Small Basis Sets Research Articles

Theoretical investigation of gas-phase molecular complex formation between 2-hydroxy thiophenol and a water molecule.

The torsional potential of OH and SH rotations in 2-hydroxy thiophenol is systematically studied using the MP2 ab initio method. The outcome of state-of-the-art calculations is used in the investigation of the structures and conformational preferences of 2-hydroxy thiophenol and aims at further interaction studies with a gas phase water molecule. SCS-MP2 and CCSD(T) complete basis set (CBS) limit interaction energies for these complexes are presented. The SCS-MP2/CBS limit is achieved using various two-point extrapolation methods with aug-cc-pVDZ and aug-cc-pVTZ basis sets. The CCSD(T) correction term is determined as the difference between CCSD(T) and SCS-MP2 interaction energies calculated using a smaller basis set. The effect of counterpoise correction on the extrapolation to the CBS limit is discussed. The performance of DFT based wB97XD, M06-2X and B3LYP-D3 functionals is tested against the benchmark energy from ab initio calculations. Hydrogen bond interactions are characterized by carrying out QTAIM, NCIPLOT, NBO and SAPT analyses.

Optimized virtual orbital subspace for faster GW calculations in localized basis.

The popularity of the GW approximation to the self-energy to access the quasiparticle energies of molecules is constantly increasing. As the other methods addressing the electronic correlation, the GW self-energy unfortunately shows a very slow convergence with respect to the basis complexity, which precludes the calculation of accurate quasiparticle energies for large molecules. Here we propose a method to mitigate this issue that relies on two steps: (i) the definition of a reduced virtual orbital subspace, thanks to a much smaller basis set; (ii) the account of the remainder through the simpler one-ring approximation to the self-energy. We assess the quality of the corrected quasiparticle energies for simple molecules, and finally we show an application to large graphene chunks to demonstrate the numerical efficiency of the scheme.

Potential use of small basis set on the calculations of electronic properties of some four-membered heterocycles: a conformational study

ABSTRACTThe potential use of small basis sets upon a low level of theory was studied on the calculations of electronic properties (dipole moment, static polarisability and static hyperpolarisabilities) of a series of 16 four-membered heterocycles with an exocyclic double bond at the position 3 (1–16). First, the calculations were performed within the Hartree–Fock (HF) approximation using 6-31G, 6-31G(d,p) and 6-31+G(d,p) as basis sets for the different conformational states of each molecule, and the results obtained were compared with the MP2/6-31+G(d,p) results reported. In the second place, in order to know the real potential of HF calculations, these were compared with those calculated using larger approaches such as MP2/6-311+G(d,p), MP2/aug-cc-pVDZ, CCS/6-311+G(d,p), CCS/aug-cc-pVDZ, CCS/aug-cc-pVTZ, CCSD/6-31+G(d) and CCSD/cc-pVDZ, taken into account only the planar and equilibrium geometries of each molecules. The HF approaches permit us to obtain a good qualitative representation of the dipole moment as a function of puckering angle in comparison with MP2, CCS and CCSD levels for all tested molecules. However, only HF/6-31+G(d,p) provides quantitative values of dipole moment for the heterocycles 1, 5 and 13 in comparison with MP2, CCS and CCSD levels. On the other hand, the polarisability and hyperpolarisabilities were quite sensitive to the quality of level of theory and basis sets. In particular, HF/6-31+G(d,p) predicted a representative approximation of alpha for the molecule 16 in comparison with larger methods as MP2/aug-cc-pVDZ, CCS/aug-cc-pVDZ and CCS/aug-cc-pVTZ, while a detailed analysis showed that HF can be used in the calculation of alpha for the molecules 3, 7, 11 and 15, but it requires the use of extended basis sets. Also, HF/6-31+G(d,p) predicted values of beta very similar to those calculated at the MP2 and CCSD levels used, for the planar and equilibrium geometry of the molecules 10 and 14. Furthermore, HF/6-31+G(d,p) described a representative dependence of this property with the puckering angle for the heterocycles 9, 10 and 14, compared with the MP2 curves.

The INV24 test set: how well do quantum-chemical methods describe inversion and racemization barriers?

