Small Basis Sets Research Articles

Synthesis, characterization, DFT and molecular docking studies for novel 1,5-diphenylpenta-1,4-dien-3-one O-benzyl oximes

The main objectives of this study are: (a) to synthesize novel 1,5-diphenylpenta-1,4-dien-3-one O-benzyl oximes in an efficient way, (b) to investigate the synthesized molecules computationally via DFT calculations, (c) to compare computationally obtained data with experimental results and (d) to perform molecular docking calculations for the newly synthesized compounds and heat shock protein HSP90A N-terminal domain to determine the binding affinities of the investigated molecules and to reveal possible receptor–ligand interactions. In the first part of the study, syntheses and characterizations of the investigated compounds have been carried out. In this part, the target compounds have been synthesized and characterized successively. In the synthesis of target compounds from corresponding oximes, ultrasound has been used alternatively and results showed that the usage of ultrasound considerably increases the reaction rate and the efficiency. In the second part, detailed density functional theory calculations have been performed on the investigated compounds with the use of Becke, three-parameter, Lee–Yang–Parr hybrid functional and various basis sets. In this part, geometry optimizations, frequency analyses, NMR spectral analyses, frontier molecular orbital calculations, and molecular electrostatic potential map calculations have been performed. In NMR spectral analyses, both continuous set of gauge transformations (CSGT) and gauge-independent atomic orbital (GIAO) methods have been used and the obtained results with the use of various basis sets have been compared. Results showed that in NMR calculations, GIAO method is more successful than CSGT method and can provide satisfactory results even with small basis sets. In the third part of the study, molecular docking calculations have been performed on the investigated compounds and HSP90A N-terminal domain. Results showed that investigated molecules show a good binding affinity for HSP90A N-terminal domain. The binding affinities were found to be in the range of − 8.7 to − 10.1 kcal/mol.

Validating additive correction schemes against gradient‐based extrapolations

AbstractThe use of additive correction schemes to obtain structures and vibrational frequencies of increasingly larger molecules is becoming more common. Such approaches, based on the cubic extrapolation formula applied directly to the quantity of interest, have been successfully validated only at the highest levels of computational accuracy: for coupled cluster methods with comparably large basis sets. Here, a systematic validation of geometries and vibrational frequencies is carried out, including more affordable and relevant levels of theory, such as the Møller‐Plesset perturbation theory applied with smaller basis sets. Comparisons of such additive schemes against the more rigorous gradient‐based extrapolation are presented. The cbs() routine of the open‐source quantum‐chemistry package Psi4 has been extended for this purpose. The results confirm that geometries and frequencies of covalently bound species obtained with additive correction schemes are in an excellent agreement with the results of gradient‐based extrapolations. However, when applied to systems involving noncovalent interactions, the errors due to such schemes are significantly larger. In general, we propose the application of gradient‐based extrapolations, as they incur no extra cost compared to additive schemes.

Ethyl + O2 in Helium Nanodroplets: Infrared Spectroscopy of the Ethylperoxy Radical.

Helium-solvated ethylperoxy radicals (CH3CH2OO•) are formed via the in situ reaction between 2A' ethyl radical and 3Σg- dioxygen. The reactants are captured sequentially through the droplet pick-up technique. Helium droplets are doped with ethyl radical via pyrolysis of di- tert-amyl peroxide or n-propylnitrite in an effusive, low-pressure source. An infrared spectrum of ethylperoxy, in the CH stretching region, is recorded with species-selective droplet beam depletion spectroscopy. Spectral assignments are made via comparisons to second-order vibrational perturbation theory with resonances (VPT2 + K) based on coupled-cluster full quartic force fields. Cubic and quartic force constants, evaluated using a small basis set, are transformed into the normal coordinate system of the higher level quadratic force constants. This transformation procedure eliminates the mismatch between normal modes, which is a source of error whenever normal coordinate force constants from different levels of theory are combined. The spectrum shows signatures of both the C1 gauche and C s trans rotamers in an approximate 2:1 ratio; this is despite the prediction that the gauche rotamer lies 44 cm-1 lower on the zero-Kelvin enthalpic potential surface for torsional interconversion. Helium droplets are 0.4 K at equilibrium; therefore, in situ ethylperoxy production is highly nonthermal.

