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.     

On the performance of long‐range‐corrected density functional theory and reduced‐size polarized LPol‐n basis sets in computations of electric dipole (hyper)polarizabilities of π‐conjugated molecules

Static longitudinal electric dipole (hyper)polarizabilities are calculated for six medium‐sized π‐conjugated organic molecules using recently developed LPol‐n basis set family to assess their performance. Dunning's correlation‐consistent basis sets of triple‐ζ quality combined with MP2 method and supported by CCSD(T)/aug‐cc‐pVDZ results are used to obtain the reference values of analyzed properties. The same reference is used to analyze (hyper)polarizabilities predicted by selected exchange‐correlation functionals, particularly those asymptotically corrected. © 2012 Wiley Periodicals, Inc.     

Ab initio prediction of the vibrational spectra of the hydrogen‐bonded complexes between CO and HONO2

The vibrational characteristics (vibrational frequencies and infrared intensities) for free and complexed CO and HONO₂ have been predicted using ab initio calculations at SCF and MP2 levels with different basis sets and B3LYP/6?31G(d,p) calculations. The ab initio calculations show that the complexation between HONO₂ and CO leads to two stable structures: CO … HONO₂ (1A) and OC … HONO₂ (1B). The changes in the vibrational characteristics from free monomers to complexes have been estimated. It was established that the most sensitive to the complexation is the stretching O? H vibration. In agreement with the experiment, its vibrational frequency in the complexes is shifted to lower frequency (Δν = ?123 cm^?1). The magnitude of the wave number shift is indicative of relatively strong hydrogen‐bonded interaction. The ab initio calculations at different levels predict an increase of the infrared intensity of the stretching O? H vibration for structure 1A more than five times and for structure 1B more than nine times. The most consistent agreement between the computed values of the frequency shifts for structure 1B and those experimentally observed suggests that this structure is preferred. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Efficiency of numerical basis sets for predicting the binding energies of hydrogen bonded complexes: evidence of small basis set superposition error compared to Gaussian basis sets

Binding energies of selected hydrogen bonded complexes have been calculated within the framework of density functional theory (DFT) method to discuss the efficiency of numerical basis sets implemented in the DFT code DMol3 in comparison with Gaussian basis sets. The corrections of basis set superposition error (BSSE) are evaluated by means of counterpoise method. Two kinds of different numerical basis sets in size are examined; the size of the one is comparable to Gaussian double zeta plus polarization function basis set (DNP), and that of the other is comparable to triple zeta plus double polarization functions basis set (TNDP). We have confirmed that the magnitudes of BSSE in these numerical basis sets are comparative to or smaller than those in Gaussian basis sets whose sizes are much larger than the corresponding numerical basis sets; the BSSE corrections in DNP are less than those in the Gaussian 6-311+G(3df,2pd) basis set, and those in TNDP are comparable to those in the substantially large scale Gaussian basis set aug-cc-pVTZ. The differences in counterpoise corrected binding energies between calculated using DNP and calculated using aug-cc-pVTZ are less than 9 kJ/mol for all of the complexes studied in the present work. The present results have shown that the cost effectiveness in the numerical basis sets in DMol3 is superior to that in Gaussian basis sets in terms of accuracy per computational cost.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities. The excellent performance of the [13.10.4/7.5.2] GTO/CGTO polarized basis sets derived for Si through Cl is illustrated by the atomic polarizability results and SCF and MBPT data for dipole moments and polarizabilities of the second-row atom hydrides. The possible applications of the electric-property oriented polarized basis sets are discussed. The basis set data for Si through Cl are those for H and C through F append the paper.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization method is used to derive the first-order polarized basis sets for Ge through Br for calculations of atomic and molecular electric properties. The performance of the [15.12.9/9.7.4] GTO/CGTO basis sets generated in this study is verified in calculations of atomic dipole polarizabilities and dipole moments and polarizabilities of the third-row atom hydrides. Whenever accurate reference data are available for comparison, the excellent performance of the derived first-order polarized basis sets is demonstrated. The role of the core polarization and relativistic contributions to atomic and molecular is also investigated. The detailed basis set data for Ge through Br are given in Appendix.     

