# Auxiliary Density

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### Andreas M. Köster – 1st expert on this subject based on the ideXlab platform

• ##### mixed second and third energy derivatives from AuxiliaryDensity perturbation theory
Molecular Physics, 2019
Co-Authors: Rogelio Isaac Delgadovenegas, Patrizia Calaminici, Andreas M. Köster

Abstract:

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…

• ##### Accuracy of AuxiliaryDensity functional theory hybrid calculations for activation and reaction enthalpies of pericyclic reactions
Journal of Molecular Modeling, 2018
Co-Authors: José R. Gómez-pérez, Patrizia Calaminici, Francisco A. Delesma, Andreas M. Köster

Abstract:

Auxiliary Density functional theory (ADFT) hybrid calculations are based on the variational fitting of the Coulomb and Fock potential and, therefore, are free of four-center electron repulsion integrals. So far, ADFT hybrid calculations have been validated successfully for standard enthalpies of formation. In this work the accuracy of ADFT hybrid calculations for the description of pericyclic reactions was quantitatively validated at the B3LYP/6-31G*/GEN-A2* level of theory. Our comparison with conventional Kohn-Sham Density functional theory (DFT) results shows that the DFT and ADFT activation and reaction enthalpies are practically indistinguishable. A systematic study of various functionals (PBE, B3LYP, PBE0, CAMB3LYP, CAMPBE0 and HSE06) and basis sets (6-31G*, DZVP-GGA and aug-cc-pVXZ; X = D, T and Q) revealed that the ADFT HSE06/aug-cc-pVTZ/GEN-A2* level of theory yields best balanced accuracy for the activation and reaction enthalpies of the studied pericyclic reactions. With the successfully validate ADFT composite approach consisting of PBE/DZVP-GGA/GEN-A2* structure and transition state optimizations and single-point HSE06/aug-cc-pVTZ/GEN-A2* energy calculations, an accurate, reliable and efficient computational approach for the study of pericyclic reactions in systems at the nanometer scale is proposed.

• ##### The melting limit in sodium clusters
Theoretical Chemistry Accounts, 2018
Co-Authors: José Manuel Vásquez-pérez, Andreas M. Köster, Patrizia Calaminici

Abstract:

Thermodynamic properties of the small sodium clusters $$\hbox {Na}_6,\, \hbox {Na}_8$$ Na 6 , Na 8 and $$\hbox {Na}_{10}$$ Na 10 have been studied by Born–Oppenheimer molecular dynamics (BOMD) simulations. The simulations were performed with Auxiliary Density functional theory as implemented in the deMon2k code. This approach has already proved accurate for the calculations of thermodynamic properties of larger sodium clusters. The Nosé–Hoover chain thermostat was applied to control the temperature. BOMD simulations were performed in the temperature range from 250 to 1000 K. The obtained trajectories were analyzed using the multiple-histogram method in order to obtain continuous functions for the energies and heat capacities. For the $$\hbox {Na}_6$$ Na 6 and $$\hbox {Na}_8$$ Na 8 clusters, besides the fragmentation of the clusters at higher temperature, no other characteristic features in the heat capacity curves are found. On the other hand, a small peak at low temperature was found in the $$\hbox {Na}_{10}$$ Na 10 heat capacity curve which is characteristic for molecular melting. Our analysis of the $$\hbox {Na}_{10}$$ Na 10 melting shows that electronic structure parameters are better suited than geometrical ones to describe the melting process due to the fluctional nature of the clusters. We find that energetical resorting of the occupied cluster orbitals is characteristic for the $$\hbox {Na}_{10}$$ Na 10 cluster melting.

### Patrizia Calaminici – 2nd expert on this subject based on the ideXlab platform

• ##### On the structural, energetic, and magnetic properties of M@Pd (M = Co, Ni, and Cu) core-shell nanoclusters and their comparison with pure Pd nanoclusters
Journal of Magnetism and Magnetic Materials, 2020
Co-Authors: H. Cruz-martínez, Patrizia Calaminici, Omar Solorza-feria, D.i. Medina

Abstract:

Abstract Electronic structure computations of pure Pd and Pd-based core–shell clusters were studied employing Auxiliary Density functional theory (ADFT). For this investigation icosahedral clusters with 13 and 55 atoms and octahedral clusters with 19 and 44 atoms were employed to analyze the change in the properties of the Pd and M@Pd core–shell clusters. All properties calculated for the M@Pd clusters are directly compared with the ones of pure palladium clusters. Spin multiplicities, spin magnetic moments, spin densities, binding energies per atom, segregation energies, and average bond lengths were calculated to understand their changes when varying the size, composition and shape of the M@Pd (M = Co, Ni, and Cu) core–shell clusters. The M1@Pd12 and M1@Pd18 (M = Co and Cu) clusters exhibit changes in the spin multiplicity and spin magnetic moment with respect to the Pd13 and Pd19 clusters, respectively, whereas the Ni1@Pd12 and Ni1@Pd18 clusters maintain the same properties as their pure Pd counterparts. The spin multiplicities and spin magnetic moments of the M6@Pd38 and M13@Pd42 (M = Co, Ni, and Cu) clusters greatly differ from their pure Pd counterparts. This study reveals that the Pd-Pd bond lengths are shorter in the M@Pd core–shell clusters compared to the ones of pure Pd clusters. This work demonstrates that the binding energy per atom of the M@Pd core–shell clusters is greater than the binding energy per atom of the pure Pd clusters. The calculated segregation energies indicate that 3d atoms prefer to be in the center of core–shell systems.

