19 research outputs found
Alternative definition of excitation amplitudes in Multi-Reference state-specific Coupled Cluster
A central difficulty of state-specific Multi-Reference Coupled Cluster
(MR-CC) formalisms concerns the definition of the amplitudes of the single and
double excitation operators appearing in the exponential wave operator. If the
reference space is a complete active space (CAS) the number of these amplitudes
is larger than the number of singly and doubly excited determinants on which
one may project the eigenequation, and one must impose additional conditions.
The present work first defines a state-specific reference-independent operator
which acting on the CAS component of the wave function
maximizes the overlap between
and the eigenvector of the CAS-SD CI
matrix . This operator may be used to generate
approximate coefficients of the Triples and Quadruples, and a dressing of the
CAS-SD CI matrix, according to the intermediate Hamiltonian formalism. The
process may be iterated to convergence. As a refinement towards a strict
Coupled Cluster formalism, one may exploit reference-independent amplitudes
provided by to define a
reference-dependent operator by fitting the eigenvector of the
(dressed) CAS-SD CI matrix. The two variants, which are internally
uncontracted, give rather similar results. The new MR-CC version has been
tested on the ground state potential energy curves of 6 molecules (up to
triple-bond breaking) and a two excited states. The non-parallelism error with
respect to the Full-CI curves is of the order of 1 m.Comment: 11 page
Deterministic construction of nodal surfaces within quantum Monte Carlo: the case of FeS
In diffusion Monte Carlo (DMC) methods, the nodes (or zeroes) of the trial
wave function dictate the magnitude of the fixed-node (FN) error. Within
standard DMC implementations, they emanate from short multideterminant
expansions, \textit{stochastically} optimized in the presence of a Jastrow
factor. Here, following a recent proposal, we follow an alternative route by
considering the nodes of selected configuration interaction (sCI) expansions
built with the CIPSI (Configuration Interaction using a Perturbative Selection
made Iteratively) algorithm. In contrast to standard implementations, these
nodes can be \textit{systematically} and \textit{deterministically} improved by
increasing the size of the sCI expansion. The present methodology is used to
investigate the properties of the transition metal sulfide molecule FeS. This
apparently simple molecule has been shown to be particularly challenging for
electronic structure theory methods due to the proximity of two low-energy
quintet electronic states of different spatial symmetry. In particular, we show
that, at the triple-zeta basis set level, all sCI results --- including those
extrapolated at the full CI (FCI) limit --- disagree with experiment, yielding
an electronic ground state of symmetry. Performing FN-DMC
simulation with sCI nodes, we show that the correct ground state
is obtained if sufficiently large expansions are used. Moreover, we show that
one can systematically get accurate potential energy surfaces and reproduce the
experimental dissociation energy as well as other spectroscopic constants.Comment: 8 pages, 2 figure and 4 table
Hybrid stochastic-deterministic calculation of the second-order perturbative contribution of multireference perturbation theory
A hybrid stochastic-deterministic approach for computing the second-order
perturbative contribution within multireference perturbation theory
(MRPT) is presented. The idea at the heart of our hybrid scheme --- based on a
reformulation of as a sum of elementary contributions associated with
each determinant of the MR wave function --- is to split into a
stochastic and a deterministic part. During the simulation, the stochastic part
is gradually reduced by dynamically increasing the deterministic part until one
reaches the desired accuracy. In sharp contrast with a purely stochastic MC
scheme where the error decreases indefinitely as (where is the
computational time), the statistical error in our hybrid algorithm displays a
polynomial decay with in the examples considered here. If
desired, the calculation can be carried on until the stochastic part entirely
vanishes. In that case, the exact result is obtained with no error bar and no
noticeable computational overhead compared to the fully-deterministic
calculation. The method is illustrated on the F and Cr molecules. Even
for the largest case corresponding to the Cr molecule treated with the
cc-pVQZ basis set, very accurate results are obtained for for an
active space of (28e,176o) and a MR wave function including up to determinants.Comment: 8 pages, 5 figure
A Jeziorski-Monkhorst fully uncontracted Multi-Reference perturbative treatment I: principles, second-order versions and tests on ground state potential energy curves
The present paper introduces a new multi-reference perturbation approach
developed at second order, based on a Jeziorsky-Mokhorst expansion using
individual Slater determinants as perturbers. Thanks to this choice of
perturbers, an effective Hamiltonian may be built, allowing for the dressing of
the Hamiltonian matrix within the reference space, assumed here to be a CAS-CI.