For years, there has been ongoing interest in experimentally and theoretically understanding inversion and racemization processes. However, to the best of our knowledge, there has been no computational study that systematically investigated how well low-level quantum-chemical methods predict inversion barriers. Herein, we provide an answer to this question and we present the INV24 benchmark set of 24 high-level, ab initio inversion barriers. INV24 covers inversion in triatomics, in pyramidal molecules, in one cyclic system, and in various helical and bowl-shaped compounds. Our results indicate that previously applied DFT approximations combined with small basis sets are not reliable enough and that at least a triple-ζ basis is needed for meaningful results. Moreover, we show that intramolecular London dispersion influences the barriers by 2 kcal/mol or more and that dispersion corrections should always be applied to DFT results. With our analysis of 34 DFT approximations, we can reproduce the well-known Jacob’s Ladder scheme with (meta-)generalized-gradient-approximation methods underestimating barriers and global-hybrid DFT functionals performing better. Range-separated hybrids or Minnesota-type hybrids are not particularly superior to more conventional methods, such as B3LYP-D3. The by far best results are achieved with dispersion-corrected double hybrids, which give results below the chemical accuracy target of 1 kcal/mol. They also outperform wave-function second-order perturbation theory approaches and we recommend using them whenever possible. Given that our systematic study of INV24 is the first of its kind, our findings have the potential to change common practice in this field and they will guide future investigations of inversion processes.

Sturmian bases for two-electron systems in hyperspherical coordinates

We give a detailed account of an ab initio spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the same structure as the one of atomic hydrogen with the Coulomb potential expressed in terms of a hyperradius and the nuclear charge replaced by an angle dependent effective charge. The simplest spectral approach consists in expanding the hyperangular wave function in a basis of hyperspherical harmonics. This expansion however, is known to be very slowly converging. Instead, we introduce new hyperangular Sturmian functions. These functions do not have an analytical expression but they treat the first term of the multipole expansion of the electron–electron interaction potential, namely the radial electron correlation, exactly. The properties of these new functions are discussed in detail. For the basis functions of the hyperradius, several choices are possible. In the present case, we use Coulomb–Sturmian functions of half integer angular momentum. We show that, in the case of H−, the accuracy of the energy and the width of the resonance states obtained through a single diagonalization of the Hamiltonian, is comparable to the values given by state-of-the-art methods while using a much smaller basis set. In addition, we show that precise values of the electric-dipole oscillator strengths for transitions in helium are obtained thereby confirming the accuracy of the bound state wave functions generated with the present method.

Density functional theory basis set convergence of sulfuric acid-containing molecular clusters

We investigate the basis set convergence of three density functionals (M06-2X, PW91, and ωB97X-D) with respect to the binding energy, thermal contribution to the Gibbs free energy, and optimized geometry. We apply correlation consistent, Pople-type, and polarization consistent basis sets with different amount of diffuse and polarization functions. Our test set contains six molecular cluster formation reactions which represent key noncovalent interactions in the atmosphere. In most cases partially augmented basis sets yield as accurate results as the fully augmented basis sets, with significant gain in computational efficiency. Relatively small basis sets are found to be sufficient to optimize geometries and to calculate thermal contributions to the Gibbs free energy. For binding energies, slightly bigger basis sets are needed to reach the complete basis set limit. The PW91 functional with the 6-311++G(3df,3pd) basis set gives a mean absolute error of 0.9kcal/mol in the binding energy, indicating that it has not reached the complete basis set limit. We estimate the effect of anharmonicity and derive scale factors to correct for it. When the lowest vibrational frequencies are treated separately, the errors arising from the anharmonicity of the remaining frequencies are small regardless of system size. We treated the low frequencies as free rotors and calculate thermal contributions to the Gibbs free energy using the quasi-harmonic approximation. We identify an error of a few percent of the total harmonic thermal contributions, which is larger than the error arising from vibrational anharmonicity.

Binding free energies in the SAMPL5 octa-acid host\u2013guest challenge calculated with DFT-D3 and CCSD(T)

