of interest in their own right. The spectral index n(k), specifying the scale dependence of the spectrum of the curvature Perturbation, will be a powerful discriminator between models, when it is measured by Planck with accuracy Δn∼0.01. The usual formula for n is derived, as well as its less familiar extension to the case of a multi-component inflaton; in both cases the key ingredient is the separate evolution of causally disconnected regions of the Universe. Primordial gravitational waves will be an even more powerful discriminator if they are observed, since most models of inflation predict that they are completely negligible. We treat in detail the new wave of models, which are firmly rooted in modern particle theory and have supersymmetry as a crucial ingredient. The review is addressed to both astrophysicists and particle physicists, and each section is fairly homogeneous regarding the assumed background knowledge.
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Models of inflation and the spectral index of the adiabatic Density Perturbation
arXiv: High Energy Physics - Phenomenology, 1996Co-Authors: David H. LythAbstract:If an adiabatic Density Perturbation is responsible for large scale structure and the cmb anisotropy, its spectral index $n$ will be measured in the forseeable future with an accuracy $\Delta n\sim .01$. This is precisely the kind of accuracy required to distinguish between many models of inflation. Most of them have an inflationary potential $V\simeq V_0(1\pm\mu\phi^p)$ with the constant term dominating. Except for $0\lsim p\lsim 2$, the prediction is $n=1\pm (2/N)(p-1)/(p-2)$, where $N$ is the number of $e$-folds of inflation after cosmological scales leave the horizon. It typically lies in the range $0.9\lsim n\lsim 1.1$. For $p=2$ one has $n=1\pm 2\Mpl^2 \mu$ where $\Mpl=(8\pi G)^{-1/2}$. A generic supergravity theory gives contributions of order $\pm H^2$ to the inflaton mass-squared $m^2$ whereas inflation requires $|m^2|
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peculiar velocity cosmic Perturbation theory and the cosmic microwave background anisotropy
Physics Letters B, 1994Co-Authors: Marco Bruni, David H. LythAbstract:Abstract It is proved that the cosmological Density Perturbation is associated with a peculiar velocity field. This allows a simple formulation of cosmological Perturbation theory, which works entirely with quasi-Newtonian fluid flow equations. As an illustration, the large scale cosmic microwave background anisotropy (Sachs-Wolfe effect) is calculated without any reference to the metric Perturbation. In addition, assuming the usual adiabatic initial condition on the Density Perturbation, we show that the dipole of the anisotropy measures our peculiar velocity relative to the average peculiar velocity within the last scattering surface of the microwave background, thus defining its frame of references.
Roberto Floresmoreno - One of the best experts on this subject based on the ideXlab platform.
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auxiliary Density Perturbation theory for restricted open shell systems
Revista de la Sociedad Química de Mexico, 2017Co-Authors: Gregorio Guzmanramirez, Francisco J Tenorio, J G Rodriguezzavala, Roberto FloresmorenoAbstract:The recently developed approach to auxiliary Density per- turbation theory (J. Chem. Phys. 2008, 128, 134105) for the purpose of calculating molecular properties is here extended to include open-shell systems. Both unrestricted and restricted formalisms are considered. A linear equation system, twice as large as the auxiliary function set is obtained in both cases. For the first time, the formulation for aux- iliary Density Perturbation theory for restricted open-shell formalism is derived.
