Diffuse Basis Sets Research Articles

Projected Atomic Orbitals As Optimal Virtual Space for Excited State Projection-Based Embedding Calculations.

The projected atomic orbital (PAO) technique is presented for the construction of virtual orbital spaces in projection-based embedding (PbE) applications. The proposed straightforward procedure produces a set of virtual orbitals that are used in the final, high-level calculation of the embedded active subsystem. The PAO scheme is demonstrated on intermolecular potentials of bimolecular complexes in ground and excited states, including Rydberg excitations. The results show the outstanding performance of the PbE method when used with PAO virtual orbitals compared with those produced using common orbital localization techniques. The good agreement of the resulting PbE potential curves with those from high-level ab initio dimer calculations, also in diffuse basis sets, confirms that the PAO technique can be suggested for future applications using top-down embedding methods.

Toward Post-Hartree-Fock Accuracy for Protein-Ligand Affinities Using the Molecules-in-Molecules Fragmentation-Based Method.

The complexity and size of large molecular systems, such as protein-ligand complexes, pose computational challenges for accurate post-Hartree-Fock calculations. This study delivers a thorough benchmarking of the Molecules-in-Molecules (MIM) method, presenting a clear and accessible strategy for layer/theory selections in post-Hartree-Fock computations on substantial molecular systems, notably protein-ligand complexes. An approach is articulated, enabling augmented computational efficiency by strategically canceling out common subsystem energy terms between complexes and proteins within the supermolecular equation. Employing DLPNO-based post-Hartree-Fock methods in conjunction with the three-layer MIM method (MIM3), this study demonstrates the achievement of protein-ligand binding energies with remarkable accuracy (errors <1 kcal mol-1), while significantly reducing computational costs. Furthermore, noteworthy correlations between theoretically computed interaction energies and their experimental equivalents were observed, with R2 values of approximately 0.90 and 0.78 for CDK2 and BZT-ITK sets, respectively, thus validating the efficacy of the MIM method in calculating binding energies. By highlighting the crucial role of diffuse or small Pople-style basis sets in the middle layer for reducing energy errors, this work provides valuable insights and practical methodologies for interaction energy computations in large molecular complexes and opens avenues for their application across a diverse range of molecular systems.

Methoxylated Quinoline-Chalcones with Potential Pesticidal Activity: From Synthesis to Supramolecular Framework

In this work, the molecular properties of the (E)-3-(4-nitrobenzylidene)-2-(4-methoxyphenyl)- 2,3-dihydro-1-(phenylsulfonyl)-quinolin-4(1H)-one were studied, both in a solid and isolated state. The effect of changing the substituent groups –OCH3 and –Cl in the phenyl portion was verified, where the structural and electronic properties were compared. The density functional theory was employed using the hybrid exchange-correlation functional with long-range correction M06-2X, combined with the polarized and diffuse basis set 6-311++G(d,p), in the gas phase. The electronic structure was also analyzed by frontier molecular orbitals and molecular electrostatic potential maps, where information about its chemical reactivity was obtained. Also, the supramolecular arrangement was analyzed by Hirshfeld surface (HS), 2D fingerprint plots, and quantum theory of atoms in molecules (QTAIM). The natural bond orbitals (NBO) calculations were carried out to analyze the stability and hyperconjugation energy. Finally, molecular docking was carried out to investigate the affinities of the quinoline-chalcone with a bacterial protein (Agrobacterium pathogens) and an ecdysone receptor-potential pesticidal activity. The results encourage further in vitro and in vivo analyses of the two kinds of organisms investigated.

Excited-state van der Waals potential energy surfaces for the NO A2Σ+ + CO2X1Σg+ collision complex.

