Type Orbitals Research Articles

Extending GPU-accelerated Gaussian integrals in the TeraChem software package to f type orbitals: Implementation and applications.

The increasing availability of graphics processing units (GPUs) for scientific computing has prompted interest in accelerating quantum chemical calculations through their use. However, the complexity of integral kernels for high angular momentum basis functions often limits the utility of GPU implementations with large basis sets or for metal containing systems. In this work, we report the implementation of f function support in the GPU-accelerated TeraChem software package through the development of efficient kernels for the evaluation of Hamiltonian integrals. The high efficiency of the resulting code is demonstrated through density functional theory (DFT) calculations on increasingly large organic molecules and transition metal complexes, as well as coupled cluster singles and doubles calculations on water clusters. Preliminary investigations into Ni(I) catalysis with DFT and the photochemistry of MnH(CH3) with complete active space self-consistent field are also carried out. Overall, our GPU-accelerated software appears to be well-suited for fast simulation of large transition metal containing systems, as well as organic molecules.

Electron-electron-ion triple-coincidence experiment of electron-initiated valence ionization of small water clusters

The ionization and fragmentation of small water clusters induced by electron impact (80 eV) is investigated. Using a multiparticle coincidence spectrometer (reaction microscope), all three charged final state particles—two outgoing electrons and one fragment ion—are detected. Nonprotonated (H2O)2+ and protonated water clusters H3O+, [H2O]2H+, [H2O]4H+, and [H2O]5H+ are identified in the measured ion spectrum. The ionization channels for formation of these species are investigated by measuring the kinetic energy distributions and the electronic states of the ions. Only a single state can lead to (H2O)2+, which is identified as ionization of water dimer with a 1b1 hole at the hydrogen bonding donor molecule, while for the protonated water species three major electronic states corresponding to the ionization of 1b1, 3a1, and 1b2 type orbitals are observed. Published by the American Physical Society 2024

Triple Electron Attachments with a New Intermediate-Hamiltonian Fock-Space Coupled-Cluster Method.

The implementation of a new intermediate-Hamiltonian Fock-space coupled-cluster (IHFSCC) scheme for the (3,0) sector of the Fock space is reported. In this IHFSCC approach, the three-body contributions in the cluster operator S(3,0) corresponding to the (3,0) sector of the Fock space are considered, while S(1,0) and S(2,0) at the (1,0) and (2,0) level only include one- and two-body operators. By introducing a suitable partition of the wave operator, the intermediate Hamiltonian, which only depends on the two-body operator of S(1,0), is obtained. S(2,0) and S(3,0) are not required within this new IHFSCC scheme, and a large reference space can be possibly employed. The performance of this (3,0) IHFSCC method in calculating triple ionization potentials and excitation energies for atoms and cations with a ground p3 configuration as well as adiabatic excitation energies for some molecules is investigated. The effect of the number of active virtual orbitals and three different types of orbitals, i.e., reference orbitals, restricted open-shell Hartree-Fock orbitals (ROHF) of the target systems, and canonicalized ROHF orbitals, on IHFSCC results, is also studied. Our calculations indicate that reasonable results can be achieved with this (3,0) IHFSCC method when a minimal reference space is employed. Further increasing the number of active orbitals does not necessarily improve the results. In addition, the IHFSCC results using canonicalized ROHF orbitals generally agree well with reference values, and they are not very sensitive to the number of active orbitals compared with results using the reference orbitals. The new (3,0) IHFSCC method can be applied to open-shell systems with three unpaired electrons with reasonable accuracy at a relatively low computational cost.

