Novel superhard semiconducting structures of C8B2N2 predicted using the first-principles approach.

Using first-principles calculations, we predicted three novel superhard semiconducting structures of C8B2N2 with a space group of P3m1. We investigated their mechanical properties and electronic structures up to 100 GPa. These three structures were successfully derived by substituting carbon (C) atoms with isoelectronic boron (B) and nitrogen (N) atoms in the P3m1 phase, which is the most stable structure of BCN and exhibits exceptional mechanical properties. Our results indicated that these structures had superior energy over previously reported t-C8B2N2, achieved by replacing C atoms in the diamond supercell with B and N atoms. To ensure their stable existence, we thoroughly examined their mechanical and dynamical stabilities, and we found that their hardness values reached 82.4, 83.1, and 82.0 GPa, which were considerably higher than that of t-C8B2N2 and even surpassing the hardness of c-BN. Calculations of the electron localization function revealed that the stronger carbon-carbon covalent bonds made them much harder than t-C8B2N2. Additionally, our further calculations of band structures revealed that these materials had indirect bandgaps of 4.164, 4.692, and 3.582 eV. These findings suggest that these materials have the potential to be used as superhard semiconductors, potentially surpassing conventional superhard materials.

Study of high-pressure thermophysical properties of orthocarbonate Sr3CO5 using deep learning molecular dynamics simulations.

The exploration of the physical attributes of the recently discovered orthocarbonate Sr3CO5 is significant for comprehending the carbon cycle and storage mechanisms within the Earth's interior. In this study, first-principles calculations are initially used to examine the structural phase transitions of Sr3CO5 polymorphs within the range of lower mantle pressures. The results suggest that Sr3CO5 with the Cmcm phase exhibits a minimal enthalpy between 8.3 and 30.3 GPa. As the pressure exceeds 30.3 GPa, the Cmcm phase undergoes a transition to the I4/mcm phase, while the experimentally observed Pnma phase remains metastable under our studied pressure. Furthermore, the structural data of SrO, SrCO3, and Sr3CO5 polymorphs are utilized to develop a deep learning potential model suitable for the Sr-C-O system, and the pressure-volume relationship and elastic constants calculated using the potential model are in line with the available results. Subsequently, the elastic properties of Cmcm and I4/mcm phases in Sr3CO5 at high temperature and pressure are calculated using the molecular dynamics method. The results indicate that the I4/mcm phase exhibits higher temperature sensitivity in terms of elastic moduli and wave velocities compared to the Cmcm phase. Finally, the thermodynamic properties of the Cmcm and I4/mcm phases are predicted in the range of 0-2000 K and 10-120 GPa, revealing that the heat capacity and bulk thermal expansion coefficient of both phases increase with temperature, with the constant volume heat capacity gradually approaching the Dulong-Petit limit as the temperature rises.

Investigation on Melting Curves and Phase Diagrams for CaO3 Using Deep Learning Potentials.

Melting in the deep rocky parts of planets plays an important role in geological processes such as planet formation, seismicity, magnetic field generation, thermal convection, and crustal evolution. Such processes are the key way to understanding the dynamics of planetary interiors and the history as well as mechanisms of planetary evolution. We herein investigate the melting curves and pressure-temperature (P-T)-phase diagrams for CaO3, a candidate mineral for the lower mantle, by means of the deep learning potential model. Using first-principles, molecular dynamics, and quasi-harmonic approximation, the reliability of the deep learning potential model is verified by calculating the high-temperature and high-pressure equations of state and phase transition pressures for the orthorhombic and tetragonal structures of CaO3 described by space groups Aea2 and P4̅21m, respectively. The melting temperatures of 975, 850, and 755 K at zero pressure are obtained by the single-phase, void, and two-phase methods, respectively, and their melting temperatures are analyzed by the radial distribution function and mean-square displacement to analyze the melting process. Finally, the melting phase diagrams of CaO3 at 0-135 GPa were obtained by the two-phase method.

Modulating the organic photovoltaic properties of non-fullerene acceptors by molecular modification based on Y6: a theoretical study.