• ##### Catalytic activity trends from pure Pd nanoclusters to M@PdPt (M = Co, Ni, and Cu) core-shell nanoclusters for the oxygen reduction reaction: A first-principles analysis
International Journal of Hydrogen Energy, 2020
Co-Authors: H. Cruz-martínez, Patrizia Calaminici, Omar Solorza-feria, M.m. Tellez-cruz, D.i. Medina

Abstract:

Abstract The trends of the catalytic activity toward the oxygen reaction reduction (ORR) from Pd44 nanoclusters to M6@Pd30Pt8 (M = Co, Ni, and Cu) core-shell nanoclusters was investigated using Auxiliary Density functional theory. The adsorption energies of O and OH were computed as predictors of the catalytic activity toward the ORR and the following tendency of the electrocatalytic activity was computed: Pt44 ≈ M6@Pd30Pt8 > M6@Pd38 > Pd44. In addition, the adsorption of O2 on the Ni6@Pd30Pt8 and Pt44 nanoclusters were investigated, finding an elongation of the O–O bond length when O2 is adsorbed on the Ni6@Pd30Pt8 and Pt44 nanoclusters, suggesting that the O2 is activated. Finally, the stabilities of the M6@Pd38 and M6@Pd30Pt8 core-shell nanoclusters were analyzed both in vacuum and in oxidative environment. From the calculated segregation energies for the bimetallic and trimetallic nanoclusters in vacuum, it can be clearly observed that the M atoms prefer to be in the center of the M6@Pd38 and M6@Pd30Pt8 nanoclusters. Nevertheless, it is observed that the segregation energies of M atoms for the M6@Pd38 nanoclusters with an oxidizing environment tend to decrease compared with their M6@Pd38 nanoclusters counterparts in vacuum, which suggests that in an oxidative environment, M atoms may tend to segregate to the surface of the M6@Pd38 nanoclusters.

• ##### mixed second and third energy derivatives from AuxiliaryDensity perturbation theory
Molecular Physics, 2019
Co-Authors: Rogelio Isaac Delgadovenegas, Patrizia Calaminici, Andreas M. Köster

Abstract:

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…

### Gerald Geudtner – 3rd expert on this subject based on the ideXlab platform

• ##### Molecular graphs of $$\hbox {Mo}_{2n}\hbox {C}_n$$ Mo
Theoretical Chemistry Accounts, 2016
Co-Authors: Domingo Cruz-olvera, Gerald Geudtner, Patrizia Calaminici

Abstract:

The analysis of the molecular graphs of the electron Density $$(\rho )$$ ( ρ ) and the molecular electrostatic potential for molybdenum carbide clusters $$\hbox {Mo}_{2n}\hbox {C}_n$$ Mo 2 n C n with n  = 1–10 is presented. For the underlying topological analysis, calculations were performed within the framework of Kohn–Sham Auxiliary Density functional theory employing the linear combination of Gaussian-type orbitals Auxiliary Density functional theory approach. The study was performed considering the ground-state structures of each cluster. Molecular graphs of the Density as well as the molecular electrostatic potential are reported. The differences in the topology of the electron Density and of the molecular electrostatic potential as well as the corresponding molecular graphs of the studied clusters are discussed. This study confirms that C–C bonds are formed for cluster sizes characterized by n  = 3, 5 and 6 and provides information about the nature of these bonds.

• ##### Molecular graphs of \hbox {Mo}_{2n}\hbox {C}_n (n = 1–10) clusters
Theoretical Chemistry Accounts, 2016
Co-Authors: Domingo Cruz-olvera, Gerald Geudtner, Patrizia Calaminici

Abstract:

The analysis of the molecular graphs of the electron Density $$(\rho )$$ and the molecular electrostatic potential for molybdenum carbide clusters $$\hbox {Mo}_{2n}\hbox {C}_n$$ with n = 1–10 is presented. For the underlying topological analysis, calculations were performed within the framework of Kohn–Sham Auxiliary Density functional theory employing the linear combination of Gaussian-type orbitals Auxiliary Density functional theory approach. The study was performed considering the ground-state structures of each cluster. Molecular graphs of the Density as well as the molecular electrostatic potential are reported. The differences in the topology of the electron Density and of the molecular electrostatic potential as well as the corresponding molecular graphs of the studied clusters are discussed. This study confirms that C–C bonds are formed for cluster sizes characterized by n = 3, 5 and 6 and provides information about the nature of these bonds.

• ##### magnetizability tensors from AuxiliaryDensity functional theory
Journal of Chemical Physics, 2012
Co-Authors: Bernardo Zunigagutierrez, Gerald Geudtner, Andreas M. Köster

Abstract:

The working equations for the calculation of the magnetizability tensor in the framework of Auxiliary Density functional theory with gauge including atomic orbitals (ADFT-GIAO) are derived. Unlike in the corresponding conventional Density functional theory implementations the numerical integration of the GIAOs is avoided in ADFT-GIAO. Our validation shows that this simplification has no effect on the accuracy of the methodology. As a result, a reliable and efficient implementation for the calculation of magnetizabilities of systems with more than 1000 atoms and 14 000 basis functions is presented.