Revealing the surface structure and morphology evolution of Co nanoparticle supported on ZrO2 surfaces

The optimization of structure-dependent activity of supported metal catalysts has driven the dynamic determination of the morphology of Co nanoparticles on ZrO2 using atomic-level simulations. Density functional theory (DFT) calculations combined with ab initio molecular dynamics (AIMD) simulations were used to investigate the surface structure, nucleation mechanism and morphology evolution of Con clusters supported on different ZrO2 facets. As the size of the Con (n = 1–5) cluster increases, the competition between Co-Co bonding and the interaction of Con clusters with the ZrO2 surface further promotes the nucleation of larger clusters. Co atoms prefer to nucleate into large clusters on both c-ZrO2(111) and t-ZrO2(101) surfaces, but this behavior is unfavorable on the m-ZrO2(-111) surface. The analysis of electric properties suggests that the types of hybrid orbitals and the number of electron transfer accounts for the difference in energies of Con clusters on ZrO2 surfaces. Further, the AIMD simulations verified the stable structure of small Co5 cluster obtained by DFT, and predicted the morphology of large Co13 clusters on ZrO2 surfaces under realistic reaction conditions, consistent with the experimental SAM images. Our work provides an intuitive understanding of structure and morphology evolution of catalysts for the targeted design of catalysts to achieve the desired activity and explore more reaction possibilities.

The updates in Libcint 6: More integrals, API refinements, and SIMD optimization techniques.

Libcint is a library designed for the evaluation of analytical integrals for Gaussian type orbitals. It prioritizes simplicity, ease of use, and efficiency for the development of quantum chemistry programs. In the release of version 6.0, Libcint supports the computation of integrals for various operators, such as overlap, Coulomb, Gaunt, Breit, attenuated Coulomb, Slater-type geminals, and Yukawa potential, as well as arbitrary orders of derivatives for these operators. To enhance the usability of the library, Libcint provides a uniform function signature for all integral functions. A code generator is included to automate the implementation of new integrals. To achieve better performance on modern central processing unit architectures, the library employs explicit single instruction multiple data parallelization in the code implementation.

Efficient periodic resolution-of-the-identity Hartree-Fock exchange method with k-point sampling and Gaussian basis sets.

Simulations of condensed matter systems at the hybrid density functional theory level pose significant computational challenges. The elevated costs arise from the non-local nature of the Hartree-Fock exchange (HFX) in conjunction with the necessity to approach the thermodynamic limit. In this work, we address these issues with the development of a new efficient method for the calculation of HFX in periodic systems, employing k-point sampling. We rely on a local atom-specific resolution-of-the-identity scheme, the use of atom-centered Gaussian type orbitals, and the truncation of the Coulomb interaction to limit computational complexity. Our real-space approach exhibits a scaling that is, at worst, linear with the number of k-points. Issues related to basis set diffuseness are effectively addressed through the auxiliary density matrix method. We report the implementation in the CP2K software package, as well as accuracy and performance benchmarks. This method demonstrates excellent agreement with equivalent Γ-point supercell calculations in terms of relative energies and nuclear gradients. Good strong and weak scaling performances, as well as graphics processing unit (GPU) acceleration, make this implementation a promising candidate for high-performance computing.

On the influence of metal nanoparticle and π-system sizes in the stability of noncovalent adducts: a theoretical study.

Herein we have computationally evaluated the relationship between Ag and Au nanoparticle (Ag/AuNP) size and π-surface extension in the formation of noncovalent complexes at the PBE0-D3/def2-TZVP level of theory. The NP-π interaction is known in supramolecular chemistry as a Regium-π bond (Rg-π), and differentiates from classical coordination bonds in strength and type of metal orbitals involved. In this study, the Rg-π complexes involved small Ag/AuNPs composed by 1 to 5 atoms and benzene, naphthalene and anthracene as π-systems, being characterized using several molecular modeling tools, including molecular electrostatic potential (MEP) calculations, energy decomposition analysis (EDA), quantum theory of atoms in molecules (QTAIM), non covalent interaction plot (NCIplot) and natural bonding orbital (NBO) methodologies. We believe the results reported herein will be useful for those scientists working in catalysis, molecular recognition and materials science fields, where structural-energetic relationships of weak interactions are crucial to achieve product selectivity, a particular molecular recognition mode or a specific molecular assembly.