Developing non-fullerene acceptors (NFAs) by modifying the backbone, side chains and end groups is the most important strategy to improve the power conversion efficiency of organic solar cells (OSCs). Among numerous developed NFAs, Y6 and its derivatives are famous NFAs in the OSC field due to their good performance. Herein, in order to understand the mechanism of tuning the photovoltaic performance by modifying the Y6's center backbone, π-spacer and side-chains, we selected the PM6:Y6 OSC as a reference and systematically studied PM6:AQx-2, PM6:Y6-T, PM6:Y6-2T, PM6:Y6-O, PM6:Y6-1O and PM6:Y6-2O OSC systems based on extensive quantum chemistry calculations. The results indicate that introducing quinoxaline to substitute thiadiazole in the backbone induces a blue-shift of absorption spectra, reduces the charge transfer (CT) distance (Δd) and average electrostatic potential (ESP), and increases the singlet-triplet energy gap (ΔEST), CT excitation energy and the number of CT states in low-lying excitations. Inserting thienyl and dithiophenyl as π spacers generates a red-shift of absorption spectra, enlarges Δd and average ESP, and reduces ΔEST and the number of CT states. Introducing furo[3,2-b]furan for substituting one thieno[3,2-b]thiophene unit in the Y6's backbone causes a red-shift of absorption spectra and increases ΔEST, Δd and average ESP as well as CT excitation energy. Introducing alkoxyl as a side chain results in a blue-shift of absorption spectra, and increases ΔEST, Δd, average ESP, CT excitation energy and the number of CT states. The rate constants calculated using Marcus theory suggest that all the molecular modifications of Y6 reduce the exciton dissociation and charge recombination rates at the heterojunction interface, while introducing furo[3,2-b]furan and alkoxyl enlarges CT rates.

Fusing Thienyl with N-Annulated Perylene Dyes and Photovoltaic Parameters for Dye-Sensitized Solar Cells.

Due to the role of dyes in dye-sensitized solar cells (DSSCs), designing novel dye sensitizers is an effective strategy to improve the power conversion efficiency. To this end, the fundamental issue is understanding the sensitizer's trilateral relationship among its molecular structure, optoelectronic properties, and photovoltaic performance. Considering the good performance of N-annulated perlyene dye sensitizers, the geometries, electronic structures, and excitations of the selected representative organic dye sensitizers C276, C277, and C278 as well as dyes adsorbed on TiO2 clusters were calculated in order to investigate the relationship between molecular structures and properties. It was found that fusing thienyl to N-annulated perlyene can elevate the highest occupied molecular orbital (HOMO) energy, reduce the orbital energy gap, increase the density of states, expand the HOMO to the benzothiadiazole moiety, enhance the charge transfer excitation, elongate the fluorescence lifetime, amplify the light harvesting efficiency, and induce a red-shift of the absorption spectra. The transition configurations and molecular orbitals of the dye-adsorbed systems support that the electron injection in DSSCs based on these dyes is a fast mode. Based on extensive analysis of the electronic structures and excitation properties of these dye sensitizers and the dye-adsorbed systems, we present new quantities as open-circuit voltage and short-circuit current density descriptors that celebrate the quantitative bridge between the photovoltaic parameters and the electronic structure-related properties in order to expose the relationship between properties and performance. The results of this work are critical for the design of novel dye sensitizers for solar cells.

Donor Halogenation Effects on Electronic Structures and Electron Process Rates of Donor/C60 Heterojunction Interface: A Theoretical Study on F nZnPc ( n = 0, 4, 8, 16) and Cl nSubPc ( n = 0, 6).

Molecular engineering is significantly important for developing electron donor and acceptor materials of active layers in organic photovoltaics (OPVs). The OPVs based on halogenated donors frequently produced high power conversion efficiencies. Here, based upon density functional theory calculations with optimally tuned range separation parameters and solid polarization effects, we studied the effects of donor halogenation on molecular geometries, electronic structures, excitation, and spectroscopic properties for F nZnPc ( n = 0, 4, 8, 16) and Cl nSubPc ( n = 0, 6) monomers and the complexes with C60 as well as the photoinduced direct charge transfer (CT), exciton dissociation (ED), and charge recombination (CR) processes that were described by rate constants calculated using Marcus theory. The tiny differences of the molecular orbital energy gap, excitation, and spectroscopic properties of F nZnPc ( n = 0, 4, 8, 16) and Cl nSubPc ( n = 0, 6) monomers suggest that halogenation cannot effectively tune the electronic and optical gap but the significant decrease of molecular orbital energies support the idea that halogenation has a remarkable influence on the energy level alignment at heterojunction interfaces. The halogenation also enhances intermolecular binding energies between C60 and donors and increases the CT excitation energies of donor/C60 complexes, which are favorable for improving open circuit voltage. Furthermore, for F nZnPc/C60 ( n = 0, 4, 8, 16) and SubPc/C60 ( n = 0, 6) complexes, the CR rates dramatically decrease (several orders) with increasing number of halogen atoms (except for F16ZnPc/C60), meaning suppression of CR processes by halogenation. As for the special case of F16ZnPc/C60, it underlines the importance of fluorination degree in molecular design of donor materials. This study provides a theoretical understanding of the halogenation effects of donors in OPVs and may be helpful in molecular design for electron donor materials.

