An extended-valence MC SCF procedure: determination of the dissociation energies of C2, N2, O2, and F2

A series of MC SCF calculations have been carried out on C₂, N₂, O₂, and F₂ with the goal of obtaining compact wavefunctions which recover a significant fraction of the electron correlation effects important for bond dissociation. The active orbital space is varied in size, with the largest spaces including the molecular orbitals derived from 2s, 2p, 3s, 3p and 4p atomic orbitals. Several basis sets ranging in size from 5s3p to 5s4p2d1f are investigated to determine the flexibility in the basis set needed with various choices of the active orbital space. The best extended-valence MC SCF (EVMC) dissociation energies are 0.2–0.5 eV less than the experimental values, indicating that further enlargement of the active orbital space is necessary to achieve 0.1 eV accuracy in the computed dissociation energies. The EVMC calculations reveal that, for the calculation of the dissociation energies, inclusion of non-valence orbitals is much more important for O₂ and F₂ than for C₂ and N₂. The EVMC results are compared with the predictions of full fourth-order perturbation theory, coupled cluster theory, and with the best available CI calculations.     

CdH分子的量子化学研究

在相对论赝势从头算全有效空间多组态自洽场方法（CASSCF）基础上，对CdH分子进行了二级电子相关（SOCI）计算，得出此体系几个电子态的电子结构、势能曲线及光谱常数，认为，静态相关效应及动态相关效应对该体系的光谱性质等都有较大影响．     

MCSCF calculation of the frequency-dependent hyperpolarizability of the lithium atom

The second electric dipole hyperpolarizability of the lithium atom is calculated using a series of multiconfiguration SCF wave functions with an increasing number of active space orbitals. In agreement with other recent calculations, we find a very large correlation correction to the hyperpolarizability. We analyze the frequency dependence of the dc Kerr hyperpolarizability γ^K(o) = γ (− o o, 0, 0) and observe very significant dispersion effects. © 1996 John Wiley & Sons, Inc.     

Development of a sum-over-states density functional theory for both electric and magnetic static response properties

It is shown that it is possible to formulate a sum-over-states (SOS) response theory for static perturbations based directly on the Kohn-Sham formulation of density functional theory (DFT). The SOS-DFT response theory affords expressions analogous to those obtained from the classical Raleigh-Schrodinger perturbation theory, where use is made of a complete set of ground and excited state energies and wave functions. The static SOS-DFT response theory is applicable for both real and imaginary perturbations. The theory is established by making use of time-dependent DFT taken to zero frequency with the use of the adiabatic approximation. In the SOS-DFT formulation the expression for electric (e.g., polarization) and magnetic (e.g., magnetization) response properties are symmetrical.     

Analytic calculation of second-order electric response properties with the normalized elimination of the small component (NESC) method

Analytic second derivatives of the relativistic energy for the calculation of electric response properties are derived utilizing the normalized elimination of the small component (NESC) method. Explicit formulas are given for electric static dipole polarizabilities and infrared intensities by starting at the NESC representation of electric dipole moments. The analytic derivatives are implemented in an existing NESC program and applied to calculate dipole moments, polarizabilities, and the infrared spectra of gold- and mercury-containing molecules as well as some actinide molecules. Comparison with experiment reveals the accuracy of NESC second order electric response properties.     

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.     

Electronic properties of Pt in bimetallic systems: photoemission and molecular-orbital studies for Pt---Al surface alloys

The adsorption of Pt on polycrystalline Al leads to the formation of surface alloys. The electronic properties of these systems have been examined using XPS and ab initio SCF calculations. The Pt---Al surface alloys display a Pt(5d) band that appears at much higher binding energy (≈ 1.8 eV) than in metallic Pt. This is accompanied by positive shifts in the Pt 4f (≈ 1.2 eV) and Al 2s (≈ 0.2 eV) levels. The Pt---Al bond is complex, involving an Al(3s, 3p) → Pt(6s, 6p) charge transfer and a Pt(5d) → Pt(6s, 6p) rehybridization that localize electrons in the region between the two metal centers.     

BaAl4Se7: a new infrared nonlinear optical material with a large band gap

The new compound BaAl(4)Se(7) has been synthesized by solid-state reaction. It crystallizes in the non-centrosymmetric space group Pc and adopts a three-dimensional framework built from AlSe(4) tetrahedra and with Ba(2+) cations in the cavities. The material has a large band gap of 3.40(2) eV. It melts congruently at 901 °C and exhibits a second harmonic generation (SHG) response at 1 μm that is about half that of AgGaS(2). From a band structure calculation, BaAl(4)Se(7) is a direct-gap semiconductor with strong hybridization of the Al 3s, Al 3p, and Se 4p orbitals near the Fermi level. The calculated birefractive index is about 0.05 for wavelength longer than 1 μm and major SHG tensor elements are: d(15) = 5.2 pm V(-1) and d(13) = 4.2 pm V(-1).     