Density functional studies on hydrogen‐bonded clusters of hydrogen halides and the interaction on halide anions

Density functional theory (DFT) calculations have been performed to study the structures and stability of X^?·(HX)_n=2–5 clusters where X = F, Cl, Br at B3LYP/6‐311++G** level of theory. The presence of halide ions in these clusters disintegrates the hydrogen halide clusters. All the hydrogen halides are then hydrogen bonded to the centrally placed halide ions, thereby forming multiple hydrogen bonds. The interaction energies have been corrected for the basis set superposition error (BSSE) using Boy's counterpoise correction method. Evidence for the destruction of hydrogen bonds in hydrogen halide clusters due to the presence of halide ions is further obtained from topological analysis and natural bond orbital analysis. The chemical hardness and chemical potential have been calculated for all the anion clusters. The above analysis reveals that hydrogen bonding in these systems is not an essentially electrostatic interaction. The nature of the stabilization interactions operative in these multiple hydrogen‐bonded clusters has been explained in terms of many‐body contribution to interaction energies. From these studies, an attempt has been made to understand the nature of the molecular properties resulting from different electronegativities of the halogens. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Basis set error estimation for DFT calculations of electronic g‐tensors for transition metal complexes

We present a detailed study of the basis set dependence of electronic g‐tensors for transition metal complexes calculated using Kohn–Sham density functional theory. Focus is on the use of locally dense basis set schemes where the metal is treated using either the same or a more flexible basis set than used for the ligand sphere. The performance of all basis set schemes is compared to the extrapolated complete basis set limit results. Furthermore, we test the performance of the aug‐cc‐pVTZ‐J basis set developed for calculations of NMR spin‐spin and electron paramagnetic resonance hyperfine coupling constants. Our results show that reasonable results can be obtain when using small basis sets for the ligand sphere, and very accurate results are obtained when an aug‐cc‐pVTZ basis set or similar is used for all atoms in the complex. © 2014 Wiley Periodicals, Inc.     

NLO‐X (X = I–III): New Gaussian basis sets for prediction of linear and nonlinear electric properties

New adjusted Gaussian basis sets are proposed for first and second rows elements (H, B, C, N, O, F, Si, P, S, and Cl) with the purpose of calculating linear and mainly nonlinear optical (L–NLO) properties for molecules. These basis sets are new generation of Thakkar‐DZ basis sets, which were recontracted and augmented with diffuse and polarization extrabasis functions. Atomic energy and polarizability were used as reference data for fitting the basis sets, which were further applied for prediction of L–NLO properties of diatomic, H₂, N₂, F₂, Cl₂, BH, BF, BCl, HF, HCl, CO, CS, SiO, PN, and polyatomic, CH₄, SiH₄, H₂O, H₂S, NH₃, PH₃, OCS, NNO, and HCN molecules. The results are satisfactory for all electric properties tested; dipole moment (µ), polarizability (α), and first hyperpolarizability (β), with an affordable computational cost. Three new basis sets are presented and called as NLO‐I (ADZP), NLO‐II (DZP), and NLO‐III (VDZP). The NLO‐III is the best choice to predict L–NLO properties of large molecular systems, because it presents a balance between computational cost and accuracy. The average errors for β at B3LYP/NLO‐III level were of 8% for diatomic molecules and 14% for polyatomic molecules that are within the experimental uncertainty. © 2014 Wiley Periodicals, Inc.     

Finite‐field method with unbiased polarizable continuum model for evaluation of the second hyperpolarizability of an open‐shell singlet molecule in solvents

The static second hyperpolarizability γ of the complexes composed of open‐shell singlet 1,3‐dipole molecule involving a boron atom and a water molecule in aqueous phase are investigated by the finite‐field (FF) method combined with a standard polarized continuum model (PCM) and with a newly proposed unbiased PCM (UBPCM). On the basis of the comparison with the results calculated by the FF method using the full quantum and the quantum‐mechanical/molecular‐mechanical and molecular‐dynamics (QM/MM‐MD) treatments, the present FF‐UBPCM method is demonstrated to remedy the artificial overestimation of the γ caused by standard FF‐PCM calculations and to well reproduce the FF‐QM/MM‐MD and FF‐full‐QM results with much lower costs. © 2013 Wiley Periodicals, Inc.     

Ab initio study of the structure,cooperativity, and vibrational properties in the mixed hydrogen‐bonded trimers of hydrogen isocyanide and water

The five trimers of H₂O···HNC···H₂O, H₂O···H₂O···HNC, HNC···H₂O···H₂O, H₂O···HNC···HNC, and HNC···HNC···H₂O have been studied with quantum chemical calculations. Their structures, harmonic vibrational frequencies and interaction energies have been calculated at the B3LYP and MP2 levels with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets. The cooperative effect on these properties has also been studied quantitatively. For HNC:(H₂O)₂ systems, the cyclic H₂O···H₂O···HNC trimer is most stable with an interaction energy of ?16.01 kcal/mol and a large cooperative energy of ?3.25 kcal/mol at the MP2/aug‐cc‐pVTZ level. For H₂O:(HNC)₂ systems, the interaction energy and cooperative energy in the H₂O···HNC···HNC trimer are larger than those in the HNC···HNC···H₂O trimer. The NH stretch frequency has a blue shift for the terminal HNC molecule in the HNC···H₂O···H₂O and HNC···HNC···H₂O trimers and a red shift in other cases. A many‐body analysis has also been performed to understand the interaction energies in these hydrogen‐bonded clusters. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Performance of numerical atom‐centered basis sets in the ground‐state correlated calculations of noncovalent interactions: Water and methane dimer cases