Such a formulation accounts then for the coupling between the static and
dynamic correlation effects. With our new definition of zeroth-order energies,
these two approaches are strictly size-extensive provided that local orbitals
are used, as numerically illustrated here and formally demonstrated in the
appendix. Also, the present formalism allows for the factorization of all
double excitation operators, just as in internally contracted approaches,
strongly reducing the computational cost of these two approaches with respect
to other determinant-based perturbation theories. The accuracy of these methods
has been investigated on ground-state potential curves up to full dissociation
limits for a set of six molecules involving single, double and triple bond
breaking. The spectroscopic constants obtained with the present methods are
found to be in very good agreement with the full configuration interaction
(FCI) results. As the present formalism does not use any parameter or
numerically unstable operation, the curves obtained with the two methods are
smooth all along the dissociation path.Comment: 4 figures, 18 page
Interplay between electronic correlation and metal-ligand delocalization in the spectroscopy of transition metal compounds: case study on a series of planar Cu complexes
We present a comprehensive theoretical study of the physical phenomena that
determine the relative energies of the three of the lowest electronic states of
each of the square-planar copper complexes \cucl, \cunh and \cuwater, and
present a detailed analysis of the extent to which truncated configuration
interaction (CI) and coupled cluster (CC) theories succeed in predicing the
excitation energies. We find that ligand-metal charge transfer (CT) single
excitations play a crucial role in the correct determination of the properties
of these systems, even though the CT processes first occur at fourth order in
perturbation theory, and propose a suitable choice of minimal active space for
describing these systems with multi-reference theories. CCSD energy differences
agree very well with near full CI values even though the diagnostics are
large, which casts doubt on the usefulness of singles-amplitude based
multi-reference diagnostics. CISD severely underestimates the excitation
energies and the failure is a direct consequence of the size-inconsisency
errors in CISD. Finally, we present reference values for the energy differences
computed using explicitly correlated CCSD(T) and BCCD(T) theory.Comment: 33 pages, 14 figure
Self-Consistent Electron-Nucleus Cusp Correction for Molecular Orbitals
We describe a method for imposing the correct electron-nucleus (e-n) cusp in
molecular orbitals expanded as a linear combination of (cuspless) Gaussian
basis functions. Enforcing the e-n cusp in trial wave functions is an important
asset in quantum Monte Carlo calculations as it significantly reduces the
variance of the local energy during the Monte Carlo sampling. In the method
presented here, the Gaussian basis set is augmented with a small number of
Slater basis functions. Note that, unlike other e-n cusp correction schemes,
the presence of the Slater function is not limited to the vicinity of the
nuclei. Both the coefficients of these cuspless Gaussian and cusp-correcting
Slater basis functions may be self-consistently optimized by diagonalization of
an orbital-dependent effective Fock operator. Illustrative examples are
reported for atoms (\ce{H}, \ce{He} and \ce{Ne}) as well as for a small
molecular system (\ce{BeH2}). For the simple case of the \ce{He} atom, we
observe that, with respect to the cuspless version, the variance is reduced by
one order of magnitude by applying our cusp-corrected scheme.Comment: 23 pages, 5 figure
Development and parallel implementation of selected configuration interaction methods