Theoretical Modelling of Photoswitching of Hyperpolarisabilities in Ruthenium Complexes

Static excited‐state polarisabilities and hyperpolarisabilities of three Ru^II ammine complexes are computed at the density functional theory (DFT) and several correlated ab initio levels. Most accurate modelling of the low energy electronic absorption spectrum is obtained with the hybrid functionals B3LYP, B3P86 or M06 for the complex [Ru^II(NH₃)₅(MeQ⁺)]³⁺ (MeQ⁺=N‐methyl‐4,4′‐bipyridinium, 3 ) in acetonitrile. The match with experimental data is less good for [Ru^II(NH₃)₅L]³⁺ (L=N‐methylpyrazinium, 2 ; N‐methyl‐4‐{E,E‐4‐(4‐pyridyl)buta‐1,3‐dienyl}pyridinium, 4 ). These calculations confirm that the first dipole‐ allowed excited state (FDAES) has metal‐to‐ligand charge‐transfer (MLCT) character. Both the solution and gas‐phase results obtained for 3 by using B3LYP, B3P86 or M06 are very similar to those from restricted active‐space SCF second‐order perturbation theory (RASPT2) with a very large basis set and large active space. However, the time‐dependent DFT λ_max predictions from the long‐range corrected functionals CAM‐B3LYP, LC‐ωPBE and wB97XB and also the fully ab initio resolution of identity approximate coupled‐cluster method (gas‐phase only) are less accurate for all three complexes. The ground state (GS) two‐state approximation first hyperpolarisability β_2SA for 3 from RASPT2 is very close to that derived experimentally via hyper‐Rayleigh scattering, whereas the corresponding DFT‐based values are considerably larger. The β responses calculated by using B3LYP, B3P86 or M06 increase markedly as the π‐conjugation extends on moving along the series 2 → 4 , for both the GS and FDAES species. All three functionals predict substantial FDAES β enhancements for each complex, increasing with the π‐conjugation, up to about sevenfold for 4 . Also, the computed second hyperpolarisabilities γ generally increase in the FDAES, but the results vary between the different functionals.     

Structure, stability and vibrational spectrum of the hydrogen-bonded complex between HNO3 and H2O. Ab initio and DFT studies

The structure, stability and vibrational spectrum of the binary complex between HONO2 and H2O have been investigated using ab initio calculations at SCF and MP2 levels with different basis sets and B3LYP/6-31G(d,p) calculations. Full geometry optimization was made for the complex studied. It was established that the hydrogen-bonded H2O...HONO2 complex has a planar structure. The corrected values of the dissociation energy at the SCF and MP2 levels and B3LYP calculations are indicative of relatively strong OH...O hydrogen-bonded interaction. The changes in the vibrational characteristics (vibrational frequencies and infrared intensities) arising from the hydrogen bonding between HONO2 and H2O have been estimated by using the ab initio calculations at SCF and MP2 levels and B3LYP/6-31G(d,p) calculations. It was established that the most sensitive to the complexation is the stretching O-H vibration from HONO2. In agreement with the experiment, its vibrational frequency in the complex is shifted to lower wavenumbers. The predicted frequency shift with the B3LYP/6-31G(d,p) calculations (-439 cm(-1)) is in the best agreement with the experimentally measured (-498 cm(-1)). The intensity of this vibration increases dramatically upon hydrogen bonding. The ab initio calculations at the SCF level predict an increase up to five times; at the MP2 level up to 10 times and the B3LYP/6-31G(d,p) predicted increase is up to 17 times. The good agreement between the predicted values of the frequency shifts and those experimentally observed show that the structure of the hydrogen-bonded complex H2O...HONO2 is reliable.     

Electric response properties of a confined gas of independent particles acted upon by a direct current electric field

Exact results for linear and nonlinear electric response properties of a non-interacting ensemble of charged particles, confined within an impenetrable box and subjected to a static, homogeneous electric field, are derived and discussed. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

Full configuration interaction calculation of the low lying valence and Rydberg states of BeH

The all-electron full configuration interaction (FCI) vertical excitation energies for some low lying valence and Rydberg excited states of BeH are presented in this article. A basis set of valence atomic natural orbitals has been augmented with a series of Rydberg orbitals that have been generated as centered onto the Be atom. The resulting basis set can be described as 4s2p1d/2s1p (Be/H) + 4s4p3d. It allows to calculate Rydberg states up to n= {3,4,5} of the s, p, and d series of Rydberg states. The FCI vertical ionization potential for the same basis set and geometry amounts to 8.298 eV. Other properties such as FCI electric dipole and quadrupole moments and FCI transition dipole and quadrupole moments have also been calculated. The results provide a set of benchmark values for energies, wave functions, properties, and transition properties for the five electron BeH molecule. Most of the states have large multiconfigurational character in spite of their essentially single excited nature and a number of them present an important Rydberg-valence mixing that is achieved through the mixed nature of the particle MO of the single excitations.     