Assessment of Ab Initio and Density Functional Theory Methods for the Excitations of Donor-Acceptor Complexes: The Case of the Benzene-Tetracyanoethylene Model.

The understanding of the excited-state properties of electron donors, acceptors and their interfaces in organic optoelectronic devices is a fundamental issue for their performance optimization. In order to obtain a balanced description of the different excitation types for electron-donor-acceptor systems, including the singlet charge transfer (CT), local excitations, and triplet excited states, several ab initio and density functional theory (DFT) methods for excited-state calculations were evaluated based upon the selected model system of benzene-tetracyanoethylene (B-TCNE) complexes. On the basis of benchmark calculations of the equation-of-motion coupled-cluster with single and double excitations method, the arithmetic mean of the absolute errors and standard errors of the electronic excitation energies for the different computational methods suggest that the M11 functional in DFT is superior to the other tested DFT functionals, and time-dependent DFT (TDDFT) with the Tamm-Dancoff approximation improves the accuracy of the calculated excitation energies relative to that of the full TDDFT. The performance of the M11 functional underlines the importance of kinetic energy density, spin-density gradient, and range separation in the development of novel DFT functionals. According to the TDDFT results, the performances of the different TDDFT methods on the CT properties of the B-TCNE complexes were also analyzed.

Molecular Docking toward Panchromatic Dye Sensitizers for Solar Cells Based upon Tetraazulenylporphyrin and Tetraanthracenylporphyrin.

Novel dye sensitizers are highly expected in the development of dye-sensitized solar cells (DSSCs) because dye sensitizers can significantly affect the power conversion efficiency (PCE). Here, the molecular docking strategy is applied to design panchromatic dye sensitizers for DSSCs to improve light-harvesting efficiency covering the full solar spectrum. Considering the broad absorption bands of tetraanthracenylporphyrins (TAnPs) and tetraazuleneporphyrins (TAzPs), based upon porphyrin dye sensitizer YD2-o-C8, the panchromatic dye sensitizers coded as H2(TAnP)-α, H2(TAzP)-γ, H2(TAzP)-ε, and H2(TAzP)-δ are designed by the substitution of the porphyrin-ring in YD2-o-C8 with TAnPs and TAzPs moieties at different positions. The geometries, electronic structures, and excitation properties of the designed dye sensitizers are investigated using density functional theory (DFT) and time-dependent DFT methods. The analysis of geometries, conjugation lengths, electronic structures, absorption spectra, transition configurations, exciton binding energies, and free energy variations for electron injection and dye regeneration supports that the designed molecules are effective to be applied as potential candidates of dye sensitizers for DSSCs. Among the designed dye sensitizers, H2(TAzP)-γ and H2(TAnP)-α must have the better performance in DSSCs.

The Role of Porphyrin-Free-Base in the Electronic Structures and Related Properties of N-Fused Carbazole-Zinc Porphyrin Dye Sensitizers.

