Infinite Basis Set Extrapolation for Double Hybrid Density Functional Theory 2: Effect of Adding Diffuse Basis Functions

We applied the Infinite Basis (IB) set extrapolation and Double Hybrid Density Functional Theory (DHDF) to calculate the electron affinities, reaction barrier heights, proton affinities, non‐covalent interactions, atomization, ionization, and alkyl bond dissociation energies. We previously found that the mean unsigned error of the B2KPLYP‐IB calculation with the combination of cc‐pVTZ and cc‐pVQZ reach the chemical accuracy limit (～2 kcal/mol) where the largest deviation occurred in the electron affinity calculations and the weak interactions between noble gases and nonpolar molecules. Here, we investigated the basis set effect using the B2KPLYP‐IB extrapolation scheme that involves (1) the addition of extra tight d basis functions to the second row elements (i.e. cc‐pV(L+d)Z), (2) the addition of extra s, p, and d diffuse basis functions, and (3) a comparison between Dunning's Correlation Consistent and Jensen's Polarization Consistent (pc‐L) basis sets. We found that the addition of extra s and p diffuse basis functions formed the minimal augmented basis sets proposed by Truhlar. This addition permitted the B2KPLYP‐IB to reach the chemical accuracy limit with the combination of the double ζ and triple ζ basis sets. Adding extra s, p diffuse functions to the pc‐L series permitted only a small improvement. This small improvement is due to the fact that the pc‐L basis sets already contain a large number of functions for the p block elements. Taken together, the results suggest that this minimal augmented basis sets is useful for due to its accuracy and affordable computational cost.     

On the validity of complete basis set extrapolation formula optimized for the equilibrium distance applied to the potential energy surface for the correlation energy of the helium dimer

Full configuration interaction calculations are performed for He₂ using various orbital basis sets of the aug‐cc‐pVXZ type, with the correlation energies being extrapolated to the complete basis set (CBS) limit. A two‐point CBS extrapolation formula has been utilized for such a purpose. It is shown that the extrapolation formula with the offset parameter k(R) optimized for the equilibrium distance is not uniformly applicable to He He distances in the very short region of the potential energy curve. The offset parameter k(R) in the repulsive region of the potential energy curve can be largely different with the one in the long‐range distances especially in the cases of basis‐sets with large cardinality number. It is also noticed that the accuracy of this extrapolation scheme may not be improved with the increasing of the cardinality number.     

强离子键体系电子相关能简捷计算方案的应用

The calculation results of electron correlation energies of KF and （KF）2 were reported. The transferability of 1s^2 K , 1s^2 F and the inner core correlation effects of K and F in both K, K^＋, KF and F, F^-, KF systems were investigated respectively. The correlation energy contributions of K and F component to KF system were calculated. By applying the simple estimation scheme to the calculation of the correlation energy of the strong ionic compound KF and （KF）2, it was shown that such a powerful scheme could not only reach the chemical accuracy but also need little computational work.     

Rapid Estimation of Basis Set Error and Correlation Energy Based on Mulliken Charges and Mulliken Matrix with the Small 6-31g* Basis Set

Good, density functional quality (B3LYP/6-31G*) ground state total electronic energies have been approximated using single point Hartree–Fock-self consistent field (HF-SCF/6-31G*) total energies and Mulliken partial charges versus. Mulliken matrix (electrons assigned to atoms and atoms pairs from Mulliken population analysis). This is a development of our rapid estimation of basis set error and correlation energy from partial charges (REBECEP) method, published earlier (see references [21,22,30]. The development is as follows: (1) A larger set of atoms (H, C, N, O, F, Si, P and S) are considered as building blocks for closed shell, neutral, ground state molecules at their equlibrium geometry; (2) geometries near equilibrium geometry are also considered; (3) A larger set, containing 115 molecules, was used to fit REBECEP parameters; (4) most importantly, electrons belonging to chemical bonds (between atom pairs) are also considered (Mulliken matrix) in addition to the atoms (Mulliken charges), using more REBECEP parameters to fit and yielding a more flexible algorithm. With these parameters a rather accurate closed shell ground state electronic total energy can be obtained from a small basis set HF-SCF calculation in the vicinity of optimal geometry. The 3.3 kcal/mol root mean square deviation of REBECEP improves to 1.5 kcal/mol when using Mulliken matrix instead of Mulliken charges.     

Two Typical Examples of Scaling Ionic Partition Scheme for Estimating Correlation Energy of A2 Type Molecules

Based on the calculation results of pair correlation energy contributions of the various electron pairs in Na2 and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the total correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of error, however, in this way, more than 90% of computational work can be saved. The most attractive result in present paper is that, in these two molecules the coefficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A^- to that of A^ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 molecules would be very useful to estimate the correlation energies of large symmetrical molecules.     