Small Basis Set Allowing the Recovery of Dispersion Interactions with Double-Hybrid Functionals.

Taking advantage of the compensation between Basis Set Superposition Error and Basis Set Incompleteness Error, a new basis is developed to improve the performances of Double Hybrid (DH) functionals in reproducing interaction energies in weak noncovalent systems. Using a self-consistent formula, containing only energy terms computed for dimers and the corresponding monomers at the same level of theory, the exponents of the more external functions of the Def2-SVPD basis were optimized on three systems extracted from the S22 set. The transferability of the obtained basis set, called DH-SVPD, was then tested on five benchmark sets, and it is assessed by considering six DH functionals, eventually corrected with empirical dispersion corrections (for a total of 16 methods). Our results show that this simple approach is able to provide accurate results for noncovalent interaction energies of all the considered systems, and, in particular, to recover the performances obtained by coupling the DH functionals with empirical dispersion corrections.

Practical band interpolation with a modified tight-binding method

We present a scheme that interpolates the energy bands of a crystal with a modified tight-binding Hamiltonian. We start from a pseudopotential plane-wave calculation of the eigenvalues in a three-dimensional coarse uniform grid of k-points in the Brillouin zone and from the evaluation of the single particle Hamiltonian and overlap matrix elements for a small localised basis set of atomic orbitals in the same k-point grid. A simple matrix manipulation procedure that replaces the eigenvalues obtained from the atomic orbital method by the eigenvalues of the plane-wave method generates the modified tight-binding Hamiltonian on the coarse grid. A subsequent three-dimensional Fourier interpolation of the modified tight-binding Hamiltonian and overlap matrices leads to a fast, yet accurate, determination of interpolated Hamiltonians and overlap matrices at an arbitrary k-point, or in a denser grid of k-points. We present examples of the application of the scheme to density functional calculations of germanium, graphite, graphene, copper and a SiGe superlattice.

Weak Interactions in Alkaline Earth Metal Dimers by Pair-Density Functional Theory

Alkaline earth dimers have small bond energies (less than 5 kcal/mol) that provide a difficult challenge for electronic structure calculations. They are especially challenging for Kohn-Sham density functional theory (KS-DFT) using generalized gradient approximations (GGAs) as the exchange-correlation density functional because GGAs often do not provide accurate results for weak interactions. Here we treat alkaline earth dimers from six different rows of the periodic table. We show that the dominant correlating configurations are the same in all six dimers. We also show that multiconfiguration pair-density functional theory (MC-PDFT) using a fully translated GGA as the on-top density functional not only performs much better than KS-DFT with GGAs in predicting equilibrium distances and dissociation energies but also performs better than the more computationally demanding complete active space second-order perturbation theory (CASPT2) with large basis sets and performs even better than CASPT2 with smaller basis sets.

The generation of ground‐state structures and electronic properties of ternary AlkTilNim clusters (k + l + m = 4) from a two‐stage density functional theory global searching approach

AbstractStructural and electronic properties of ternary clusters AlkTilNim, where k, l, and m are integers and k + l + m = 4, are investigated. These clusters are generated and studied by performing a two‐stage density functional theory (DFT) calculations using the Slater, Vosko, Wilks, and Nusair (SVWN) and Becke three‐parameter, Lee‐Yang‐Parr (B3LYP) functional exchange correlations. In the first stage, an unbiased global search algorithm coupled with a DFT code with a light exchange‐correlation and smaller basis sets are used to generate the lowest energy cluster structures. It is then followed by further optimization using another round of DFT calculation with heavy exchanged correlations and large basis set. Electronic properties of the structures obtained via the two‐stage procedure are then studied via DFT calculations. The results are illustrated in the form of ternary diagram. Our DFT calculations find that the stability of the cluster increases with the increase in the number of nickel atoms inside the clusters. Our findings provide new insight into the ternary metallic cluster through the structure, stability, chemical order, and electronic properties studies.