We have tried to calculate the free energy for the binding of six small ligands to two variants of the octa-acid deep cavitand host in the SAMPL5 blind challenge. We employed structures minimised with dispersion-corrected density-functional theory with small basis sets and energies were calculated using large basis sets. Solvation energies were calculated with continuum methods and thermostatistical corrections were obtained from frequencies calculated at the HF-3c level. Care was taken to minimise the effects of the flexibility of the host by keeping the complexes as symmetric and similar as possible. In some calculations, the large net charge of the host was reduced by removing the propionate and benzoate groups. In addition, the effect of a restricted molecular dynamics sampling of structures was tested. Finally, we tried to improve the energies by using the DLPNO–CCSD(T) approach. Unfortunately, results of quite poor quality were obtained, with no correlation to the experimental data, systematically too positive affinities (by ~50 kJ/mol) and a mean absolute error (after removal of the systematic error) of 11–16 kJ/mol. DLPNO–CCSD(T) did not improve the results, so the accuracy is not limited by the energy function. Instead, four likely sources of errors were identified: first, the minimised structures were often incorrect, owing to the omission of explicit solvent. They could be partly improved by performing the minimisations in a continuum solvent with four water molecules around the charged groups of the ligands. Second, some ligands could bind in several different conformations, requiring sampling of reasonable structures. Third, there is an indication the continuum-solvation model has problems to accurately describe the binding of both the negatively and positively charged guest molecules. Fourth, different methods to calculate the thermostatistical corrections gave results that differed by up to 30 kJ/mol and there is an indication that HF-3c overestimates the entropy term. In conclusion, it is a challenge to calculate binding affinities for this octa-acid system with quantum–mechanical methods.

Numerical test of SAC-CI methods for calculating vertical ionization energies

Valence, vertical ionization energies of a representative set of closed-shell molecules were calculated with the symmetry-adapted-cluster, configuration-interaction (SAC-CI) method using ten basis sets for its level 1 and level 2 operator inclusion criteria, whereas for its more stringent level 3 scheme, 15 basis sets were used. SAC-CI level 3 is capable of producing mean unsigned errors of approximately 0.2 eV with quadruple $$\zeta$$ correlation-consistent basis sets. Fortuitously better results may be obtained when smaller basis sets are used. Anomalous behavior with respect to the basis set size may occur when the level 1 and level 2 options are employed.

Assessment of multireference approaches to explicitly correlated full configuration interaction quantum Monte Carlo.

The Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method has proved able to provide near-exact solutions to the electronic Schrödinger equation within a finite orbital basis set, without relying on an expansion about a reference state. However, a drawback to the approach is that being based on an expansion of Slater determinants, the FCIQMC method suffers from a basis set incompleteness error that decays very slowly with the size of the employed single particle basis. The FCIQMC results obtained in a small basis set can be improved significantly with explicitly correlated techniques. Here, we present a study that assesses and compares two contrasting "universal" explicitly correlated approaches that fit into the FCIQMC framework: the [2]R12 method of Kong and Valeev [J. Chem. Phys. 135, 214105 (2011)] and the explicitly correlated canonical transcorrelation approach of Yanai and Shiozaki [J. Chem. Phys. 136, 084107 (2012)]. The former is an a posteriori internally contracted perturbative approach, while the latter transforms the Hamiltonian prior to the FCIQMC simulation. These comparisons are made across the 55 molecules of the G1 standard set. We found that both methods consistently reduce the basis set incompleteness, for accurate atomization energies in small basis sets, reducing the error from 28 mEh to 3-4 mEh. While many of the conclusions hold in general for any combination of multireference approaches with these methodologies, we also consider FCIQMC-specific advantages of each approach.

Anatomy of molecular properties evaluated with explicitly correlated electronic wave functions

ABSTRACTStatic electric dipole and quadrupole moments were evaluated at the explicitly correlated second-order Møller–Plesset (MP2-F12) level for BH, CO, H2O, and HF molecules. The electron correlation contributions to the multipole moments were further decomposed into the direct (unrelaxed) and indirect (orbital response) components; we found that both components are equally important for the conventional (MP2) contribution, whereas the F12 correction to these properties originates primarily from the orbital response effects. Finally, the direct contribution dominates in the perturbative Hartree–Fock basis set incompleteness (CABS singles) correction. Two basis set families were employed: the standard aug-cc-pVXZ series and the cc-pVXZ-F12 series designed specifically for the F12 methods. The aug-cc-pVXZ MP2-F12 multipole moments usually have smaller basis set errors than the cc-pVXZ-F12 counterparts, albeit their differences are small at the triple (X = T) and quadruple (X = Q) zeta level. With the MP2-F12 calculations, the basis set errors of dipole and quadrupole moments can be reduced to ∼0.001 a.u., or roughly 0.1%, at the aug-cc-pVDZ and aug-cc-pVTZ levels, respectively.

Composite electron propagator methods for calculating ionization energies.