Numerical atom‐centered basis sets (orbitals) (NAO) are known for their compactness and rapid convergence in the Hartree–Fock and density‐functional theory (DFT) molecular electronic‐structure calculations. To date, not much is known about the performance of the numerical sets against the well‐studied Gaussian‐type bases in correlated calculations. In this study, one instance of NAO [Blum et al., The Fritz Haber Institute ab initio Molecular Simulations Package (FHI‐aims), 2009] was thoroughly examined in comparison to the correlation‐consistent basis sets in the ground‐state correlated calculations on the hydrogen‐bonded water and dispersion‐dominated methane dimers. It was shown that these NAO demonstrate improved, comparing to the unaugmented correlation‐consistent based, convergence of interaction energies in correlated calculations. However, the present version of NAO constructed in the DFT calculations on covalently‐bound diatomics exhibits enormous basis‐set superposition error (BSSE)—even with the largest bases. Moreover, these basis sets are essentially unable to capture diffuse character of the wave function, necessary for example, for the complete convergence of correlated interaction energies of the weakly‐bound complexes. The problem is usually treated by addition of the external Gaussian diffuse functions to the NAO part, what indeed allows to obtain accurate results. However, the operation increases BSSE with the resulting hybrid basis sets even further and breaks down the initial concept of NAO (i.e., improved compactness) due to the significant increase in their size. These findings clearly point at the need in the alternative strategies for the construction of sufficiently‐delocalized and BSSE‐balanced purely‐numerical bases adapted for correlated calculations, possible ones were outlined here. For comparison with the considered NAOs, a complementary study on the convergence properties of the correlation‐consistent basis sets, with a special emphasis on BSSE, was also performed. Some of its conclusions may represent independent interest. © 2013 Wiley Periodicals, Inc.     

Effects of π bond type,backbone size,and halogen on structural and spectroscopic properties of hydrogen‐bonded complexes of the X?H … π type between alkenes or alkynes and haloacids (HF and HCl)

The effects of CC bond type (double or triple), substituent (H or methyl), and halogen (F and Cl) on three properties of hydrogen‐bonded complexes formed between unsaturated hydrocarbons and HX (X?F, Cl) are studied. The properties comprise hydrogen bond distances (R_H), stabilization energies (SE), and frequency shifts (Δν). A 2³ factorial design technique, along with ab initio (HF and MP2) and DFT (B3LYP and PBE1PBE) calculations, has been employed. All three responses are mainly affected by the halogen, and when it is changed from F to Cl, R_H tends to increase, while SE tends to decrease. Surprisingly, the type of substituent is more important than the type of CC bond, for all three responses. Both effects tend to decrease R_H. Significant interaction effects are obtained for the type of CC bond along with the type of substituent, and for the type of substituent along with the type of halogen. Both interaction effects are smaller than the main effects and also tend to decrease R_H. The greatest SE values are obtained with PBE1 functional (BSSE + ZPE corrected values). Again, the next more important effect is due to the type of substituent, and the replacement of H by CH₃ group tends to increase SE. The effect due to the CC bond type is not significant, at all computational levels. The only interaction effect that is significant for SE (corrected) and Δν is between factors 1 (CC bond type) and 2 (substituent), but only at HF and B3LYP levels, and it tends to increase both properties. As the halogen changes from F to Cl, Δν tends to decrease. In contrast, changing the substituent from H to CH₃ leads to greater values of Δν. The effect of CC bond type is not significant at HF level, and when it is changed from double to triple Δν is decreased, at B3LYP and PBE1 levels. A suggestion as to how the results may point toward a better experimental detection of similar (π‐type) complexes is also given. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Real‐space grid representation of momentum and kinetic energy operators for electronic structure calculations

We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators on discrete coordinate eigenkets defined on a uniform grid. Starting from the discretization of integrals involving canonical commutations, simple closed‐form expressions of the matrix elements are obtained. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the derivative approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method. © 2018 Wiley Periodicals, Inc.     