Incremental embedding: A density matrix embedding scheme for molecules.

The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding methods mainly focus on systems composed of weakly correlated parts and are insufficient when division across chemical bonds is unavoidable. Recently, density matrix embedding theory and other methods based on the Schmidt decomposition have emerged as a fresh approach to this problem. Despite their success on model systems, these methods can prove difficult for realistic systems because they rely on either a rigid, non-overlapping partition of the system or a specification of some special sites (i.e., "edge" and "center" sites), neither of which is well-defined in general for real molecules. In this work, we present a new Schmidt decomposition-based embedding scheme called incremental embedding that allows the combination of arbitrary overlapping fragments without the knowledge of edge sites. This method forms a convergent hierarchy in the sense that higher accuracy can be obtained by using fragments involving more sites. The computational scaling for the first few levels is lower than that of most correlated wave function methods. We present results for several small molecules in atom-centered Gaussian basis sets and demonstrate that incremental embedding converges quickly with fragment size and recovers most static correlation in small basis sets even when truncated at the second lowest level.

New compact density matrix averaged ANO basis sets for relativistic calculations.

When including relativistic effects in quantum chemical calculations, basis sets optimized for relativistic Hamiltonians such as the atomic natural orbital-relativistic core-correlated (ANO-RCC) basis set have to be used to avoid large errors that appear upon contraction of the basis set. While the large size of the ANO-RCC basis set in terms of primitive basis functions allows for highly accurate calculations, it also hinders its applicability to large sized systems due to the computational costs. To tackle this problem, a new compact relativistic ANO basis set, the ANO-eXtra Small (XS) basis set, is introduced for elements H-Ca. The number of primitive basis functions in ANO-XS is about half that of the ANO-RCC basis set. This greatly reduces the computational costs in the integral calculations especially when used in combination with Cholesky decomposition. At the same time, the ANO-XS basis set is able to predict molecular properties such as bond lengths and excitation energies with reasonable errors compared to the larger ANO-RCC basis set. The main intention for the ANO-XS basis set is to be used in conjunction with the ANO-RCC basis set for large systems that can be divided with regions demanding different qualities of basis sets. This is exemplified in CASPT2 calculations for an Ir(C3H4N)3 complex, where substituting the larger ANO-RCC for the compact ANO-XS basis set at the ligand atoms yields only minor differences for a large number of excited states compared to calculations employing the ANO-RCC basis set on all atoms. Thus, accurate calculations including relativistic effects for large systems become more affordable with the new ANO-XS basis set.

Efficiently Capturing Weak Interactions in ab Initio Molecular Dynamics with on-the-Fly Basis Set Extrapolation.

Weak interactions have a critical role in accurately portraying conformational change. However, the computational study of these often requires large basis electronic structure calculations that are generally cost-prohibitive within ab initio molecular dynamics. Here, we present a new approach to efficiently obtain AIMD trajectories in agreement with large, triple-ζ, polarized valence basis functions, at much reduced computational cost. For example, it follows from our studies that AIMD trajectories can indeed be constructed in agreement with basis sets such as 6-311++G(2df,2pd) with computational effort commensurate with those from much smaller basis sets such as 6-31+G(d), for polypeptide systems with 100+ atoms. The method is based on molecular fragmentation and allows a range-specified repartitioning of intramolecular (and potentially intermolecular) interactions where noncovalent interactions are selectively assembled using a piece-wise reconstruction based on a set-theoretic inclusion-exclusion principle generalization of ONIOM. Through a simplex decomposition of molecular systems the approach efficiently provides the necessary many-body interactions to faithfully represent noncovalent interactions at the large basis limit. Conformational stabilization energies are provided at close to the complete-basis limit at much reduced cost, and similarly AIMD trajectories (both Born-Oppenheimer and Car-Parrinello-type) are obtained in agreement with very large basis set sizes, in an extremely efficient and accurate manner. The method is demonstrated through simulations on polypeptide fragments of a variety of sizes.