Accurate ionization energies of molecules may be determined efficiently with composite electron-propagator (CEP) techniques. These methods estimate the results of a calculation with an advanced correlation method and a large basis set by performing a series of more tractable calculations in which large basis sets are used with simpler approximations and small basis sets are paired with more demanding correlation techniques. The performance of several CEP methods, in which diagonal, second-order electron propagator results with large basis sets are combined with higher-order results obtained with smaller basis sets, has been tested for the ionization energies of closed-shell molecules from the G2 set. Useful compromises of accuracy and computational efficiency employ complete-basis-set extrapolation for second-order results and small basis sets in third-order, partial third-order, renormalized partial-third order, or outer valence Green's function calculations. Analysis of results for vertical as well as adiabatic ionization energies leads to specific recommendations on the best use of regular and composite methods. Results for 22 organic molecules of interest in the design of photovoltaic devices, benzo[a]pyrene, Mg-octaethylporphyrin, and C60 illustrate the capabilities of CEP methods for calculations on large molecules.

A machine learning correction for DFT non-covalent interactions based on the S22, S66 and X40 benchmark databases.

Background Non-covalent interactions (NCIs) play critical roles in supramolecular chemistries; however, they are difficult to measure. Currently, reliable computational methods are being pursued to meet this challenge, but the accuracy of calculations based on low levels of theory is not satisfactory and calculations based on high levels of theory are often too costly. Accordingly, to reduce the cost and increase the accuracy of low-level theoretical calculations to describe NCIs, an efficient approach is proposed to correct NCI calculations based on the benchmark databases S22, S66 and X40 (Hobza in Acc Chem Rev 45: 663–672, 2012; Řezáč et al. in J Chem Theory Comput 8:4285, 2012).ResultsA novel type of NCI correction is presented for density functional theory (DFT) methods. In this approach, the general regression neural network machine learning method is used to perform the correction for DFT methods on the basis of DFT calculations. Various DFT methods, including M06-2X, B3LYP, B3LYP-D3, PBE, PBE-D3 and ωB97XD, with two small basis sets (i.e., 6-31G* and 6-31+G*) were investigated. Moreover, the conductor-like polarizable continuum model with two types of solvents (i.e., water and pentylamine, which mimics a protein environment with ε = 4.2) were considered in the DFT calculations. With the correction, the root mean square errors of all DFT calculations were improved by at least 70 %. Relative to CCSD(T)/CBS benchmark values (used as experimental NCI values because of its high accuracy), the mean absolute error of the best result was 0.33 kcal/mol, which is comparable to high-level ab initio methods or DFT methods with fairly large basis sets. Notably, this level of accuracy is achieved within a fraction of the time required by other methods. For all of the correction models based on various DFT approaches, the validation parameters according to OECD principles (i.e., the correlation coefficient R2, the predictive squared correlation coefficient q2 and q_{cv}^{2} from cross-validation) were >0.92, which suggests that the correction model has good stability, robustness and predictive power.ConclusionsThe correction can be added following DFT calculations. With the obtained molecular descriptors, the NCIs produced by DFT methods can be improved to achieve high-level accuracy. Moreover, only one parameter is introduced into the correction model, which makes it easily applicable. Overall, this work demonstrates that the correction model may be an alternative to the traditional means of correcting for NCIs.Graphical abstractA machine learning correction model efficiently improved the accuracy of non-covalent interactions(NCIs) calculated by DFT methods. The application of the correction model is easy and flexible, so it may be an alternative correction means for NCIs by first-principle calculations.Electronic supplementary materialThe online version of this article (doi:10.1186/s13321-016-0133-7) contains supplementary material, which is available to authorized users.

DFT study of zigzag (n, 0) single-walled carbon nanotubes: 13C NMR chemical shifts