Excited state van der Waals (vdW) potential energy surfaces (PESs) of the NO A2Σ+ + CO2X1Σg+ system are thoroughly investigated using coupled cluster theory and complete active space perturbation theory to second order (CASPT2). First, it is shown that pair natural orbital coupled cluster singles and doubles with perturbative triples yields comparable accuracy compared to CCSD(T) for molecular properties and vdW-minima at a fraction of computational cost of the latter. Using this method in conjunction with highly diffuse basis sets and counterpoise correction for basis set superposition error, the PESs for different intermolecular orientations are investigated. These show numerous vdW-wells, interconnected for all geometries except one, with a maximum depth of up to 830 cm-1; considerably deeper than those on the ground state surface. Multi-reference effects are investigated with CASPT2 calculations. The long-range vdW-surfaces support recent experimental observations relating to rotational energy transfer due the anisotropy in the potentials.

Theoretical study of low-energy electron collision with normal-pentane using R-matrix method

Low-energy electron collisions with normal-pentane (n-C5H12) that initiate the plasma to assist combustion are critical in understanding the underlying physics and chemistries. In the present work, we studied this collisional process using the R-matrix method at the static-exchange plus polarization and close-coupling model levels. The scattering calculation was performed by running the UKRmol+ code using the Quantemol Electron Collision interface to obtain elastic differential, momentum transfer, integral, and electronic excitation cross sections up to 20 eV and ionization cross sections up to 1000 eV. Our computed cross-section data are in better agreement with the available experimental results both regarding the magnitude and shape. We also demonstrated the importance of using a diffuse basis set in describing the scattering due to the Rydberg nature of the lowest unoccupied molecular orbitals of n-C5H12.

Spectral properties of B40 enhanced by small molecule adsorption.

The luminescence characteristics of small molecule excited B40 have not been studied yet, and it may have a potential application value in quantum dot luminescence. Herein, the adsorption and fluorescence emission spectra of small molecules (pyridine, pyrazine and benzene) adsorbed on B40 are studied using first-principles. The results show that the absorption of pyridine and pyrazine on B40 can form stable chemisorption structures pyridine-B40 and pyrazine-B40, while benzene adsorption can form physisorption structure benzene-B40. Moreover, the adsorbed pyridine can enhance the intensity of emission spectra of B40. And the pyrazine adsorbed can obviously enhance the intensity of absorption and emission spectra of B40 and cause the spectra to redshift to the visible light range. And the adsorption of benzene has almost no enhancement effect on absorption and emission spectra of B40. In addition, the influence of different computational basis sets on spectra characteristics has also been discussed and the results show that the main peaks of absorption and emission spectra calculated by the diffuse function augmented basis sets are redshifted relatively. This finding provides a strategy for quantum dot luminescence and a theoretical reference for experimental research.

Diffuse Basis Functions for Relativistic s and d Block Gaussian Basis Sets

Diffuse s, p, and d functions have been optimized for use with previously reported relativistic basis sets for the s and d blocks of the periodic table. The functions were optimized on the 4:1 weighted average of the s2 and p2 configurations of the anion, with the d shell in the dn+1 configuration for the d blocks. Exponents were extrapolated for groups 2 and 12, which have unstable or weakly bound anions. The diffuse basis sets have been tested by application to calculations of electron affinities of the group 11 elements (Cu, Ag, and Au), double electron affinities of the group 11 monocations, and potential energy curves of Mg2 and Ca2 van der Waals dimers, as well as some response properties of the group 1 anions (Rb-, Cs-, and Fr-), the group 2 elements (Sr, Ba, and Ra), and RbLi, CsLi, and FrLi molecules.

A New Enthalpy of Formation Test Set Designed for Organic Fluorine Containing Compounds

AbstractThe deviations of gas phase enthalpy of formation predicted by density functional theory on the fluorine containing system are larger than those on other systems in most cases. Therefore, an enthalpy of formation test set composed of 41 organic fluorine containing compounds is proposed, and in this work it is called OFCC41 test set. Twenty exchange‐correlation functionals are estimated by CCSD(T)/CBS as benchmark. The first part of the results indicates that CAM‐B3LYP, ωB97X, and M06 are the most suitable functionals to predict enthalpies of formation for fluorine containing compounds. The remainder of this work is primarily concerned with diffuse basis sets and size‐dependent effects. Diffuse basis sets ma‐SVP and ma‐TZVP can generally improve the prediction performance. For very small molecules, using ma‐SVP is sufficient while for larger molecules more completed basis sets are demanded. Size‐dependent effect of prediction accuracy on different molecules is revealed by using a simple strategy, that the different sizes of molecules are distinguished with three intervals and given the corresponding mean absolute errors. This study provides a test set designed for organic fluorinated compounds and contributes to the selection of some functionals suitable for fluorine containing system.