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.

Electron Propagator Methods for Vertical Electron Detachment Energies of Anions: Benchmarks and Case Studies.

Ab initio electron propagator methods are efficient and accurate means of calculating vertical electron detachment energies of closed-shell, molecular anions with nuclei from the first three periods. Basis set extrapolations enable definitive comparisons between electron propagator results and benchmarks defined by total energy differences obtained with coupled-cluster, single, double, plus perturbative triple substitution theory. The best compromises of accuracy and efficiency are provided by the renormalized, partial third-order, diagonal (P3+) self-energy and by the nondiagonal, renormalized, second-order (NR2) approximation. The outer-valence Green function, the two-particle-one-hole Tamm-Dancoff approximation, the third-order algebraic diagrammatic construction, and the renormalized third-order methods also are examined. A detailed analysis of errors for small anions is performed. Case studies include F-(H2O) and Cl-(H2O) complexes, C5H5-, two P2N3- pentagonal rings, and a superhalide, Al(BO2)4-, whose electron detachment energy is more than double those of the halide anions. These applications illustrate the versatility of electron propagator methods, their utility for interpreting negative-ion photoelectron spectra, and their promise in the discovery of unusual properties and patterns of chemical bonding. Composite methods, which combine basis set effects calculated at the relatively efficient diagonal, second-order level and higher correlation effects calculated with small basis sets, provide excellent estimates of basis set-extrapolated P3+ or NR2 results and facilitate applications to large molecules. In the P3+ and NR2 methods, a judicious choice of low-order couplings between hole operators that correspond to the assumptions of Koopmans's theorem and operators that describe final-state relaxation and polarization and initial-state correlation leads to predictive accuracy, computational efficiency, and interpretive lucidity.

Stepwise basis set selection.

The computational cost of quantum chemical methods grows rapidly with increasing level of theory and basis set size. At increasing costs, higher accuracies can be reached, forcing a compromise between cost and accuracy for most molecular systems. Heats of reaction, however, are mostly determined by a subset of atoms that experience significant bonding and/or electronic changes. To exploit this fact, the Stepwise Basis Builder (SBB) algorithm selectively adds basis functions to reactive atoms and maintains small basis sets on spectator atoms. This article introduces the SBB algorithm and how it chooses a basis for each atom, predicts calculation errors, and uses these predicted errors to reach target levels of accuracy. Benchmarks show SBB heats of reaction and activation barriers converge to values consistent with higher-quality calculations using a greatly reduced number of basis functions. © 2018 Wiley Periodicals, Inc.

A compact and accurate set of basis functions for model-based reconstructions

Abstract Model-based perfusion reconstruction (MBPR) by using a weighting sum of basis functions, is used to describe the dynamic contrast agent distribution by superposition of incorporated prior knowledge. It handles temporal under-sampling in measurements acquired with a slowly rotating X-ray-based imaging system, in our case a C-arm based computed tomography (CT). However, here challenging issue arises that the computing complexity increases proportional to the number of prior knowledge elements. Thus, the aim of this study is to analyze clinical data and elaborate basis functions, that maps various patients with a small orthonormal basis set (ONB). This work is based on five reconstructed clinical perfusion CT data sets. For each patient, regions of interest were manually figured out in order to enhance the content. Therefore, bones and catheters have to be removed out of the data, to prevent a falsification of the curves by them. The principal component analysis (PCA) to compress the relevant information of perfusion and create an ONB was used. In order to achieve an ONB which also optimal maps unknown patients, the cross validation method was used, i.e. the datasets of four patients were utilized for the estimation of the ONB, while the remaining patient was used for evaluation. Finally, the ONB gets evaluated by the mean-absolute-percentage-error (MAPE) of MBPR. A compact ONB with three basis functions that maps all five patients without a significant d eviation o f t he approximated curves and the original ones is obtained. Especially, regions with high blood supply can be reconstructed very accurately and a reduction of noise is qualitatively visible in the image. An optimum ONB for the MBPR requires that the curves can be modeled as exactly as possible with a few basis elements. The use of only a few elements also leads to short computing times. In this work a good approximation of the curves with three basis elements is received. This results in an improved MBPR that in turn can lead to a higher precision of stroke diagnostics and treatments by using C-Arm CT.