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analytic second derivatives from auxiliary Density Perturbation theory
Journal of Chemical Physics, 2016Co-Authors: Rogelio Isaac Delgadovenegas, Roberto Floresmoreno, Daniel Mejiarodriguez, Patrizia Calaminici, Andreas M. KösterAbstract:The working equations for the calculation of analytic second energy derivatives in the framework of auxiliary Density functional theory (ADFT) are presented. The needed Perturbations are calculated with auxiliary Density Perturbation theory (ADPT) which is extended to Perturbation dependent basis and auxiliary functions sets. The obtained ADPT equation systems are solved with the Eirola-Nevanlinna algorithm. The newly developed analytic second ADFT energy derivative approach was implemented in deMon2k and validated with respect to the corresponding finite difference approach by calculating the harmonic frequencies of small molecules. Good agreement between these two methodologies is found. To analyze the scaling of the new analytic second ADFT energy derivatives with respect to the number of processors in parallel runs, the harmonic frequencies of the carbon fullerene C240 are calculated with varying numbers of processors. Fair scaling up to 720 processors was found. As showcase applications, symmetry unrestricted optimization and frequency analyses of icosahedral carbon fullerenes with up to 960 atoms are presented.
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static and dynamic first hyperpolarizabilities from time dependent auxiliary Density Perturbation theory
International Journal of Quantum Chemistry, 2012Co-Authors: Javier Carmonaespindola, Roberto Floresmoreno, Andreas M. KösterAbstract:A new approach for the calculation of static and dynamic hyperpolarizabilities in the framework of auxiliary Density Perturbation theory is derived. It takes advantage of the Wigner's 2n+1 rule. As a byproduct dynamic quadratic response equations are obtained. Even though the final equations are similar to other approaches they present subtle differences due to their rooting in auxiliary Density functional theory. The numerical stability and accuracy of the new approach is validated with respect to other theoretical and experimental results. © 2012 Wiley Periodicals, Inc.
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time dependent auxiliary Density Perturbation theory
Journal of Chemical Physics, 2010Co-Authors: Javier Carmonaespindola, Roberto Floresmoreno, Andreas M. KösterAbstract:The recently developed auxiliary Density Perturbation theory is extended to time-dependent Perturbations. As its static counterpart, it is based on auxiliary Density functional theory in which the Coulomb and exchange-correlation potentials are expressed through one auxiliary function Density. As in the case of static Perturbations a noniterative alternative to the corresponding coupled perturbed Kohn–Sham method is formulated. The new methodology is validated by local and gradient corrected dynamical polarizability calculations. Comparison with experiment indicates that for low frequencies reliable dynamical polarizabilities are obtained. Our discussion also shows that the computational performance of time-dependent auxiliary Density Perturbation theory is similar to the previously described static approach. In order to demonstrate the potential of this new methodology, dynamic polarizabilities of C60, C180, and C240 are calculated.
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auxiliary Density Perturbation theory
Journal of Chemical Physics, 2008Co-Authors: Roberto Floresmoreno, Andreas M. KösterAbstract:A new approach, named auxiliary Density Perturbation theory, for the calculation of second energy derivatives is presented. It is based on auxiliary Density functional theory in which the Coulomb and exchange-correlation potentials are expressed by auxiliary function densities. Different to conventional coupled perturbed Kohn–Sham equations the perturbed Density matrix is obtained noniteratively by solving an inhomogeneous equation system with the dimension of the auxiliary function set used to expand the auxiliary function Density. A prototype implementation for the analytic calculation of molecular polarizabilities is presented. It is shown that the polarizabilities obtained with the newly developed auxiliary Density Perturbation approach match quantitative with the ones from standard Density functional theory if augmented auxiliary function sets are used. The computational advantages of auxiliary Density Perturbation theory are discussed, too.
Javier Carmonaespindola - One of the best experts on this subject based on the ideXlab platform.
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static and dynamic first hyperpolarizabilities from time dependent auxiliary Density Perturbation theory
International Journal of Quantum Chemistry, 2012Co-Authors: Javier Carmonaespindola, Roberto Floresmoreno, Andreas M. KösterAbstract:A new approach for the calculation of static and dynamic hyperpolarizabilities in the framework of auxiliary Density Perturbation theory is derived. It takes advantage of the Wigner's 2n+1 rule. As a byproduct dynamic quadratic response equations are obtained. Even though the final equations are similar to other approaches they present subtle differences due to their rooting in auxiliary Density functional theory. The numerical stability and accuracy of the new approach is validated with respect to other theoretical and experimental results. © 2012 Wiley Periodicals, Inc.