Dye sensitizers can significantly affect power conversion efficiency of dye-sensitized solar cells (DSSCs). Porphyrin-based dyes are promising sensitizers due to their performances in DSSCs. Here, based upon a N-fused carbazole-zinc porphyrin-free-base porphyrin triad containing an ethynyl-linkage (coded as DTBC), the novel porphyrin dyes named DTBC-MP and DTBC-TP were designed by varying the porphyrin-free-base units in the π conjugation of DTBC in order to study the effect of porphyrin-free-base in the modification of electronic structures and related properties. The calculated results indicate that, the extension of the conjugate bridge with the porphyrin-free-base unit results in elevation of the highest occupied molecular orbital (HOMO) energies, decrease of the lowest unoccupied molecular orbital (LUMO) energies, reduction of the HOMO-LUMO gap, red-shift of the absorption bands, and enhancement of the absorbance. The free energy changes demonstrate that introducing more porphyrin-free-base units in the conjugate bridge induces a faster rate of electron injection. The transition properties and molecular orbital characters suggest that the different transition properties might lead to a different electron injection mechanism. In terms of electronic structure, absorption spectra, light harvesting capability, and free energy changes, the designed DTBC-TP is a promising candidate dye sensitizer for DSSCs.

Understanding the electronic structures and absorption properties of porphyrin sensitizers YD2 and YD2-o-C8 for dye-sensitized solar cells.

The electronic structures and excitation properties of dye sensitizers determine the photon-to-current conversion efficiency of dye sensitized solar cells (DSSCs). In order to understand the different performance of porphyrin dye sensitizers YD2 and YD2-o-C8 in DSSC, their geometries and electronic structures have been studied using density functional theory (DFT), and the electronic absorption properties have been investigated via time-dependent DFT (TDDFT) with polarizable continuum model for solvent effects. The geometrical parameters indicate that YD2 and YD2-o-C8 have similar conjugate length and charge transfer (CT) distance. According to the experimental spectra, the HSE06 functional in TDDFT is the most suitable functional for describing the Q and B absorption bands of porphyrins. The transition configurations and molecular orbital analysis suggest that the diarylamino groups are major chromophores for effective CT excitations (ECTE), and therefore act as electron donor in photon-induced electron injection in DSSCs. The analysis of excited states properties and the free energy changes for electron injection support that the better performance of YD2-o-C8 in DSSCs result from the more excited states with ECTE character and the larger absolute value of free energy change for electron injection.

The role of the conjugate bridge in electronic structures and related properties of tetrahydroquinoline for dye sensitized solar cells.

To understand the role of the conjugate bridge in modifying the properties of organic dye sensitizers in solar cells, the computations of the geometries and electronic structures for 10 kinds of tetrahydroquinoline dyes were performed using density functional theory (DFT), and the electronic absorption and fluorescence properties were investigated via time dependent DFT. The population analysis, molecular orbital energies, radiative lifetimes, exciton binding energies (EBE), and light harvesting efficiencies (LHE), as well as the free energy changes of electron injection ( ) and dye regeneration ( ) were also addressed. The correlation of charge populations and experimental open-circuit voltage (Voc) indicates that more charges populated in acceptor groups correspond to larger Voc. The elongating of conjugate bridge by thiophene units generates the larger oscillator strength, higher LHE, larger absolute value of , and longer relative radiative lifetime, but it induces the decreasing of EBE and . So the extending of conjugate bridge with thiopene units in organic dye is an effective way to increase the harvest of solar light, and it is also favorable for electron injection due to their larger . While the inversely correlated relationship between EBE and LHE implies that the dyes with lower EBE produce more efficient light harvesting.

First-principles study on the high-pressure physical properties of orthocarbonate Ca2CO4.

Orthorhombic Ca2CO4 is a recently discovered orthocarbonate whose high-pressure physical properties are critical for understanding the deep carbon cycle. Here, we study the structure, elastic and seismic properties of Ca2CO4-Pnma at 20-140 GPa using first-principles calculations, and compare them with the results of CaCO3 polymorphs. The results show that the structural parameters of Ca2CO4-Pnma are in good agreement with the experimental results. It could be the potential host of carbon in the Earth's mantle subduction slab, and its low wave velocity and small anisotropy may be the reason why it cannot be detected in seismic observation. The thermodynamic properties of Ca2CO4-Pnma at high temperature and high pressure are obtained using the quasi-harmonic approximation method. This study is helpful in understanding the behavior of Ca-carbonate in the Earth's lower mantle conditions.

High-performance phononic crystal sensing structure for acetone solution concentration sensing.