In English

The equilibrium and spatial structure of the polycyclic aromatic hydrocarbon C96H24, chosen as a model of the graphene plane, as well as the systems obtained from it by removing the diatomic molecule C2 (C94H24) and then replacing four carbon atoms with four nitrogen atoms (C90N4H24) have been studied by the DFT method (B3LYP) in the 6-31G** basis using Grimme corrections to account for dispersion interactions. In the same approximation, the energetics of the formation of a complex of an iron atom in zero oxidation degree (Fe0) with C90N4H24 ([C90N4H24Fe]0) in the square planar field of the ligand has been studied. The types of molecular orbitals of the ligand, which correspond to the symmetry of the atomic d-orbitals of the Fe atom, have been determined. Interaction diagrams of the d-orbitals of the Fe atom with some molecular orbitals of the ligand C90N4H24 of the corresponding symmetry are constructed. It is concluded that the binding of the transition metal atom on the double vacancy of the graphene plane can be rationally described based on the local symmetry of the coordination center and molecular orbitals of the ligand and the formed complex.

Discrimination of leucine and isoleucine via fragmentation by electromagnetic field.

We conduct comparative numerical studies of the effects of electric dipole field and electromagnetic radiation field on the amino acids leucine and isoleucine. Since they are structural isomers, distinguishing them by mass is a non-trivial task, while determination of protein structure can be crucial on many occasions. We emphasize the influence of the magnetic field of radiation by utilizing a modified basis sets with correction coefficients to the [Formula: see text] and [Formula: see text] orbitals following the Anisotropic Gaussian Type Orbitals method. Studying the electric potential of the isomers in dipole electric or electromagnetic fields proves that the different layout of leucine vs isoleucine is the main reason why some fragments could not be formed during chemical bond cleavage. Comparison of the chemical structure of the fragments created due to the decomposition of the isomers in the dipole electric or electromagnetic fields shows that their decomposition products are different. These findings can be used also for discrimination between the two isoleucine conformers, for which the cleavage starts at different values of the dipole electric field strength, as well as the products of the decomposition reaction are not identical. Our numerical calculations of the fragmentation outcomes, taking into account the magnetic field effects, can serve as a guidance for discrimination between the isomers/conformers. We applied the Becke's three-parameter hybrid functional approach with non-local correlation by Lee, Yang, and Parr ([Formula: see text]), together with the [Formula: see text] basis set as it is implemented in the GAUSSIAN09 quantum chemistry package in order to obtain the most stable conformers of leucine and isoleucine. We used the options provided by GAUSSIAN09 to add finite external field in order to perform the calculations of leucine and isoleucine in the electric dipole and electromagnetic fields. The Anisotropic Gaussian Type Orbitals method was used to obtain the correction coefficients which modify the original [Formula: see text] basis set in order to account for the effects of magnetic field of radiation. Results were visualized and the electrical potentials analyzed by the Molden visualization program.

Lah Number Mediated Analytical Two‐center Two‐electron Integrals of Coulomb Green Function of H‐like Orbitals for 1Σ States

AbstractEnergetics of two‐center two‐electron (2c–2e) systems carry challenges in theoretical understanding of Schrödinger equation (SE) for well‐known divergence of Coulomb interactions and nuclear separation (R) in modified H‐like AOs, Slater type orbitals (STOs), Gaussian type orbitals (GTOs), B‐spline, Sturmian function and etc. employed to VBT and MOT. Certain elegant computational and analytical techniques were developed for STO, GTO and other square integrable basis set within Born‐Oppenheimer (BO) approximation. STOs and GTOs have an essential limitation of absence of radial nodes. Thus, analytical treatment has become an urge for H‐like AOs. We have considered the diatomic molecules only for the sake of simplicity. Employing Sheffer identity in associated Laguerre polynomial/Whittaker‐M function forms of H‐like AOs and transforming integrals into elliptic coordinates with two nuclei on two foci furnishes exact, analytical and simple Coulomb integrals (Js) in terms of R. Lah number originated from for nuclear coordinates only due to Sheffer identity shows that energetics of diatomic molecules can be anticipated as extremum function of R. Therefore, the optimization of potential energy surface (PES) of electrons as gradient of R may lead to σ‐bond formation. In this paper, we have developed diagonal Js for bound states of H2 molecule.