Electronic structure of the ground and excited states of neutral and charged silicon hydrides, SiHx0/+/−, x = 1–4

The ground and excited electronic states of the titled species are investigated with multi-reference configuration interaction and diffuse basis sets. We found that in addition to the valence orbitals, the inclusion of the 4s, 4p, and especially 3d orbitals (although with minimal population) of silicon in the active space of the reference complete active space self-consistent field wavefunction are necessary for the proper convergence of the calculations. We also demonstrate that the aug-cc-pVTZ basis set provides quite accurate results compared to both larger basis sets and basis set limit results at a lower computational cost. The excited states involve excitations within the 3s and 3p orbitals of silicon (especially for the mono- and di-hydrides), followed by excitations from the Si-H bonding orbitals to either silicon valence or Rydberg (4s, 4p) orbitals. The number of electronic states per energy unit decrease as we add hydrogen atoms, and the first excited state of SiH4 is at 9.0 eV and leads to SiH3 + H. All species have stable ground state structures with all hydrogen atoms bound to silicon, except for SiH4+ and SiH4-. The former dissociates to SiH2+ + H2, while the latter loses an electron or can dissociate forming H2 as well.

Adiabatic potential energy surfaces and photodissociation mechanisms for highly excited states of H2O

Full-dimensional adiabatic potential energy surfaces of the electronic ground state X̃ and nine excited states Ã, Ĩ, B̃, C̃, D̃, D̃′, D̃″, Ẽ′ and F̃ of H2O molecule are developed at the level of internally contracted multireference configuration interaction with the Davidson correction. The potential energy surfaces are fitted by using Gaussian process regression combining permutation invariant polynomials. With a large selected active space and extra diffuse basis set to describe these Rydberg states, the calculated vertical excited energies and equilibrium geometries are in good agreement with the previous theoretical and experimental values. Compared with the well-investigated photodissociation of the first three low-lying states, both theoretical and experimental studies on higher states are still limited. In this work, we focus on all the three channels of the highly excited state, which are directly involved in the vacuum ultraviolet photodissociation of water. In particular, some conical intersections of D̃–Ẽ′, Ẽ′-F̃, ÖĨ and Ĩ–C̃ states are clearly illustrated for the first time based on the newly developed potential energy surfaces (PESs). The nonadiabatic dissociation pathways for these excited states are discussed in detail, which may shed light on the photodissociation mechanisms for these highly excited states.

Highly efficient implementation of the analytical gradients of pseudospectral time-dependent density functional theory.

The accuracy and efficiency of time-dependent density functional theory (TDDFT) excited state gradient calculations using the pseudospectral method are presented. TDDFT excited state geometry optimizations of the G2 test set molecules, the organic fluorophores with large Stokes shifts, and the Pt-complexes show that the pseudospectral method gives average errors of 0.01-0.1 kcal/mol for the TDDFT excited state energy, 0.02-0.06pm for the bond length, and 0.02-0.12° for the bond angle when compared to the results from conventional TDDFT. TDDFT gradient calculations of fullerenes (Cn, n up to 540) with the B3LYP functional and 6-31G** basis set show that the pseudospectral method provides 8- to 14-fold speedups in the total wall clock time over the conventional methods. The pseudospectral TDDFT gradient calculations with a diffuse basis set give higher speedups than the calculations for the same basis set without diffuse functions included.

Efficient implementation of the single-reference algebraic diagrammatic construction theory for charged excitations: Applications to the TEMPO radical and DNA base pairs.