13C NMR chemical shifts of selected finite-size models of pristine zigzag single walled carbon nanotubes (SWCNTs) with a diameter of ∼0.4–0.8nm and length up to 2.2nm were studied theoretically. Results for finite SWCNTs models containing 1, 4 and 10 adjacent bamboo-type units were compared with data obtained for infinite tubes in order to estimate the reliability of small finite models in predicting magnetic properties of real-size nanotubes and to assess their tube-length dependence. SWCNTs were fully optimized using unrestricted density functional theory (DFT-UB3LYP/6-31G*). Cyclacenes, as the shortest models of open-ended zigzag SWCNTs, with systematically varying diameter were calculated as well. GIAO NMR calculations on the SWCNT and cyclacene models were performed using the BHandH density functional combined with relatively small STO-3Gmag basis set, developed by Leszczyński and coworkers for accurate description of magnetic properties. Regular changes of carbon 13C chemical shifts along the tube axis of real size (6, 0) and (9, 0) zigzag carbon nanotubes were shown. The 13C NMR shifts according to increasing diameter calculated for zigzag (n, 0, n=5–10) cyclacenes followed the trends observed for zigzag (n, 0) SWCNTs. The results for 4-units long SWCNTs match reasonably well with the data obtained for infinite zigzag (n, 0) SWCNTs, especially to those with bigger diameter (n=8-15). The presence of rim hydrogens obviously affects theoretical 13C chemical shieldings and shifts in cyclacenes and thus cyclacenes can provide only approximate estimation of 13C NMR parameters of real-size SWCNTs. The NMR properties predicted for the longest 10-units long models of SWCNTs reliably correspond to results obtained for infinite nanotubes. They were thus able to accurately predict also recently reported experimental chemical shift of chiral (6, 5) SWCNT.

ChemInform Abstract: Computational Catalysis Using the Artificial Force Induced Reaction Method

AbstractReview: 33 refs.

ChemInform Abstract: Small Atomic Orbital Basis Set First‐Principles Quantum Chemical Methods for Large Molecular and Periodic Systems: A Critical Analysis of Error Sources

AbstractReview: 123 refs.

Pseudospectral Gaussian quantum dynamics: Efficient sampling of potential energy surfaces.

Trajectory-based Gaussian basis sets have been tremendously successful in describing high-dimensional quantum molecular dynamics. In this paper, we introduce a pseudospectral Gaussian-based method that achieves accurate quantum dynamics using efficient, real-space sampling of the time-dependent basis set. As in other Gaussian basis methods, we begin with a basis set expansion using time-dependent Gaussian basis functions guided by classical mechanics. Unlike other Gaussian methods but characteristic of the pseudospectral and collocation methods, the basis set is tested with N Dirac delta functions, where N is the number of basis functions, rather than using the basis function as test functions. As a result, the integration for matrix elements is reduced to function evaluation. Pseudospectral Gaussian dynamics only requires O(N) potential energy calculations, in contrast to O(N(2)) evaluations in a variational calculation. The classical trajectories allow small basis sets to sample high-dimensional potentials. Applications are made to diatomic oscillations in a Morse potential and a generalized version of the Henon-Heiles potential in two, four, and six dimensions. Comparisons are drawn to full analytical evaluation of potential energy integrals (variational) and the bra-ket averaged Taylor (BAT) expansion, an O(N) approximation used in Gaussian-based dynamics. In all cases, the pseudospectral Gaussian method is competitive with full variational calculations that require a global, analytical, and integrable potential energy surface. Additionally, the BAT breaks down when quantum mechanical coherence is particularly strong (i.e., barrier reflection in the Morse oscillator). The ability to obtain variational accuracy using only the potential energy at discrete points makes the pseudospectral Gaussian method a promising avenue for on-the-fly dynamics, where electronic structure calculations become computationally significant.

Efficient polarized basis sets for evaluation of static and dynamic molecular electric properties

New medium size Gaussian-type basis set R-ORP for evaluation of static and dynamic electric properties in molecular systems is presented. It is obtained in a close resemblance to the original ORP basis set, from the source basis set through addition of two first-order polarization functions whose exponent values are optimized with respect to the finite field restricted open-shell Hartree–Fock (ROHF) atomic polarizabilities. As the source set the VTZ basis set of Ahlrichs and coworkers, augmented with additional diffuse functions and contracted to the form [6s/3s] for hydrogen and [11s7p/4s3p] for carbon through fluorine, is chosen. The resulting basis set is of the form [6s2p/3s2p] for hydrogen and [11s7p2d/4s3p2d] for other atoms. Presented basis set is next tested in the CCSD static and dynamic molecular polarizability and hyperpolarizability calculations for a set of ten and four test molecules, respectively, for which very accurate reference data exist. Additionally, the recently developed ORP basis set is employed in the calculations to examine the limits of its applicability. Results are compared to the literature data obtained in both, large and diffuse, as well as reduced-size basis sets. In the case of polarizability calculations, the aug-pc-1 and R-ORP are the optimal choices among the investigated smaller basis sets, with the overall performance of the aug-pc-1 set being better. Among the larger sets, the ORP performs better in the case of average polarizability, while the RMSE values for polarizability anisotropy are practically identical for d-aug-cc-pVDZ and ORP sets. Finally, the R-ORP and ORP basis sets compete other small bases in the evaluation of the first hyperpolarizability in investigated systems. © 2016 Wiley Periodicals, Inc.