On the calculation of lanthanide systems. The spectral parameters of praseodymium trivalent ion

In this work, taking the Pr(III) ion as a suitable case study, the authors test the capacity of a series of Gaussian Type Orbitals (GTOs) basis sets to account for the atomic spectra of lanthanide ions. An extended relevance of this assessment can be found in modeling the luminescence of lanthanide-based materials. It was selected the Pr(III) case because it shows a rather rich collection of experimental data, emerging from the f2 and fd configurations. The energy barycenters of spectral multiplets can be equated analytically in terms of the so-called Slater-Condon parameters. By multi-configurational ab initio procedures, with basis sets from existing GTO repositories, the calculated f→f transitions are moderately higher than the experimental values, while the relative energies of Fd states undergo both under- and over-estimation. The GTO shortcomings, that are impacting the accuracy, were debated, the critical perspective spreading the seeds of future development.

A Bi−directional method for evaluating integrals involving higher transcendental functions. HyperRAF: A Julia package for new hyper−radial functions

The electron repulsion integrals over Slater−type orbitals with non−integer principal quantum numbers are investigated. These integrals are useful in both non−relativistic and relativistic calculations of many−electron systems. They involve hyper−geometric functions that are practically difficult to compute. Relationships free from hyper−geometric functions for expectation values of Coulomb potential (r21−1) are derived. These relationships are new and show that the complication coming from two−range nature of Laplace expansion for the Coulomb potential is removed. This is achieved by utilizing auxiliary functions represented in finite power series. They serve as essential components in deriving straightforward recurrence relationships for electron repulsion integrals. In the context of computing the expectation values of potentials with arbitrary power, the methodology presented here for evaluation of these integrals forms the initial condition. It is also adapted to multi−center integrals. Program summaryProgram Title: HyperRAFCPC Library link to program files:https://doi.org/10.17632/6pbv2y7s42.1Developer's repository link:https://github.com/abagciphys/HyperRAF.gitLicensing provisions: MITProgramming language:Julia Programming Language [1]Supplementary material: An exploratory variant of the software program written in the Mathematica Programming Language [2].External routines/libraries:Nemo, a computer algebra package for the Julia programming language [3], JRAF, a Julia package for computation of relativistic molecular auxiliary functions [4].Nature of problem: Definite integrals involving higher transcendental functions given by,fmn1(a,b,x)=xm−1e−bxΓ[n,ax], andfmn2(a,b,x)=xm−1e−bxγ[n,ax] are frequently encountered in atomic physics, with the electron repulsion integral being a notable illustration.For exclusive solutions to these integrals, one can refer to Erdélyi's [5] or Gradshteyn and Ryzhik's [6] books. The solutions are obtained by using the series representation of incomplete gamma functions. The result is hyper−geometric functions of the form F12[1,b,c;z], where b=m+n, c=m+1, z=b/(a+b) for fmn1(a,b,x) and c=n+1, z=a/(a+b) for fmn2(a,b,x), respectively. Due to the non−trivial structure of infinite series that are used to define them, the computation for hyper−geometric poses challenges. Convergence of their series strictly depends on the values of parameters. Computational issues such as cancellation or round−off error emerge.Solution method: This research introduces novel bi−directional hyper−radial functions that are used to establish fresh recurrence relationships for electron repulsion integrals, eliminating the dependence on hyper−geometric functions. Dual functionality is inherent in the hyper−radial functions as they offer alternative solutions for definite integrals involving higher transcendental functions. Additionally, they transform the representation of the hyper−geometric functions into finite power series.

DFT Study of WS2-Based Nanotubes Electronic Properties under Torsion Deformations.

In this study, the influence of torsional deformations on the properties of chiral WS2-based nanotubes was investigated. All calculations presented in this study were performed using the density functional theory (DFT) and atomic gaussian type orbitals basis set. Nanotubes with chirality indices (8, 2), (12, 3), (24, 6) and (36, 9) corresponding to diameters of 10.68 Å, 14.90 Å, 28.26 Å and 41.90 Å, respectively, are examined. Our results reveal that for nanotubes with smaller diameters, the structure obtained through rolling from a slab is not optimal and undergoes spontaneous deformation. Furthermore, this study demonstrates that the nanotube torsion deformation leads to a reduction in the band gap. This observation suggests the potential for utilizing such torsional deformations to enhance the photocatalytic activity of the nanotubes.

X-ray Spectroscopy Study of Defect Contribution to Lithium Adsorption on Porous Carbon.