X‐ray Photoelectron Spectroscopy of Pyridinium‐Based Ionic Liquids: Comparison to Imidazolium‐ and Pyrrolidinium‐Based Analogues

We investigate eight 1‐alkylpyridinium‐based ionic liquids of the form [C_nPy][A] by using X‐ray photoelectron spectroscopy (XPS). The electronic environment of each element of the ionic liquids is analyzed. In particular, a reliable fitting model is developed for the C 1s region that applies to each of the ionic liquids. This model allows the accurate charge correction of binding energies and the determination of reliable and reproducible binding energies for each ionic liquid. Shake‐up/off phenomena are determinedfor both C 1s and N 1s spectra. The electronic interaction between cations and anions is investigated for both simple ionic liquids and an example of an ionic‐liquid mixture; the effect of the anion on the electronic environment of the cation is also explored. Throughout the study, a detailed comparison is made between [C₈Py][A] and analogues including 1‐octyl‐1‐methylpyrrolidinium‐ ([C₈C₁Pyrr][A]), and 1‐octyl‐3‐methylimidazolium‐ ([C₈C₁Im][A]) based samples, where X is common to all ionic liquids.     

Auxiliary basis sets for density‐fitting second‐order Møller–Plesset perturbation theory: Weighted core‐valence correlation consistent basis sets for the 4d elements Y–Pd

Auxiliary basis sets (ABS) specifically matched to the cc‐pwCVnZ‐PP and aug‐cc‐pwCVnZ‐PP orbital basis sets (OBS) have been developed and optimized for the 4d elements Y‐Pd at the second‐order Møller‐Plesset perturbation theory level. Calculation of the core‐valence electron correlation energies for small to medium sized transition metal complexes demonstrates that the error due to the use of these new sets in density fitting is three to four orders of magnitude smaller than that due to the OBS incompleteness, and hence is considered negligible. Utilizing the ABSs in the resolution‐of‐the‐identity component of explicitly correlated calculations is also investigated, where it is shown that i‐type functions are important to produce well‐controlled errors in both integrals and correlation energy. Benchmarking at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations level indicates impressive convergence with respect to basis set size for the spectroscopic constants of 4d monofluorides; explicitly correlated double‐ζ calculations produce results close to conventional quadruple‐ζ, and triple‐ζ is within chemical accuracy of the complete basis set limit. © 2013 Wiley Periodicals, Inc.     

Alternative Representations of the Correlation Energy in Density‐Functional Theory: A Kinetic‐Energy Based Adiabatic Connection

The adiabatic‐connection framework has been widely used to explore the properties of the correlation energy in density‐functional theory. The integrand in this formula may be expressed in terms of the electron–electron interactions directly, involving intrinsically two‐particle expectation values. Alternatively, it may be expressed in terms of the kinetic energy, involving only one‐particle quantities. In this work, we explore this alternative representation for the correlation energy and highlight some of its potential for the construction of new density functional approximations. The kinetic‐energy based integrand is effective in concentrating static correlation effects to the low interaction strength regime and approaches zero asymptotically, offering interesting new possibilities for modeling the correlation energy in density‐functional theory     

Substitution effects in the 15N NMR chemical shifts of heterocyclic azines evaluated at the GIAO‐DFT level

A systematic study of the accuracy factors for the computation of ¹⁵N NMR chemical shifts in comparison with available experiment in the series of 72 diverse heterocyclic azines substituted with a classical series of substituents (CH₃, F, Cl, Br, NH₂, OCH₃, SCH₃, COCH₃, CONH₂, COOH, and CN) providing marked electronic σ‐ and π‐electronic effects and strongly affecting ¹⁵N NMR chemical shifts is performed. The best computational scheme for heterocyclic azines at the DFT level was found to be KT3/pcS‐3//pc‐2 (IEF‐PCM). A vast amount of unknown ¹⁵N NMR chemical shifts was predicted using the best computational protocol for substituted heterocyclic azines, especially for trizine, tetrazine, and pentazine where experimental ¹⁵N NMR chemical shifts are almost totally unknown throughout the series. It was found that substitution effects in the classical series of substituents providing typical σ‐ and π‐electronic effects followed the expected trends, as derived from the correlations of experimental and calculated ¹⁵N NMR chemical shifts with Swain–Lupton's F and R constants.     