An efficient hybrid orbital representation for quantum Monte Carlo calculations.

The scale and complexity of the quantum system to which real-space quantum Monte Carlo (QMC) can be applied in part depends on the representation and memory usage of the trial wavefunction. B-splines, the computationally most efficient basis set, can have memory requirements exceeding the capacity of a single computational node. This situation has traditionally forced a difficult choice of either using slow internode communication or a potentially less accurate but smaller basis set such as Gaussians. Here, we introduce a hybrid representation of the single particle orbitals that combine a localized atomic basis set around atomic cores and B-splines in the interstitial regions to reduce the memory usage while retaining the high speed of evaluation and either retaining or increasing overall accuracy. We present a benchmark calculation for NiO demonstrating a superior accuracy while using only one eighth of the memory required for conventional B-splines. The hybrid orbital representation therefore expands the overall range of systems that can be practically studied with QMC.

Evaluation of Gas-to-Liquid 17O Chemical Shift of Water: A Test Case for Molecular and Periodic Approaches.

Modeling liquid water features is a challenging and ongoing task that brings together a number of computational issues related to the description both of its electronic and geometrical structure. In order to go a step further in the understanding of this peculiar liquid, we present a thorough analysis of NMR gas-to-liquid 17O and 1H shifts of water using density functional theory based molecular dynamics. In order to be as consistent as possible, we consider the influence of basis sets, exchange-correlation functionals, and structural models, in both molecular and periodic schemes, to evaluate 17O and 1H nuclear shieldings. We show that strong error compensations between functional and basis-set expansion can be obtained in molecular approaches which artificially produces good 17O gas-to-liquid shifts with relatively small basis sets. We also demonstrate that, despite their ability to provide reliable liquid phase structures, generalized-gradient approximation based exchange-correlation functionals lead to strongly inconsistent values for 17O gas-to-liquid shift. This latter property is shown to be strongly influenced by intramolecular electronic delocalization, accentuated by the surrounded molecules. In contrast, 1H is less sensitive to this effect. By including a Hartree-Fock exchange term, through the use of hybrid functionals which partially correct the self-interaction error, better agreement with experimental values is obtained. The present study provides a detailed guideline to properly evaluate gas-to-liquid shifts in hydrogen bonded systems and emphasizes that, for nuclear shieldings, an accurate electronic structure evaluation prevails over the description of the liquid structure.

Excitation energies from diffusion Monte Carlo using selected configuration interaction nodes.

Quantum Monte Carlo (QMC) is a stochastic method that has been particularly successful for ground-state electronic structure calculations but mostly unexplored for the computation of excited-state energies. Here, we show that within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using selected configuration interaction (sCI) expansions, one is able to obtain accurate excitation energies at the fixed-node diffusion Monte Carlo (FN-DMC) level. This evidences that the fixed-node errors in the ground and excited states obtained with sCI wave functions cancel out to a large extent. Our procedure is tested on two small organic molecules (water and formaldehyde) for which we report all-electron FN-DMC calculations. For both the singlet and triplet manifolds, accurate vertical excitation energies are obtained with relatively compact multideterminant expansions built with small (typically double-ζ) basis sets.

Post-CCSD(T) contributions to total atomization energies in multireference systems.