A two-dimensional phononic crystal sensor model with high-quality factor and excellent sensitivity for sensing acetone solutions and operating at 25-45 kHz is proposed. The model for filling solution cavities is based on reference designs of quasi-crystal and gradient cavity structures. The transmission spectrum of sensor is simulated by the finite element method. High-quality factor of 45,793.06 and sensitivity of 80,166.67 Hz are obtained for the acetone concentration with 1-9.1%, and quality factor of 61,438.09 and sensitivity of 24,400.00 Hz are obtained for the acetone concentration range of 10-100%, which indicated the sensor could still achieve high sensitivity and quality factor at operating frequencies from 25 to 45 kHz. To verify the application of the sensor to sensing other solutions, the sensitivity for sound velocity and density is calculated as 24.61 m-1 and 0.7764 m3/(kg × s), respectively. It indicates the sensor is sensitive to acoustic impedance changes of the solution and equally suitable for sensing other solutions. The simulation results reveal the phononic crystal sensor possessed high-performance in composition capture in pharmaceutical production and petrochemical industry, which can provide theoretical reference for the design of new biochemical sensors for reliable detection of solution concentration.

Comparative study on high-pressure physical properties of monoclinic MgCO3 and Mg2CO4.

The physical properties of Mg-carbonate at high temperature and pressure are crucial for understanding the deep carbon cycle. Here, we use first-principles calculations to study the physical properties of MgCO3-C2/m and Mg2CO4-P21/c under high pressure. The research shows that the structure and equation of state of MgCO3-C2/m are in good agreement with the experimental results, and the phase transition pressure of Mg2CO4 from pnma to P21/c structure is 44.66 GPa. By comparing the elastic properties, seismic properties and anisotropy of MgCO3-C2/m and Mg2CO4-P21/c, it is found that the elastic modulus and sound velocity of Mg2CO4-P21/c are smaller than those of MgCO3-C2/m, while the anisotropy is larger than that of MgCO3-C2/m. These results indicate that Mg2CO4-P21/c exists in the deep mantle and may be the main reason why carbonate cannot be detected. The minimum thermal conductivity of MgCO3-C2/m and Mg2CO4-P21/c is the largest in the [010] direction and the smallest in the [001] direction. The thermodynamic properties of MgCO3-C2/m and Mg2CO4-P21/c are predicted using the quasi-harmonic approximation (QHA) method.

First-principles calculations of high-pressure physical properties anisotropy for magnesite.

The first-principles calculations based on density functional theory with projector-augmented wave are used to study the anisotropy of elastic modulus, mechanical hardness, minimum thermal conductivity, acoustic velocity and thermal expansion of magnesite (MgCO3) under deep mantle pressure. The calculation results of the phase transition pressure, equation of state, elastic constants, elastic moduli, elastic wave velocities and thermal expansion coefficient are consistent with those determined experimentally. The research results show that the elastic moduli have strong anisotropy, the mechanical hardness gradually softens with increasing pressure, the conduction velocity of heat in the [100] direction is faster than that in the [001] direction, the plane wave velocity anisotropy first increases and then gradually decreases with increasing pressure, and the shear wave velocity anisotropy increases with the increase of pressure, the thermal expansion in the [100] direction is greater than that in the [001] direction. The research results are of great significance to people's understanding of the high-pressure physical properties of carbonates in the deep mantle.

Tunable characteristics of low-frequency bandgaps in two-dimensional multivibrator phononic crystal plates under prestrain.

In view of the influence of variability of low-frequency noise frequency on noise prevention in real life, we present a novel two-dimensional tunable phononic crystal plate which is consisted of lead columns deposited in a silicone rubber plate with periodic holes and calculate its bandgap characteristics by finite element method. The low-frequency bandgap mechanism of the designed model is discussed simultaneously. Accordingly, the influence of geometric parameters of the phononic crystal plate on the bandgap characteristics is analyzed and the bandgap adjustability under prestretch strain is further studied. Results show that the new designed phononic crystal plate has lower bandgap starting frequency and wider bandwidth than the traditional single-sided structure, which is due to the coupling between the resonance mode of the scatterer and the long traveling wave in the matrix with the introduction of periodic holes. Applying prestretch strain to the matrix can realize active realtime control of low-frequency bandgap under slight deformation and broaden the low-frequency bandgap, which can be explained as the multiple bands tend to be flattened due to the localization degree of unit cell vibration increases with the rise of prestrain. The presented structure improves the realtime adjustability of sound isolation and vibration reduction frequency for phononic crystal in complex acoustic vibration environments.

