Nuclear orbital

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A nuclear orbital refers to a mathematical function that describes the wave-like behavior of an electron in an atom, representing regions in space where there is a high probability of finding the electron. These orbitals are characterized by specific shapes and energy levels, determined by quantum mechanics.

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Key research themes

1. How can natural orbital methods overcome the challenges of describing nuclear halo structures and improve ab initio nuclear calculations?

This research area focuses on developing and applying natural orbital techniques to address the multiscale complexity of nuclear many-body systems, particularly weakly-bound halo nuclei such as 6He. The goal is to enhance convergence and computational efficiency of ab initio nuclear structure calculations by using optimized single-particle orbitals that better capture short-range correlations and long-range halo features simultaneously.

Natural orbital description of the halo nucleus 6He

by Chrysovalantis Constantinou

2023

Key finding: This paper demonstrates that diagonalizing the one-body density matrix to construct natural orbitals significantly accelerates convergence of no-core configuration interaction (NCCI) calculations for 6He compared to... Read more

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Natural orbitals for theab initiono-core configuration interaction approach

by Chrysovalantis Constantinou

2023, Physical Review C

Key finding: The authors implement natural orbitals within the NCCI framework and show that these orbitals maximize occupation of low-lying orbitals, thus reducing the number of configurations needed for accurate many-body wave functions.... Read more

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2. What are the mechanisms and signatures of nuclear orbiting phenomena in low energy heavy-ion collisions and dinuclear systems?

This theme investigates the formation and properties of long-lived dinuclear complexes in low-energy nuclear reactions, known as orbiting, where two nuclei maintain their identities with inhibited nucleon exchange. Understanding these transient molecular states sheds light on reaction dynamics beyond the compound nucleus picture, the role of entrance channel effects, and excitation energy distributions in nuclear scattering and breakup processes.

Nuclear Orbiting At Low Energy Nuclear Collisions

by Amlan Ray

2023, Nuclear Physics A

Key finding: The study identifies projectile-like fragment emissions exhibiting 1/sinθ c.m. angular distributions and strong entrance channel dependence, characteristic of orbiting dinuclear complexes in light and medium-heavy ion... Read more

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3. How can computational methods combining nuclear and electronic degrees of freedom advance nuclear orbital calculations beyond the Born-Oppenheimer approximation with improved scaling?

This research area develops and applies nuclear molecular orbital (NMO) methods that treat selected nuclei quantum-mechanically along with electrons within unified wave functions. By employing localized Hartree product nuclear wave functions and auxiliary density functional theory (ADFT) for electrons, these approaches achieve cubic computational scaling while capturing nuclear quantum effects—making calculations on larger nuclei and systems tractable beyond traditional methods relying on Born-Oppenheimer separation.

Non-Born–Oppenheimer self-consistent field calculations with cubic scaling

by Roberto Flores-Moreno

2016, Chemical Physics

Key finding: The authors introduce a method combining electronic ADFT and a localized Hartree product for nuclear wave functions (ADFT/LHP) that achieves cubic scaling in basis size, a significant improvement over traditional quartic... Read more

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Non-Born-Oppenheimer Self-Consistent Field Calculations with Cubic Scaling

by Felix Moncada

2012

Key finding: This paper presents the derivation and implementation of the ADFT/LHP approach, demonstrating combined computational efficiency and accuracy for including nuclear quantum effects in molecular systems. By employing an... Read more

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Localized Hartree Products as Nuclear Wavefunctions

by Felix Moncada

2011

Key finding: The study argues that replacing nuclear Slater determinants with Hartree products in nuclear orbital molecular orbital (NOMO) frameworks drastically reduces computational cost without compromising physical accuracy. The... Read more

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All papers in Nuclear orbital

LOWDIN: The any particle molecular orbital code

by Sergio Gonzalez

2023, International Journal of Quantum Chemistry

LOWDIN is a computational program that implements the Any Particle Molecular Orbital (APMO) method. The current version of the code encompasses Hartree-Fock, second-order Mïller-Plesset, configuration interaction, density functional, and... more