Cette thĂšse, ayant pour thĂšme les algorithmes de la chimie quantique, s'inscrit dans le cade du changement de paradigme observĂ© depuis une douzaines d'annĂ©es, dans lequel les mĂ©thodes de calcul sĂ©quentielles se doivent d'ĂȘtre progressivement remplacĂ©es par des mĂ©thodes parallĂšles. En effet, l'augmentation de la frĂ©quences des processeurs se heurtant Ă des barriĂšres physiques difficilement franchissables, l'augmentation de la puissance de calcul se fait par l'augmentation du nombre d'unitĂ©s de calcul. Toutefois, lĂ oĂč une augmentation de la frĂ©quence conduisait mĂ©caniquement Ă une exĂ©cution plus rapide d'un code, l'augmentation du nombre de cĆurs peut se heurter Ă des barriĂšres algorithmiques, qui peuvent nĂ©cessiter une adaptation ou un changement d'algorithme. Parmi les mĂ©thodes dĂ©veloppĂ©es afin de contourner ce problĂšme, on trouve en particulier celles de type Monte-Carlo (stochastiques), qui sont intrinsĂšquement "embarrassingly parallel", c'est Ă dire qu'elles sont par construction constituĂ©es d'une multitudes de tĂąches indĂ©pendantes, et de ce fait particuliĂšrement adaptĂ©es aux architectures massivement parallĂšles. Elles ont Ă©galement l'avantage, dans de nombreux cas, d'ĂȘtre capables de produire un rĂ©sultat approchĂ© pour une fraction du coĂ»t calculatoire de l'Ă©quivalent dĂ©terministe exacte. Lors de cette thĂšse, des implĂ©mentations massivement parallĂšles de certains algorithmes dĂ©terministes de chimie quantique ont Ă©tĂ© rĂ©alisĂ©es. Il s'agit des algorithmes suivants : CIPSI, diagonalisation de Davidson, calcul de la perturbation au second ordre, shifted-Bk, et Coupled Cluster Multi RĂ©fĂ©rences. Pour certains, une composante stochastique a Ă©tĂ© introduite en vue d'amĂ©liorer leur efficacitĂ©. Toutes ces mĂ©thodes ont Ă©tĂ© implĂ©mentĂ©es sur un modĂšle de tĂąches distribuĂ©es en TCP, oĂč un processus central distribue des tĂąches par le rĂ©seau et collecte les rĂ©sultats. En d'autres termes, des nĆuds esclaves peuvent ĂȘtre ajoutĂ©s au cours du calcul depuis n'importe quelle machine accessible depuis internet. L'efficacitĂ© parallĂšle des algorithmes implĂ©mentĂ©s dans cette thĂšse a Ă©tĂ© Ă©tudiĂ©e, et le programme a pu donner lieu Ă de nombreuses applications, notamment pour permettre d'obtenir des Ă©nergies de rĂ©fĂ©rences pour des systĂšmes molĂ©culaires difficiles.This thesis, whose topic is quantum chemistry algorithms, is made in the context of the change in paradigm that has been going on for the last decade, in which the usual sequential algorithms are progressively replaced by parallel equivalents. Indeed, the increase in processors' frequency is challenged by physical barriers, so increase in computational power is achieved through increasing the number of cores. However, where an increase of frequency mechanically leads to a faster execution of a code, an increase in number of cores may be challenged by algorithmic barriers, which may require adapting of even changing the algorithm. Among methods developed to circumvent this issue, we find in particular Monte-Carlo methods (stochastic methods), which are intrinsically "embarrassingly parallel", meaning they are by design composed of a large number of independent tasks, and thus, particularly well-adapted to massively parallel architectures. In addition, they often are able to yield an approximate result for just a fraction of the cost of the equivalent deterministic, exact computation. During this thesis, massively parallel implementations of some deterministic quantum chemistry algorithms were realized. Those methods are: CIPSI, Davidson diagonalization, computation of second-order perturbation, shifted-Bk, Multi-Reference Coupled-Cluster. For some of these, a stochastic aspect was introduced in order to improve their efficiency. All of them were implemented on a distributed task model, with a central process distributing tasks and collecting results. In other words, slave nodes can be added during the computation from any location reachable through Internet. The efficiency for the implemented algorithms has been studied, and the code could give way to numerous applications, in particular to obtain reference energies for difficult molecular systems
Développement et implémentation parallÚle de méthodes d'interaction de configurations sélectionnées