Lithium adsorption on high-surface-area porous carbon (PC) nanomaterials provides superior electrochemical energy storage performance dominated by capacitive behavior. In this study, we demonstrate the influence of structural defects in the graphene lattice on the bonding character of adsorbed lithium. Thermally evaporated lithium was deposited in vacuum on the surface of as-grown graphene-like PC and PC annealed at 400 °C. Changes in the electronic states of carbon were studied experimentally using surface-sensitive X-ray photoelectron spectroscopy and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. NEXAFS data in combination with density functional theory calculations revealed the dative interactions between lithium sp2 hybridized states and carbon π*-type orbitals. Corrugated defective layers of graphene provide lithium with new bonding configurations, shorter distances, and stronger orbital overlapping, resulting in significant charge transfer between carbon and lithium. PC annealing heals defects, and as a result, the amount of lithium on the surface decreases. This conclusion was supported by electrochemical studies of as-grown and annealed PC in lithium-ion batteries. The former nanomaterial showed higher capacity values at all applied current densities. The results demonstrate that the lithium storage in carbon-based electrodes can be improved by introducing defects into the graphene layers.

Complete and orthonormal sets of exponential-type orbitals with non-integer quantum numbers

Atomic and molecular orbitals show exponential decrease at long range. Complete orthonormal basis sets for atoms should satisfy this criterion. A number of such bases have been used in physics (e.g. Coulomb Sturmians). The challenge of this work is first adapting Slater type Orbitals for this role, as they are not radially orthogonal. Even more important is their generalization to non-integer quantum numbers that have applications for configuration interaction. This generalization requires the whole apparatus of non-integer calculus that is presented using the Riemann–Liouville approach.

Applicability of noninteger bessel type orbital basis sets: numerical and analytical approaches

Recently, usefulness of the noninteger principal quantum numbers for Bessel type orbitals was discussed by Weniger in (Adv Quant Chem 83:209–237, 2021). In this study, we analyzed the applicability and numerical accuracy of basis sets of noninteger Bessel type orbitals to electronic structure calculations. Both numerical and analytical approaches are applied to two-electron atomic systems. The results of the numerical test demonstrated the potential of the noninteger values of principal quantum number for the improving of Bessel type functions approach in use of LCAO methods. Nevertheless, the analytical approach is still not suitable and in development and needs to be investigated further.The performance of the presented basis functions is also compared to the numerical Hartree–Fock results.

Molecular properties calculated with Gaussian basis sets optimized in molecule’s local environments

Both of centers and exponents of atom-derived standard Gaussian basis sets are re-optimized in structure unit group (SUG) environments which have been recently proposed [Chem. Phys. Lett. 765(2021) 138285]. For McLean’s 6-311G, Gaussian type orbitals belong in SUG’s core- and hydrogen atoms are float-scaled by iterative searching of minimum SUG-energy, and applied to calculate molecular energy and its components, virial ratio and dipole moment. Results are compared with ones calculated by using the highest quality basis sets (6-311++G(3fd,3dp), aug-cc-pVQZ).

Toward Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy.

Pair atomic density fitting (PADF) has been identified as a promising strategy to reduce the scaling with system size of quantum chemical methods for the calculation of the correlation energy like the direct random-phase approximation (RPA) or second-order Møller-Plesset perturbation theory (MP2). PADF can however introduce large errors in correlation energies as the two-electron interaction energy is not guaranteed to be bounded from below. This issue can be partially alleviated by using very large fit sets, but this comes at the price of reduced efficiency and having to deal with near-linear dependencies in the fit set. One posibility is to use global density fitting (DF), but in this work, we introduce an alternative methodology to overcome this problem that preserves the intrinsically favorable scaling of PADF. We first regularize the Fock matrix by projecting out parts of the basis set which gives rise to orbital products that are hard to describe by PADF. After having thus obtained a reliable self-consistent field solution, we then also apply this projector to the orbital coefficient matrix to improve the precision of PADF-MP2 and PADF-RPA. We systematically assess the accuracy of this new approach in a numerical atomic orbital framework using Slater type orbitals (STO) and correlation consistent Gaussian type basis sets up to quintuple-ζ quality for systems with more than 200 atoms. For the small and medium systems in the S66 database we show the maximum deviation of PADF-MP2 and PADF-RPA relative correlation energies to DF-MP2 and DF-RPA reference results to be 0.07 and 0.14 kcal/mol, respectively. When the new projector method is used, the errors only slightly increase for large molecules and also when moderately sized fit sets are used the resulting errors are well under control. Finally, we demonstrate the computational efficiency of our algorithm by calculating the interaction energies of large, non-covalently bound complexes with more than 1000 atoms and 20000 atomic orbitals at the RPA@PBE/CC-pVTZ level of theory.