Specific Intermolecular Interactions in the Supramolecular Structure of 5‐Hydroxy‐6‐Methyluracil: A DFT Study of the Hydrogen‐bonded Dimers

Studying the self‐assembly of uracil derivatives has great importance for biochemistry and nanotechnology. For example, modification of the sorbent surfaces by 5‐hydroxy‐6‐methyluracil (HMU ) enhances their adsorption activity. It is assumed that these changes are caused by the self‐assembly of the network‐like supramolecular associates of the uracil derivative on the sorbent surface. In the present work, the relative stabilities of 15 hydrogen‐bonded dimers HMU have been studied by the TPSSh /TZVP density functional theory method and the strengths of the noncovalent interactions analyzed in terms of the reduced density gradient and natural bond orbital approaches. It was found that the symmetric dimer stabilized by two intermolecular hydrogen bonds N1 –H∙∙∙O–C2 (dimer 1‐1) is the most stable. This suggests that the self‐assembly of HMU should occur through the intermediate formation of the dimer 1‐1. The results may be useful for understanding the processes of self‐assembly of the uracil derivatives and the rationalized design of the uracil‐based supramolecular structures with specific properties.     

Quantitative investigation of local electric field through absorption spectrum in dye‐sensitized solar cells: Atomistic simulations

The local transient electric field in dye‐sensitized solar cells (DSSCs), created by heterointerfacial charge transfer on illumination, exerts an important role in the internal photoelectronic processes occurring at dye/semiconductor heterointerface in the time‐resolved measurement, for example, transient absorption spectroscopy. Herein, on the basis of theoretical simulations, we proposed a general strategy to quantitatively examine the nature of local electric field (microscopic nature) through absorption spectra of adsorbed dye molecule (macroscopic observation). A controllably modulated external electric field is imposed on the sensitized system to couple to local electric field, resulting in the absorption spectrum shift of ground‐state dye molecules. By fitting absorption spectrum under applied external electric field with Gauss–Stark equation, the quantitative property of local electric field would be obtained. The Gauss–Stark equation reflects the quantitative relationship between the local electric field and absorption spectrum shift of adsorbed ground‐state dye molecule. Our study not only provides origin and magnitude of Stark effect in DSSCs but also offers a promising route to explore the elementary photoelectronic processes experimentally and theoretically.     

A polarizable dipole–dipole interaction model for evaluation of the interaction energies for NH···OC and CH···OC hydrogen‐bonded complexes

In this article, a polarizable dipole–dipole interaction model is established to estimate the equilibrium hydrogen bond distances and the interaction energies for hydrogen‐bonded complexes containing peptide amides and nucleic acid bases. We regard the chemical bonds N? H, C?O, and C? H as bond dipoles. The magnitude of the bond dipole moment varies according to its environment. We apply this polarizable dipole–dipole interaction model to a series of hydrogen‐bonded complexes containing the N? H···O?C and C? H···O?C hydrogen bonds, such as simple amide‐amide dimers, base‐base dimers, peptide‐base dimers, and β‐sheet models. We find that a simple two‐term function, only containing the permanent dipole–dipole interactions and the van der Waals interactions, can produce the equilibrium hydrogen bond distances compared favorably with those produced by the MP2/6‐31G(d) method, whereas the high‐quality counterpoise‐corrected (CP‐corrected) MP2/aug‐cc‐pVTZ interaction energies for the hydrogen‐bonded complexes can be well‐reproduced by a four‐term function which involves the permanent dipole–dipole interactions, the van der Waals interactions, the polarization contributions, and a corrected term. Based on the calculation results obtained from this polarizable dipole–dipole interaction model, the natures of the hydrogen bonding interactions in these hydrogen‐bonded complexes are further discussed. © 2013 Wiley Periodicals, Inc.     

Contrasting electronic requirements for CH binding and CH activation in d6 half‐sandwich complexes of rhenium and tungsten

A computational study of the interaction half‐sandwich metal fragments (metal = Re/W, electron count = d⁶), containing linear nitrosyl (NO⁺), carbon monoxide (CO), trifluorophosphine (PF₃), N‐heterocyclic carbene (NHC) ligands with alkanes are conducted using density functional theory employing the hybrid meta‐GGA functional (M06). Electron deficiency on the metal increases with the ligand in the order NHC < CO < PF₃ < NO⁺. Electron‐withdrawing ligands like NO⁺ lead to more stable alkane complexes than NHC, a strong electron donor. Energy decomposition analysis shows that stabilization is due to orbital interaction involving charge transfer from the alkane to the metal. Reactivity and dynamics of the alkane fragment are facilitated by electron donors on the metal. These results match most of the experimental results known for CO and PF₃ complexes. The study suggests activation of alkane in metal complexes to be facile with strong donor ligands like NHC. © 2015 Wiley Periodicals, Inc.