Optoelectronic properties of diathiafulvalene-functionalized diketopyrrolopyrrole-fullerene molecular dyad.

Single component molecular dyad donor-acceptor junction is an important type of organic solar cells. Understanding the optoelectronic properties of molecular dyad plays the critical role to develop active layer materials for such kind of solar cells. Here, diathiafulvalene-functionalized diketopyrrolopyrrole-fullerene (DFDPP-Ful) was selected as the representative system, and the geometries, electronic structures and excitation properties of DFDPP-Ful monomer and dimer were systematically investigated based on extensive quantum chemistry calculations. The transition configurations and molecular orbitals show that the effective electron donor and acceptor are DFDPP and fullerene moieties, respectively. It also found the light harvesting is dominated by local excitation in DFDPP moiety. Meanwhile, the hybridization and quasi-degeneration between charge transfer (CT) and local excitation exist. The dimer data suggest that the increased excited states contribute to the expanding of absorption spectra, and the excitations exhibit both the intermolecular and intra-molecular CTs. Also, the remarkable CT energy differences among the different dimer models for the lowest CT excited states support the strong interface and energy disorder in such system. Therefore, the suggestions for developing molecular dyad of single component organic solar cells would be the combination of increasing light absorption, enhancing CT and local excitation hybridization, as well as suppressing energy and interface disorder by the aid of molecular design.

The bis-dimethylfluoreneaniline organic dye sensitizers for solar cells: A theoretical study and design.

Development of novel dye sensitizers with suitable optoelectronic properties is effective to improve the power conversion efficiency of dye-sensitized solar cells (DSSCs). Considering the effectiveness of conjugate bridges in modification of optoelectronic properties, based on the dye sensitizers C201, C203, C204 and C205, five kinds of organic dye sensitizers are designed with different thiophene-based moieties and the functionalized graphene flakes (GFs) as conjugate bridges. The performances of these dye sensitizers are analyzed in terms of the calculated geometries, electronic structures and excitation properties. The transition configurations and molecular orbitals of dye sensitizers suggest that bis-dimethylfluoreneaniline is effective electron donor, and the transitions of optical absorption in visible region are charge transfer excitations. The conjugate lengths, energy level alignments, light harvesting capabilities, excitation character, and transition properties, as well as the free energy variations for electron injection and dye regeneration support that the designed dye sensitizers are effective to be applied in DSSCs. Particularly, introducing the functionalized GF into conjugate bridges significantly elongate conjugate length, reduce orbital energy gap, lead to denser distribution of orbital energy, generate red-shift of absorption spectra, enhance light harvesting capability, increase absorption bands and coefficients. Therefore, introducing the functionalized GF into conjugate bridges is effective, and the designed panchromatic dye sensitizer C20x-GF-BTD must be better than other designed dye sensitizers for DSSCs.

The phase transition, and elastic and thermodynamic properties of CaS derived from first-principles calculations.

First-principles calculations of the crystal structures, phase transition, and elastic properties of B1-B2 phase calcium sulfide (CaS) have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values (for crystal structures and the phase transition) are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c(ij), the aggregate elastic modulus, the deviation from the Cauchy relation, and the elastic anisotropy on pressure have been investigated. The normalized elastic constants c(ij)' have been introduced to investigate the elasticity of CaS in detail. Moreover, the variation of the Poisson ratio, Debye temperature, and longitudinal and transverse elastic wave velocity with pressure P up to 70 GPa at 0 K have been investigated for the first time.

Calculations of bond dissociation energies and dipole moments in energetic materials using density-functional methods.

We compare the effectiveness of six exchange/correlation functional combinations (Becke/Lee, Yang and Parr; Becke-3/Lee, Yang and Parr; Becke/Perdew-Wang 91; Becke-3/Perdew-Wang 91; Becke/Perdew 86; Becke-3/Perdew 86) for computing C-N, O-O and N-NO2 dissociation energies and dipole moments of five compounds. The studied compounds are hexabydro-1,3,5-trinitro-1,3,5-triazine (RDX), dimethylnitramine, cyanogen, nitromethane and ozone. The Becke-3/Perdew 86 in conjunction with 6-31G** is found to give the best results, although for the dipole moments of RDX, there is a slightly difference that B3P86/6-31G** is less reliable than B3P86/6-31+G**.