We present an efficient implementation of the second- and third-order single-reference algebraic diagrammatic construction (ADC) theory for electron attachment and ionization energies and spectra [EA/IP-ADC(n), n = 2, 3]. Our new EA/IP-ADC program features spin adaptation for closed-shell systems, density fitting for efficient handling of the two-electron integral tensors, and vectorized and parallel implementation of tensor contractions. We demonstrate capabilities of our efficient implementation by applying the EA/IP-ADC(n) (n = 2, 3) methods to compute the photoelectron spectrum of the (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) radical, as well as the vertical and adiabatic electron affinities of TEMPO and two DNA base pairs (guanine-cytosine and adenine-thymine). The spectra and electron affinities computed using large diffuse basis sets with up to 1028 molecular orbitals are found to be in good agreement with the best available results from the experiment and theoretical simulations.

QUESTDB: A database of highly accurate excitation energies for the electronic structure community

AbstractWe describe our efforts of the past few years to create a large set of more than 500 highly accurate vertical excitation energies of various natures (π → π*, n → π*, double excitation, Rydberg, singlet, doublet, triplet, etc.) in small‐ and medium‐sized molecules. These values have been obtained using an incremental strategy which consists in combining high‐order coupled cluster and selected configuration interaction calculations using increasingly large diffuse basis sets in order to reach high accuracy. One of the key aspects of the so‐called QUEST database of vertical excitations is that it does not rely on any experimental values, avoiding potential biases inherently linked to experiments and facilitating theoretical cross comparisons. Following this composite protocol, we have been able to produce theoretical best estimates (TBEs) with the aug‐cc‐pVTZ basis set for each of these transitions, as well as basis set corrected TBEs (i.e., near the complete basis set limit) for some of them. The TBEs/aug‐cc‐pVTZ have been employed to benchmark a large number of (lower‐order) wave function methods such as CIS(D), ADC(2), CC2, STEOM‐CCSD, CCSD, CCSDR(3), CCSDT‐3, ADC(3), CC3, NEVPT2, and so on (including spin‐scaled variants). In order to gather the huge amount of data produced during the QUEST project, we have created a website (https://lcpq.github.io/QUESTDB_website) where one can easily test and compare the accuracy of a given method with respect to various variables such as the molecule size or its family, the nature of the excited states, the type of basis set, and so on. We hope that the present review will provide a useful summary of our effort so far and foster new developments around excited‐state methods.This article is categorized under: Electronic Structure Theory &gt; Ab Initio Electronic Structure Methods

Towards understanding the interaction of (S)-thalidomide with nucleobases

Interaction of (S)-thalidomide molecule with four nucleobases: adenine, guanine, cytosine and thymine, is investigated in details employing density functional theory methods. Different mutual positions of the molecules are considered, with the starting geometries enabling hydrogen bond interactions between the monomers. Optimization of geometrical parameters is carried out within the B3LYP/6-311G** approximation and followed by evaluation of vibrational frequencies. Binding and interaction energies are calculated employing exchange-correlation functionals including long-range corrections and properly diffuse basis sets. The strongest interaction exists within the (S)-thalidomide–guanine complex. Interestingly, in one of the investigated (S)-thalidomide–guanine complexes two bifurcated hydrogen bonds are observed. The two hydrogens involved in one of them are bonded to a carbon atom in the α position relative to carbonyl group. The present study can be useful in the design of new anticancer and antiviral drugs interacting selectively with DNA or RNA.

A simple computational approach for pKa calculation of organosulfur compounds

The present work is related to predicting the pKa values of organosulfur compounds through the density functional theory (DFT). In this study, 22 organosulfur compounds were considered to calculate the theoretical pKa values. The main emphasis was given on the substitution of different groups on the sulfur atom. The computations were performed in the presence of dimethyl sulfoxide (DMSO) as solvent. Experimentally, the order of increase of acidity is; sulfides &lt; sulfoxides &lt; sulfones. The herein computed pKa values also follow the same order. The theoretical pKa values were computed using the DFT method B3LYP, with the basis sets 6-31G(d), 6-31+G(d,p) and the IEFPCM bulk solvation model. The majority of the pKa values computed through the diffuse function basis set were in excellent agreement with the experimental ones. Hence this computational approach, B3LYP/6-31+G(d,p)/IEFPCM, could be utilized to predict the pKa values of these types of organosulfur compounds.