DSD‐PBEP86‐NL and DOD‐PBEP86‐NL functionals for noncovalent interactions: Basis set effects and tentative applications to large noncovalent systems

Basis set effects on the DSD‐PBEP86‐NL and DOD‐PBEP86‐NL functionals for noncovalent interactions have been extensively studied in this work. The cc‐pVXZ (X = D, T, Q, 5, 6) and augmented aug‐cc‐pVXZ (X = D, T, Q) basis sets are systematically tested without counterpoise (CP) corrections against the well‐known S66 database. Additionally, the basis sets of def2‐TZVPP and def2‐TZVPPD are also examined. Based on our computations, the performances of the aug‐cc‐pVQZ, cc‐pV5Z, and cc‐pV6Z basis sets are very approximate to those obtained with the def2‐QZVP basis set for both the DSD‐PBEP86‐NL and DOD‐PBEP86‐NL functionals. Note that the short‐range attenuation parameters for these two functionals were directly optimized using the def2‐QZVP basis set without CP corrections against the S66 database. Generally speaking, the cc‐pVXZ (X = D, T, Q), aug‐cc‐pVXZ (X = D, T, Q), def2‐TZVPP, and def2‐TZVPPD basis sets favor half CP correction for these two functionals. Nevertheless, the aug‐cc‐pVQZ basis set already performs well without any CP correction, especially for the DOD‐PBEP86‐NL functional. With respect to accuracy and computational cost, the cc‐pVTZ and def2‐TZVPP basis sets with half CP corrections are recommended for these two functionals to evaluate interaction energies of large noncovalent complexes.     

Complete one‐ and two‐center partitioning scheme for the total energy in the Hartree–Fock theory

We proposed a complete calculation scheme for attributing the total energy by the Hartree–Fock theory to atoms (E_A) and the region between two atoms (E_AB). It was pointed out that the conventional method using the Fock matrix includes a large amount of mutual contamination in both E_A and E_AB. The new scheme was derived from the basic expression of the total energy. Calculated results by the new scheme satisfy the theoretical requirements. The scaling effect on partitioned energies was also examined. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 35–46, 1999     

Accurate Quantum‐Chemical Prediction of Enthalpies of Formation of Small Molecules in the Gas Phase

The coupled‐cluster approach, including single and double excitations and perturbative corrections for triple excitations, is capable of predicting molecular electronic energies and enthalpies of formation of small molecules in the gas phase with very high accuracy (specifically, with error bars less than 5 kJ mol^?1), provided that the electronic wavefunction is dominated by the Hartree–Fock configuration. This capability is illustrated by calculations on molecules containing O–H and O–F bonds, namely OH, FO, H₂O, HOF, and F₂O. To achieve this very high accuracy, it is imperative to account for electron‐correlation effects in a quantitative manner, either by using explicitly correlated two‐particle basis functions (R12 functions) or by extrapolating to the limit of a complete basis. Besides taking into account harmonic zero‐point vibrational energies, it is also necessary to account for anharmonic corrections to the zero‐point vibrational energies, to include the core orbitals into the coupled‐cluster calculations, and to account for spin–orbit corrections and scalar relativistic effects. These additional corrections constitute small but significant contributions in the range of 1–4 kJ mol^?1 to the enthalpies of formation of the aforementioned molecules. The highly accurate coupled‐cluster results, obtained by employing R12 functions and by including various corrections, are compared with standard Kohn–Sham density‐functional calculations as well as with the Gaussian‐2 and complete‐basis‐set model chemistries.     

Conductive Microporous Covalent Triazine‐Based Framework for High‐Performance Electrochemical Capacitive Energy Storage

Nitrogen‐enriched porous nanocarbon, graphene, and conductive polymers attract increasing attention for application in supercapacitors. However, electrode materials with a large specific surface area (SSA) and a high nitrogen doping concentration, which is needed for excellent supercapacitors, has not been achieved thus far. Herein, we developed a class of tetracyanoquinodimethane‐derived conductive microporous covalent triazine‐based frameworks (TCNQ‐CTFs) with both high nitrogen content (>8 %) and large SSA (>3600 m² g^?1). These CTFs exhibited excellent specific capacitances with the highest value exceeding 380 F g^?1, considerable energy density of 42.8 Wh kg^?1, and remarkable cycling stability without any capacitance degradation after 10 000 cycles. This class of CTFs should hold a great potential as high‐performance electrode material for electrochemical energy‐storage systems.     

Interesting properties of Thomas–Fermi kinetic and Parr electron–electron‐repulsion DFT energy functional generated compact one‐electron density approximation for ground‐state electronic energy of molecular systems

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N‐dimensions to a (nonlinear, approximate) density functional of three spatial dimension one‐electron density for an N‐electron system, which is tractable in the practice, is a long desired goal in electronic structure calculation. If the Thomas‐Fermi kinetic energy (～∫ρ^5/3d r ₁) and Parr electron–electron repulsion energy (～∫ρ^4/3d r ₁) main‐term functionals are accepted, and they should, the later described, compact one‐electron density approximation for calculating ground state electronic energy from the 2nd Hohenberg–Kohn theorem is also noticeable, because it is a certain consequence of the aforementioned two basic functionals. Its two parameters have been fitted to neutral and ionic atoms, which are transferable to molecules when one uses it for estimating ground‐state electronic energy. The convergence is proportional to the number of nuclei (M) needing low disc space usage and numerical integration. Its properties are discussed and compared with known ab initio methods, and for energy differences (here atomic ionization potentials) it is comparable or sometimes gives better result than those. It does not reach the chemical accuracy for total electronic energy, but beside its amusing simplicity, it is interesting in theoretical point of view, and can serve as generator function for more accurate one‐electron density models. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009     