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A generalized any-particle propagator theory: Prediction of proton affinities and acidity properties with the proton propagator

by Jonathan Romero

2023, The Journal of Chemical Physics

We have recently extended the electron propagator theory to the treatment of any type of particle using an Any-Particle Molecular Orbital (APMO) wavefunction as reference state. This approach, called APMO/PT, has been implemented in the... more

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LOWDIN: The any particle molecular orbital code

by Jonathan Romero

2023, International Journal of Quantum Chemistry

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Hydrogen isotope effects on covalent and noncovalent interactions: The case of protonated rare gas clusters

by Jonathan Romero

2023, International Journal of Quantum Chemistry

We investigate hydrogen isotope and nuclear quantum effects on geometries and binding energies of small protonated rare gas clusters (Rg n X þ , Rg ¼ He,Ne,Ar, X ¼ H,D,T, and n ¼ 1-3) with the any particle molecular orbital (APMO) MP2... more

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A generalized any-particle propagator theory: Prediction of proton affinities and acidity properties with the proton propagator

by ROBERTO FLORES MORENO

2023, The Journal of Chemical Physics

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LOWDIN: The any particle molecular orbital code

by Jonathan Romero

2023, International Journal of Quantum Chemistry

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Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

by María Pilar de Lara-Castells

2021, The Journal of Chemical Physics

An interface between the APMO code and the electronic structure package MOLPRO is presented. The any particle molecular orbital APMO code [González et al., Int. J. Quantum Chem. 108, 1742 (2008)] implements the model where electrons and... more

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GPW (GAPW) electronic structure calculations

by pan chang

2018

The density is the probability distribution of the wave functions the potential and hence also the total energy are unique functional of the electronic density n(r)

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Hybrid Functionals with Variationally Fitted Exact Exchange

by Jorge Martin del Campo Ramirez

2016

The fitting coefficients are collected in the vector x. The Coulomb matrix ¢ is defined as L he Coulomb matrix G 1s symmetric and positive aennite which guarantees the minimization in Eq. (11). In principle, the very efficient Cholesky decomposition algorithm can be used to solve the fitting equation system. ill However, if very large auxiliary function sets are used, G tends to become I-conditioned. In order to avoid numerical instabilities by solving the fi tting equations with the Cholesky decomposition approach, deMon2k performs a singular value decomposition (SVD) at the beginning of the SCF and uses a robust numerical solver’ that acts only on the nonredundant space of the SVD for subsequent solutions. Performing a full SVD is time consuming; however, the stability gained during the initial SCF and the application of the numerical solver even for different geometries (for exam- ple, in a geometry optimization or along a BOMD trajectory) overcompen- sate the computational load of the SVD.

Bear in mind that the contribution from the Becke 88 exchange func- tional’* appearing in the B3LYP energy expression is only from the nonlocal part of the functional. The variation of any of these energy expressions with respect to the MO coefficients, under the MO ortho- normality constraints, leads to Roothaan—Hall equation systems. The hybrid ADFT Kohn—-Sham matrix has contributions from the variation of Egxx, the expansion of the auxiliary orbital products (Eq. 28). Note, however, that this is the result of a variational fitting as described above. If the approxi- mated exact exchange energy expression of Eq. (35) is added to the self- interaction including Hartree energy with Coulomb fitting, the variationally fitted self-interaction-free Hartree-Fock energy expression is obtained.”” On the other hand, if the fitted exact exchange energy is combined with exchange-correlation functionals, hybrid ADFT energy expressions without four-center ERIs are obtained. In particular, we find the following ADFT or DF-DFT energy expressions for the here discussed B3LYP (J (Eq. 36b), and M06-2X (Eq. 36c) functionals: Eq. 36a), PBI - EO E

Figure 1 CPU timing breakdown for single-point calculations of linear alkane chains 2mploying the B3LYP hybrid functional and the auxiliary density functional theory ADFT) methodology.

Timings are very different for the hybrid meta-GGA M06-2X. Figure 3 shows that the most demanding computational task here 1s the calculation of the exchange-correlation contribution. For the largest alkane, this task accounts for almost 50% of the total CPU time. The increased workload arises from the computation of the kinetic energy density t(r) and the t-dependent part of the Kohn—Sham matrix on the grid that prevents the use of ADFT. Nevertheless, the difference between LDF-DFT and LDF-ADFT timings is rather small for linear alkane chains (compare

Figure 4 Comparison of amylose, helix (top) and linear alkane chain C49Hg2 (bottom) extension. End-to-end distance is about 50 A for the amylose helix and 49 A for the alkane chain.