Theoretical Investigations on MIL-100(M) (M=Cr, Sc, Fe) with High Adsorption Selectivity for Nitrogen and Carbon Dioxide over Methane.

The removal of impurity gases (N2 , CO2 ) in natural gas is critical to the efficient use of natural gas. In this work, the selective adsorption for N2 and CO2 over CH4 on MIL-100 (M) (M=4 Cr, 10 Cr, 6 Fe, 1 In, 1 Sc, 3 V) is studied by density functional theory (DFT) calculations. The calculated adsorption energy of the large-size cluster model (LC) of MIL-100 (M) shows that the 4 MIL-100 (4 Cr) is the best at the refinement of natural gas due to the lower adsorption energy of CH4 (-2.58 kJ/mol) in comparison with that of N2 (-21.49 kJ/mol) and CO2 (-23.82 kJ/mol). 1 MIL-100 (1 Sc) and 1 MIL-100 (6 Fe) can also achieve selective adsorption and follows the order 4 MIL-100 (4 Cr)>1 MIL-100 (1 Sc)>1 MIL-100 (6 Fe). In the research of the selective adsorption mechanism of MIL-100 (M) (M=4 Cr, 1 Sc, 6 Fe), the independent gradient model (IGM) indicates that these outstanding adsorbents interact with CO2 and N2 mainly through the electrostatic attractive interaction, while the van der Walls interaction dominates in the interaction with CH4. The atomic Projected Density of State (PDOS) further confirms that CH4 contributes least to the intermolecular interaction than that of CO2 and N2 . Through the scrutiny of molecular orbitals, it is found that electrons transfer from the gas molecule to the metal site in the adsorption of CO2 and N2 . Not only does the type of the metallic orbitals, but also the delocalization of the involved orbitals determines the selective adsorption performance of MIL-100. Both Cr and Sc share their orbitals with the gases, making 1 MIL-100 (1 Sc) another potential effective separator for CH4 . Additionally, the comparison of adsorption energy and PDOS shows that the introduction of ligands such as benzene impedes the electron donation from gas molecules (CO2 , N2 ) to the metal site, indicating electron-withdrawing ligands will further favor the adsorption.

Scientific Analysis of Rose Essential Oils: Viewed from Various Perspectives

The use of essential oils in the world each year has increased with the increasing development of modern industries such as the perfume industry, cosmetics, food, aroma therapy and medicine. Essential oils or also known as etheric oils are a large group of vegetable oils in the form of viscous liquids at room temperature but volatile so that they give a distinctive aroma. Some components of essential oils are hydrocarbon compounds (hydrogen-carbon) and oxygen. One source of essential oils can be obtained from rose extract. This study aims to analyze the physical, chemical, and beneficial properties of several components of the rose essential oil. This research approach uses a qualitative approach with a literature study method, then the data were analyzed using descriptive analysis. The results obtained conclude that the essential oil content in roses with the highest percentage is n-nonadekane, -phenylethylacetate, phenylethylalcohol, and 2-Isopropyl-5-methyl-9-methylene-bicyclo-1-decene, -Fernesene, and -cadinene. From these structures there are 2 types of hybrid orbitals, namely sp3 and sp2, when viewed from the type of bond π and σ; whereas if viewed from the isomerism, these structures have skeletal, functional groups, and optical isomers. Some of the constituents in the volatile oil components can be reacted (nucleophilic addition with HCl and electrophilic with bromine). The existence of these differences causes the chemical and physical properties of the structure of the essential oil content to vary according to their usefulness.