Automatic algorithms for completeness‐optimization of Gaussian basis sets

We present the generic, object‐oriented C++ implementation of the completeness‐optimization approach (Manninen and Vaara, J. Comput. Chem. 2006, 27, 434) in the freely available ERKALE program, and recommend the addition of basis set stability scans to the completeness‐optimization procedure. The design of the algorithms is independent of the studied property, the used level of theory, as well as of the role of the optimized basis set: the procedure can be used to form auxiliary basis sets in a similar fashion. This implementation can easily be interfaced with various computer programs for the actual calculation of molecular properties for the optimization, and the calculations can be trivially parallelized. Routines for general and segmented contraction of the generated basis sets are also included. The algorithms are demonstrated for two properties of the argon atom—the total energy and the nuclear magnetic shielding constant—and they will be used in upcoming work for generation of cost‐efficient basis sets for various properties. © 2014 Wiley Periodicals, Inc.     

Aqueous Manganese Dioxide Ink for Paper‐Based Capacitive Energy Storage Devices

We report a simple approach based on a chemical reduction method to synthesize aqueous inorganic ink comprised of hexagonal MnO₂ nanosheets. The MnO₂ ink exhibits long‐term stability and continuous thin films can be formed on various substrates without using any binder. To obtain a flexible electrode for capacitive energy storage, the MnO₂ ink was printed onto commercially available A4 paper pretreated with multiwalled carbon nanotubes. The electrode exhibited a maximum specific capacitance of 1035 F g^?1 (91.7 mF cm^?2). Paper‐based symmetric and asymmetric capacitors were assembled, which gave a maximum specific energy density of 25.3 Wh kg^?1 and a power density of 81 kW kg^?1. The device could maintain a 98.9 % capacitance retention over 10 000 cycles at 4 A g^?1. The MnO₂ ink could be a versatile candidate for large‐scale production of flexible and printable electronic devices for energy storage and conversion.     

Aptamer‐Based Luminescence Energy Transfer from Near‐Infrared‐to‐Near‐Infrared Upconverting Nanoparticles to Gold Nanorods and Its Application for the Detection of Thrombin

A new luminescence energy transfer (LET) system has been designed for the detection of thrombin in the near‐infrared (NIR) region by utilizing NIR‐to‐NIR upconversion lanthanide nanophosphors (UCNPs) as the donor and gold nanorods (Au NRs) as the acceptor. The use of upconverting NaYF₄:Yb³⁺,Tm³⁺ nanoparticles with sharp NIR emission peaks upon NIR excitation by an inexpensive infrared continuous wave laser diode provided large spectral overlap between the donor and the acceptor. Both the Au NRs and carboxyl‐terminated NaYF₄:Yb³⁺,Tm³⁺ UCNPs were first modified with different thrombin aptamers. When thrombin was added, a LET system was then formed because of the specific recognition between the thrombin aptamers and thrombin. The LET system was used to monitor thrombin concentrations in aqueous buffer and human blood samples. The limits of detection for thrombin are as low as 0.118 nM in buffer solution and 0.129 nM in human serum. The method was also successfully applied to thrombin detection in blood samples.     

A New Strategy for Storage and Transportation of Sensitive High‐Energy Materials: Guest‐Dependent Energy and Sensitivity of 3D Metal–Organic‐Framework‐Based Energetic Compounds

Reaction of Co(II) with the nitrogen‐rich ligand N,N‐bis(1H‐tetrazole‐5‐yl)‐amine (H₂bta) leads to a mixed‐valence, 3D, porous, metal–organic framework (MOF)‐based, energetic material with the nitrogen content of 51.78%, [Co₉(bta)₁₀(Hbta)₂(H₂O)₁₀]_n?(22 H₂O)_n ( 1 ). Compound 1 was thermohydrated to produce a new, stable, energetic material with the nitrogen content of 59.85% and heat of denotation of 4.537 kcal cm^?3, [Co₉(bta)₁₀(Hbta)₂(H₂O)₁₀]_n ( 2 ). Sensitivity tests show that 2 is more sensitivity to external stimuli than 1 , reflecting guest‐dependent energy and sensitivity of 3D, MOF‐based, energetic materials. Less‐sensitive 1 can be regarded as a more safe form for storage and transformation to sensitive 2 .