Figure 5 CPU timing breakdown for the first two SCF iterations for amylose helices described with the PBEO hybrid functional and the auxiliary density functional theory (ADFT) methodology.

Figure 6 CPU timing breakdown for the first two SCF iterations for amylose helices described with the PBEO hybrid functional and the density-fitting density functional the- ory (DF-DFT) methodology.

All energies are in kcal/mol. Vn order to validate our hybrid DFA implementations, we compared several properties that depend on energy differences. First, we performed calculations of standard enthalpies of formation AH?” using the G3/99X test set.””"’" The protocol for calculating AHf’* was the one established by Curtiss and collaborators.”” The values of mean absolute error (MAE) BI with respect to experiment’ are reported in Tables 1, 2, and 3 for B3LYP, PBEO, and MO “Heats of formation.” S 6-2X, respectively. They are listed under the entry tandard DFT results from NW Chem calculations for these three DFAs are also included in each table under the “DFT” column. As Tables 1-3 show, all the DFT reference. T | LDF-DFT MAI M06-2X functional. Al Fs are in excellent agreement with he largest deviation is only 0.05 kcal/mol for the though M06-2X uses a significant fraction of exact exchange (54%), part of the observed small deviations may also arise from LDF-EXX computation, for example, integration errors specific to the M06 suite.”” The use of LDF-ADFT increases the MAE for heats of formation with B3LYP, but decreases the same quantity for PBEO. This difference between LDF-DFT and LDF-ADFT is mainly sources other than the

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Non-Born–Oppenheimer self-consistent field calculations with cubic scaling

by Roberto Flores-Moreno

2016, Chemical Physics

An efficient nuclear molecular orbital methodology is presented. This approach combines an auxiliary density functional theory for electrons (ADFT) and a localized Hartree product (LHP) representation for the nuclear wave function. A... more

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Spin in density-functional theory

by Markus Reiher

2016, International Journal of Quantum Chemistry

The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. While density-functional theory (DFT) is widely applied in this area, the... more

to arrive at (employing the convention of implicit summation over repeated indices) and by reordering the different terms we get

and smart algorithms for inverse quantum chemistry.

Kohn-Sham reference systems of noninteracting electrons.

interacting reference system leads to these Euler-Lagrange equations The minimization of the total energy functional BE [Pa; Pa) of the spin-unrestricted non-

agrees with the corresponding one of the fully interacting system.

Table of Contents Graphics and Text are discussed, and we suggest some possible future directions for Spin-DFT.

the nonrelativistic spin density, ere the superscript “U” and “L” denote the upper and lower components, respectively.

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Structure and dynamics of small protonated rare-gas clusters using quantum and classical methods

by Francesco Filippone

2015, Computer Physics Communications

The possible structures of small He and Ar clusters containing H + as ionic impurity are shown to be amenable to a detailed analysis of their structures and of the dynamical evolution by means of Ab Initio Molecular Dynamics (AIMD)... more

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Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

by Malgorzata Biczysko

2015, The Journal of Chemical Physics

An interface between the APMO code and the electronic structure package MOLPRO is presented. The any particle molecular orbital APMO code [González et al., Int. J. Quantum Chem. 108, 1742 implements the model where electrons and light... more

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Hydrogen isotope effects on covalent and noncovalent interactions: The case of protonated rare gas clusters

by Andres Reyes

2015, International Journal of Quantum Chemistry

We investigate hydrogen isotope and nuclear quantum effects on geometries and binding energies of small protonated rare gas clusters (RgX + n , Rg=He,Ne,Ar, X=H,D,T and n=1-3) with the Any Particle Molecular Orbital (APMO) MP2 level of... more

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LOWDIN: The any particle molecular orbital code

by Felix Moncada

2015

LOWDIN is a computational program that implements the Any Particle Molecular Orbital (APMO) method. The current version of the code encompasses Hartree–Fock, second-order Møller–Plesset, configuration interaction, density functional, and... more