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time dependent auxiliary Density Perturbation theory
Journal of Chemical Physics, 2010Co-Authors: Javier Carmonaespindola, Roberto Floresmoreno, Andreas M. KösterAbstract:The recently developed auxiliary Density Perturbation theory is extended to time-dependent Perturbations. As its static counterpart, it is based on auxiliary Density functional theory in which the Coulomb and exchange-correlation potentials are expressed through one auxiliary function Density. As in the case of static Perturbations a noniterative alternative to the corresponding coupled perturbed Kohn–Sham method is formulated. The new methodology is validated by local and gradient corrected dynamical polarizability calculations. Comparison with experiment indicates that for low frequencies reliable dynamical polarizabilities are obtained. Our discussion also shows that the computational performance of time-dependent auxiliary Density Perturbation theory is similar to the previously described static approach. In order to demonstrate the potential of this new methodology, dynamic polarizabilities of C60, C180, and C240 are calculated.
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comparison of the auxiliary Density Perturbation theory and the noniterative approximation to the coupled perturbed kohn sham method case study of the polarizabilities of disubstituted azoarene molecules
Journal of Physical Chemistry A, 2010Co-Authors: Sapana V Shedge, Javier Carmonaespindola, Andreas M. KösterAbstract:We present a theoretical study of the polarizabilities of free and disubstituted azoarenes employing auxiliary Density Perturbation theory (ADPT) and the noniterative approximation to the coupled perturbed Kohn−Sham (NIA-CPKS) method. Both methods are noniterative but use different approaches to obtain the perturbed Density matrix. NIA-CPKS is different from the conventional CPKS approach in that the perturbed Kohn−Sham matrix is obtained numerically, thereby yielding a single-step solution to CPKS. ADPT is an alternative approach to the analytical CPKS method in the framework of the auxiliary Density functional theory. It is shown that the polarizabilities obtained using these two methods are in good agreement with each other. Comparisons are made for disubstituted azoarenes, which give support to the push−pull mechanism. Both methods reproduce the same trend for polarizabilities because of the substitution pattern of the azoarene moiety. Our results are consistent with the standard organic chemistry “ac...
Marco Bruni - One of the best experts on this subject based on the ideXlab platform.
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peculiar velocity cosmic Perturbation theory and the cosmic microwave background anisotropy
Physics Letters B, 1994Co-Authors: Marco Bruni, David H. LythAbstract:Abstract It is proved that the cosmological Density Perturbation is associated with a peculiar velocity field. This allows a simple formulation of cosmological Perturbation theory, which works entirely with quasi-Newtonian fluid flow equations. As an illustration, the large scale cosmic microwave background anisotropy (Sachs-Wolfe effect) is calculated without any reference to the metric Perturbation. In addition, assuming the usual adiabatic initial condition on the Density Perturbation, we show that the dipole of the anisotropy measures our peculiar velocity relative to the average peculiar velocity within the last scattering surface of the microwave background, thus defining its frame of references.
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peculiar velocity cosmic Perturbation theory and the cmb anisotropy
arXiv: Astrophysics, 1993Co-Authors: Marco Bruni, David H. LythAbstract:This is a somewhat extended version of the original July 93 report. It is proved that the cosmological Density Perturbation is associated with a peculiar velocity field. This allows a simple formulation of cosmological Perturbation theory, which works entirely with quasi-Newtonian fluid flow equations. As an illustration, the large scale cosmic microwave background anisotropy (Sachs-Wolfe effect) is calculated without any reference to the metric Perturbation. In addition, assuming the usual adiabatic initial condition on the Density Perturbation, we show that the dipole of the anisotropy measures our peculiar velocity relative to the average peculiar velocity within the last scattering surface of the microwave background, thus defining its frame of reference.