We examine the magnitude and the basis set convergence of post-coupled-cluster with single, double, and perturbative triple excitations (CCSD(T)) contributions (up to CCSDTQ567) for a wide and diverse set of 21 first- and second-row molecules with up to four non-hydrogen atoms. We focus on multireference systems for which post-CCSD(T) effects are particularly pronounced. The considered molecules are BN(1∑+), C2(1∑+), O2, FO, P2, S2, ClO, N2O, NO2, O3, FNO, FO2, F2O, S2O, S3, ClNO, ClOO, Cl2O, N2C2, P4, and S4. This set spans the gamut from molecules dominated by moderate nondynamical correlation (e.g., FO, ClO, NO2, S2O, N2C2, and P4) to systems dominated by strong nondynamical correlation (e.g., BN, C2, FO2, O3, ClOO, and S4). We examine the basis set convergence of the CCSDT, CCSDT(Q), CCSDTQ, CCSDTQ(5), CCSDTQ5, CCSDTQ5(6), CCSDTQ56, CCSDTQ56(7), and CCSDTQ567 methods. The largest basis sets employed in each category are cc-pV6Z (CCSDT(Q)), cc-pV5Z (CCSDTQ), cc-pVTZ (CCSDTQ5(6)), and cc-pVDZ (CCSDTQ567). Apart from examining the basis-set convergence of post-CCSD(T) contributions near the one-particle basis-set limit, this work explores cost-effective approaches for obtaining these contributions from fairly small basis sets. We consider both effective basis-set extrapolations and scaling factors. An important finding is that extrapolating the perturbative connected quadruples, (Q), from the cc-pVDZ(4s3p1d) and cc-pVTZ basis sets yields near basis-set limit results and represents a significant improvement relative to cc-pV{D,T}Z extrapolation at no additional computational cost (where cc-pVDZ(4s3p1d) is an extended version of the cc-pVDZ basis set). Combining the (Q)/cc-pV{D(4s3p1d),T}Z extrapolations with the fully iterative connected quadruples, Q-(Q), contribution calculated with the cc-pVDZ (or even the cc-pVDZ(3s2p)) basis set is a cost-effective way for obtaining the connected quadruples component close to the basis-set limit (where cc-pVDZ(3s2p) is a truncated version of the cc-pVDZ basis set). In addition, we show that the (5)/cc-pVDZ(3s2p) and (6)/cc-pVDZ(3s2p) components provide reasonable approximations for the connected quintuple and sextuple components close to the basis-set limit, respectively.

All-electron triple zeta basis sets for the actinides

Abstract Non-relativistic and Douglas-Kroll-Hess (DKH) segmented all-electron basis sets of valence triple zeta quality plus polarization functions (TZP) for the actinides are developed. To describe accurately the properties that depend on a good description of the electrons far away from the nuclei, the corresponding augmented sets (ATZP and ATZP-DKH) are reported as well. For the actinide monoxides, bond distances, dissociation energies, natural charges and populations of the valence orbitals of the actinides, and bond indices are calculated with the B3LYP/TZP-DKH procedure. For Am and No, the B3LYP/ATZP-DKH static mean dipole polarizabilities are also computed. To assess the performance of these small size all-electron basis sets, comparison with theoretical and experimental data reported previously in the literature is done. These sets must be also helpful on calculations of properties involving simultaneously core and valence electrons.

Combination of large and small basis sets in electronic structure calculations on large systems.

Two basis sets-a large and a small one-are associated with each nucleus of the system. Each atom has its own separate one-electron basis comprising the large basis set of the atom in question and the small basis sets for the partner atoms in the complex. The perturbed atoms in molecules and solids model is at core of the approach since it allows for the definition of perturbed atoms in a system. It is argued that this basis set approach should be particularly useful for periodic systems. Test calculations are performed on one-dimensional arrays of H and Li atoms. The ground-state energy per atom in the linear H array is determined versus bond length.