Avoiding Electron Spill-Out in QM/MM Calculations on Excited States with Simple Pseudopotentials.

QM/MM calculations of electronic excitations with diffuse basis sets often have large errors due to spill-out of electrons from the quantum subsystem. The Pauli repulsion of the electrons by the environment has to be included to avoid this. We propose transferable atomic all-electron pseudopotentials that can readily be combined with most MM force fields to avoid electron spill-out. QM/MM excitation energies computed with time-dependent Hartree-Fock and the algebraic diagrammatic construction through second-order are benchmarked against supermolecular calculations to validate these new pseudopotentials. The QM/MM calculations with pseudopotentials give accurate results that are stable with augmentation of the basis set with diffuse functions. We show that the largest contribution to residual deviations from full QM calculations is caused by the missing London dispersion interaction.

Optimal diffuse augmented atomic basis sets for extrapolation of the correlation energy

AbstractWe seek correlation‐consistent diffuse‐augmented double‐zeta and triple‐zeta basis sets that perform optimally in extrapolating the correlation energy to the one‐electron complete basis set limit, denoted oAVXZ and oAV(X + d)Z. The novel basis sets are method‐dependent in that they are trained to perform optimally for the correlation energy at each specific level of theory. They are shown to yield accurate results in calculating both the energy and tensorial properties such as polarizabilities while not significantly altering the Hartree‐Fock energy. Quantitatively, complete basis set limit (CBS)‐/(oAVdZ,oAVtZ)‐extrapolated correlation energies typically outperform, by 3‐ to 5‐fold, the ones calculated with traditional ansatzes of similar flexibility. Attaining energies of CBS/(AVtZ,AVqZ) type or better accuracy, they frequently outperform expensive raw explicitly correlated ones. Promisingly, a limited test on CBS‐extrapolated energies based on conventional basis sets has shown that they compare well even with extrapolated explicitly correlated ones. Calculated atomization and dissociation energies, molecular geometries, ionization potentials, and electron affinities also tend to outperform the ones obtained with traditional Dunning's ansatzes from which the new basis sets have been determined. The method for basis set generation is simple, and there is no reason of principle why the approach could not be adapted for handling other bases in the literature.

Nature of the 11Bu and 21Ag Excited States of Butadiene and the Goldilocks Principle of Basis Set Diffuseness.

Butadiene, being the simplest conjugated organic molecule, has been studied extensively by experiments and various high-level theoretical methods. Previous studies conclude that the complete active space (CAS) self-consistent field (SCF) method was unable to obtain the correct 11Bu and 21Ag state ordering and that it introduces artificial valence-Rydberg mixing into the 11Bu state because of the lack of external correlation. Basis sets and initial guesses specifically constructed for this problem were able to improve the vertical excitation energy of the 11Bu state but did not resolve the controversy of the nature of the 11Bu state. In the present work, we demonstrate that, using standard intermediately diffuse basis sets such as jul-cc-pVTZ and ma-TZVP, CASSCF is able to obtain the 11Bu and 21Ag states of trans-butadiene with much improved vertical excitation energy and reasonable wave function characteristics, and it provides a good reference wave function (capable of yielding quantitative excitation energies for excited states) for three methods that treat electron correlation in different ways, namely, multiconfiguration pair-density functional theory (MC-PDFT), CAS second-order perturbation theory (PT2), and multistate (MS) CASPT2. We demonstrate that a combined analysis of the orbital second moments, state second moments, and MC-PDFT energy components is a very useful approach in determining excited-state characteristics and assigning states, and we show that basis sets without diffuse functions or with very diffuse basis functions are not stable or accurate in predicting the excited states of butadiene. We show that the 21Ag state is valence-like and has an atypical double/single excitation character and the 11Bu state has a certain degree of Rydberg character that is not artificial, settling the decades of controversy of the characters of these states.