Many-Electron Integrals over Gaussian Basis Functions. I. Recurrence Relations for Three-Electron Integrals.

Explicitly correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations and can often achieve chemical accuracy with relatively small Gaussian basis sets. In most calculations, the many three- and four-electron integrals that formally appear in the theory are avoided through judicious use of resolutions of the identity (RI). However, for the intrinsic accuracy of the F12 wave function to not be jeopardized, the associated RI auxiliary basis set must be large. Here, inspired by the Head-Gordon-Pople and PRISM algorithms for two-electron integrals, we present an algorithm to directly compute three-electron integrals over Gaussian basis functions and a very general class of three-electron operators without invoking RI approximations. A general methodology to derive vertical, transfer, and horizontal recurrence relations is also presented.

Computational Catalysis Using the Artificial Force Induced Reaction Method.

The artificial force induced reaction (AFIR) method in the global reaction route mapping (GRRM) strategy is an automatic approach to explore all important reaction paths of complex reactions. Most traditional methods in computational catalysis require guess reaction paths. On the other hand, the AFIR approach locates local minima (LMs) and transition states (TSs) of reaction paths without a guess, and therefore finds unanticipated as well as anticipated reaction paths. The AFIR method has been applied for multicomponent organic reactions, such as the aldol reaction, Passerini reaction, Biginelli reaction, and phase-transfer catalysis. In the presence of several reactants, many equilibrium structures are possible, leading to a number of reaction pathways. The AFIR method in the GRRM strategy determines all of the important equilibrium structures and subsequent reaction paths systematically. As the AFIR search is fully automatic, exhaustive trial-and-error and guess-and-check processes by the user can be eliminated. At the same time, the AFIR search is systematic, and therefore a more accurate and comprehensive description of the reaction mechanism can be determined. The AFIR method has been used for the study of full catalytic cycles and reaction steps in transition metal catalysis, such as cobalt-catalyzed hydroformylation and iron-catalyzed carbon-carbon bond formation reactions in aqueous media. Some AFIR applications have targeted the selectivity-determining step of transition-metal-catalyzed asymmetric reactions, including stereoselective water-tolerant lanthanide Lewis acid-catalyzed Mukaiyama aldol reactions. In terms of establishing the selectivity of a reaction, systematic sampling of the transition states is critical. In this direction, AFIR is very useful for performing a systematic and automatic determination of TSs. In the presence of a comprehensive description of the transition states, the selectivity of the reaction can be calculated more accurately. For relatively large molecular systems, the computational cost of AFIR searches can be reduced by using the ONIOM(QM:QM) or ONIOM(QM:MM) methods. In common practice, density functional theory (DFT) with a relatively small basis set is used for the high-level calculation, while a semiempirical approach or a force field description is used for the low-level calculation. After approximate LMs and TSs are determined, standard computational methods (e.g., DFT with a large basis set) are used for the full molecular system to determine the true LMs and TSs and to rationalize the reaction mechanism and selectivity of the catalytic reaction. The examples in this Account evidence that the AFIR method is a powerful approach for accurate prediction of the reaction mechanisms and selectivities of complex catalytic reactions. Therefore, the AFIR approach in the GRRM strategy is very useful for computational catalysis.

Assessment of the basis set effect on the structural and electronic properties of organic-protected gold nanoclusters

We have investigated the structural and optical properties of five monolayer-protected gold nanoclusters with a combination of exchange–correlation functionals, namely B-PBE for the geometry relaxation and CAM-B3LYP for the time-dependent calculations. We have tested the accuracy of five different basis sets in reproducing the experimental structures of these nanoclusters, and we have found that even a rather small basis set (single zeta) can outperform a significantly larger one (double zeta) if some selected atoms are treated with polarization functions. Namely, the sulfur and phosphorous atoms of the capping thiols and phosphines usually are hypervalent when bonded to the gold inner core; therefore, polarization functions allow them significantly more structural flexibility. With the two best performing basis sets, we carried out optical calculations and found that the resulting UV–Vis profiles are largely similar, in particular the energy and orbital contributions of the optical gaps are very close. The results support the use of the small basis set proposed here to investigate larger nanoclusters with general hybrid and range-corrected hybrid functionals.