This thesis, whose topic is quantum chemistry algorithms, is made in the context of the change in paradigm that has been going on for the last decade, in which the usual sequential algorithms are progressively replaced by parallel equivalents. Indeed, the increase in processors' frequency is challenged by physical barriers, so increase in computational power is achieved through increasing the number of cores. However, where an increase of frequency mechanically leads to a faster execution of a code, an increase in number of cores may be challenged by algorithmic barriers, which may require adapting of even changing the algorithm. Among methods developed to circumvent this issue, we find in particular Monte-Carlo methods (stochastic methods), which are intrinsically "embarrassingly parallel", meaning they are by design composed of a large number of independent tasks, and thus, particularly well-adapted to massively parallel architectures. In addition, they often are able to yield an approximate result for just a fraction of the cost of the equivalent deterministic, exact computation. During this thesis, massively parallel implementations of some deterministic quantum chemistry algorithms were realized. Those methods are: CIPSI, Davidson diagonalization, computation of second-order perturbation, shifted-Bk, Multi-Reference Coupled-Cluster. For some of these, a stochastic aspect was introduced in order to improve their efficiency. All of them were implemented on a distributed task model, with a central process distributing tasks and collecting results. In other words, slave nodes can be added during the computation from any location reachable through Internet. The efficiency for the implemented algorithms has been studied, and the code could give way to numerous applications, in particular to obtain reference energies for difficult molecular systems.Cette thĂšse, ayant pour thĂšme les algorithmes de la chimie quantique, s'inscrit dans le cade du changement de paradigme observĂ© depuis une douzaines d'annĂ©es, dans lequel les mĂ©thodes de calcul sĂ©quentielles se doivent d'ĂȘtre progressivement remplacĂ©es par des mĂ©thodes parallĂšles. En effet, l'augmentation de la frĂ©quences des processeurs se heurtant Ă des barriĂšres physiques difficilement franchissables, l'augmentation de la puissance de calcul se fait par l'augmentation du nombre d'unitĂ©s de calcul. Toutefois, lĂ oĂč une augmentation de la frĂ©quence conduisait mĂ©caniquement Ă une exĂ©cution plus rapide d'un code, l'augmentation du nombre de cĆurs peut se heurter Ă des barriĂšres algorithmiques, qui peuvent nĂ©cessiter une adaptation ou un changement d'algorithme. Parmi les mĂ©thodes dĂ©veloppĂ©es afin de contourner ce problĂšme, on trouve en particulier celles de type Monte-Carlo (stochastiques), qui sont intrinsĂšquement "embarrassingly parallel", c'est Ă dire qu'elles sont par construction constituĂ©es d'une multitudes de tĂąches indĂ©pendantes, et de ce fait particuliĂšrement adaptĂ©es aux architectures massivement parallĂšles. Elles ont Ă©galement l'avantage, dans de nombreux cas, d'ĂȘtre capables de produire un rĂ©sultat approchĂ© pour une fraction du coĂ»t calculatoire de l'Ă©quivalent dĂ©terministe exacte. Lors de cette thĂšse, des implĂ©mentations massivement parallĂšles de certains algorithmes dĂ©terministes de chimie quantique ont Ă©tĂ© rĂ©alisĂ©es. Il s'agit des algorithmes suivants : CIPSI, diagonalisation de Davidson, calcul de la perturbation au second ordre, shifted-Bk, et Coupled Cluster Multi RĂ©fĂ©rences. Pour certains, une composante stochastique a Ă©tĂ© introduite en vue d'amĂ©liorer leur efficacitĂ©. Toutes ces mĂ©thodes ont Ă©tĂ© implĂ©mentĂ©es sur un modĂšle de tĂąches distribuĂ©es en TCP, oĂč un processus central distribue des tĂąches par le rĂ©seau et collecte les rĂ©sultats. En d'autres termes, des nĆuds esclaves peuvent ĂȘtre ajoutĂ©s au cours du calcul depuis n'importe quelle machine accessible depuis internet. L'efficacitĂ© parallĂšle des algorithmes implĂ©mentĂ©s dans cette thĂšse a Ă©tĂ© Ă©tudiĂ©e, et le programme a pu donner lieu Ă de nombreuses applications, notamment pour permettre d'obtenir des Ă©nergies de rĂ©fĂ©rences pour des systĂšmes molĂ©culaires difficiles
La substance spinoziste d'aprĂšs les manuscrits d'auditeurs de Hegel
Garniron Pierre. La substance spinoziste d'aprĂšs les manuscrits d'auditeurs de Hegel. In: Raison prĂ©sente, n°43, Juillet â AoĂ»t â Septembre 1977. SpĂ©cial Spinoza. pp. 81-106