Multireference exciplex binding energies: Basis set convergence and error

AbstractIn multichromophore systems, characterization of electronic structure requires characterization of exciplexes, electron‐hole pairs delocalized over multiple molecules. Computing exciplex binding energy requires an accurate description of both the noncovalent interactions between the chromophores and their excited electronic states. The critical role of basis set selection for accurate description of noncovalent interactions is well known, but for some of the most accurate excited‐state methods, basis set dependence is incompletely understood. In this work, the impact of basis set size and diffuseness on CASSCF/NEVPT2 binding energies is determined for three systems in their lowest singlet excited states: the benzene excimer, the cis‐butadiene‐benzene exciplex, and the benzene‐naphthalene exciplex. We demonstrate that excellent CBS binding energies may be obtained using the moderately‐sized jun‐cc‐pV(D + d)Z and jun‐cc‐pV(T + d)Z basis sets and a simple N−3 model. Repeating this procedure with the N = 3, 4 basis sets from the most diffuse basis set family applied to each system yields a binding energy of 56.6 ± 1.2 kJ/mol for the benzene excimer and binding energies of 11.1 ± 0.5 kJ/mol and 19.2 ± 1.7 kJ/mol for the cis‐butadiene‐benzene exciplex and the benzene‐naphthalene exciplex, respectively.

Practical approach for beryllium atomic clusters: TD-DFT potential energy surfaces from equilibrium to dissociation for excited states of 2s → 2p

To shed light on the spectroscopic energy-smearing mechanism of the recently developed technique for multi-element analysis (e.g., forensic tests on artworks), which is called plume laser-induced fluorescence, practically computer simulations need to be accurate and fast enough for generating wide-range excited-state potential energy surfaces (PESs) from equilibrium to dissociation of large (non-equilibrated) atomic clusters. Currently, all the very high-level post-Hartree–Fock theories (e.g., coupled-cluster theory) are computationally too expensive for this purpose (e.g., taking at least ~ 23 years). After considering the extensive applications of time-dependent density-functional theory (TD-DFT) in computing the optical properties of many-body systems, we wonder how TD-DFT performs in the wide-range-PES generations because no such TD-DFT application is found by us in the literature (perhaps due to its insufficient static/non-dynamical correlation energy). In this work, we carried out TD-DFT calculations on beryllium atomic clusters from Be1 to Be50 (in contrast to open-shell H2 or Li2 system, we think the individual closed-shell Be systems at the dissociation limit could help TD-DFT to describe the static/non-dynamical correlation. For example, it is usually considered that Be2 has zero non-dynamical correlation energy in the literature) with and without Tamm–Dancoff approximation (TDA). Electronic excited-state properties (e.g., PES, equilibrium position, dissociation energy, fork intersection) associated with 2s → 2p are systematically investigated at a total of 48 levels of TD-DFT. Our calculations are thoroughly benchmarked against experimental results and (very) high-level theoretical values. In short, we find that for accurate simulations, it is necessary to use diffuse basis sets and the TDA approximation. TD-DFT with the small basis set 3-21+G* took ~ 2 min to finish a single-point excitation energy calculation on a linear Be50 (a toy model), while the large basis set 6-311+G(2df,2p) took 30 min. By contrast, a couple-cluster theory EOM-CCSD with 6-311+G(2df,2p) took 2.5 h to do the same but merely for a smaller linear Be10. In general, we suggest that TD-DFT:TDA with 3-21+G* should be practically fast and accurate enough for emulating our desired wide-range excited-state PESs of large Be atomic clusters (including conical intersection points of close energies) in the future studies. Nevertheless, benchmarking work on (much) larger sizes of Be clusters will always be more desirable whenever its computational costs at very high level of theories becomes more tractable.