Low-lying electronic states of FeNC and FeCN: a theoretical journey into isomerization and quartet/sextet competition

With several levels of multireference and restricted open-shell single-reference electronic structure theory, optimum structures, relative energetics, and spectroscopic properties of the low-lying (6)Delta, (6)Pi, (4)Delta, (4)Pi, and (4)Sigma(-) states of linear FeNC and FeCN have been investigated using five contracted Gaussian basis sets ranging from Fe[10s8p3d], C/N[4s2p1d] to Fe[6s8p6d3f2g1h], C/N[6s5p4d3f2g]. Based on multireference configuration interaction (MRCISD+Q) results with a correlation-consistent polarized valence quadruple-zeta (cc-pVQZ) basis set, appended with core correlation and relativistic corrections, we propose the relative energies: T(e)(FeNC), (6)Delta(0)<(6)Pi (2300 cm(-1))<(4)Delta (2700 cm(-1))<(4)Pi (4200 cm(-1))<(4)Sigma(-); and T(e)(FeCN), (6)Delta(0)<(6)Pi (1800 cm(-1))<(4)Delta (2500 cm(-1))<(4)Pi (2900 cm(-1))<(4)Sigma(-). The (4)Delta and (4)Pi states have massive multireference character, arising mostly from 11sigma-->12sigma promotions, whereas the sextet states are dominated by single electronic configurations. The single-reference CCSDT-3 (coupled cluster singles and doubles with iterative partial triples) method appears to significantly overshoot the stabilization of the quartet states provided by both static and dynamical correlation. The (4,6)Delta and (4,6)Pi states of both isomers are rather ionic, and all have dipole moments near 5 D. On the ground (6)Delta surface, FeNC is predicted to lie 0.6 kcal mol(-1) below FeCN, and the classical barrier for isocyanide/cyanide isomerization is about 6.5 kcal mol(-1). Our data support the recent spectroscopic characterization by Lei and Dagdigian [J. Chem. Phys. 114, 2137 (2000)] of linear (6)Delta FeNC as the first experimentally observed transition-metal monoisocyanide. Their assignments for the ground term symbol, isotopomeric rotational constants, and the Fe-N omega(3) stretching frequency are confirmed; however, we find rather different structural parameters for (6)Delta FeNC:r(e)(Fe-N)=1.940 A and r(N-C)=1.182 A at the cc-pVQZ MRCISD+Q level. Our results also reveal that the observed band of FeNC originating at 27 236 cm(-1) should have an analog in FeCN near 23 800 cm(-1) of almost equal intensity. Therefore, both thermodynamic stability and absorption intensity factors favor the eventual observation of FeCN via a (6)Pi<--(6)Delta transition in the near-UV.     

Reduced-size polarized basis sets for calculations of molecular electric properties. IV. First-row transition metals

Recent studies of the perturbation-dependent basis sets have indicated the possibility of a significant reduction of the size of the usual CGTO sets without considerable loss of accuracy in calculations of molecular electric properties. The resulting (ZPolX) basis sets have been developed for several atoms of the first and second row of the Periodic Table. The same method of the ZPolX basis set generation is extended for the first-row transition metals and the corresponding contracted ZPolX basis sets of the size [6s5p3d1f] are determined for both nonrelativistic and scalar relativistic calculations. The performance of the ZPolX basis sets is verified in calculations on the first-row transition metal oxides at the level of the ROHF, ROHF/CASPT2, and ROHF/CCSD(T) approximations. Also the study of the dipole polarizability of TiCl₄ confirms the excellent features of these very compact basis sets. The ZPolX basis sets for nonrelativistic and relativistic calculations of molecular electric properties are available on the web page http://www.chem.uni.torun.pl/zchk/basis-sets.html.     

The calculation of frequency-dependent hyperpolarizabilities including electron correlation effects

The theory for the calculation of the frequency-dependent hyperpolarizabilities β(?2ω; 0, ω), β(?ω; 0, ω), and β(0; ω, ?ω) is discussed. New relations between these tensors are derived for those wave functions that obey the time-dependent Hellmann–Feynman theorem (e.g., the self-consistent field [SCF] or the exact wave function). Using second-order Møller–Plesset perturbation theory (MP2), expressions are obtained for the hyperpolarizabilities in terms of derivatives of appropriately defined linear polarizability tensors with respect to a static electric field. Results are presented for ammonia and formaldehyde for the optical Kerr effect and for secondharmonic generation. These results indicate that it is desirable to determine the frequency-dependent contribution to the hyperopolarizability at the MP2 rather than the SCF level of theory, in cases where the static hyperpolarizability has a large contribution from electron correlation and/or where the frequency-dependent contribution may be more significant, such as for secondharmonic generation.     

Synthesis, Character and Crystal Structure of the Complex {Er（DMSO）7} PW12O40

The synthesis, X-ray crystal structure, thermal properties and electrochemistry of the new complex formulated as {Er(DMSO)7}PW12O40 are reported. The single-crystal X-ray analysis reveals that the crystal crystallizes in the monoclinic system, space group P21/c with a = 11.767(2), b = 14.909(3), c = 34.905(7) , β = 98.97(3)°, Mr = 3591.33, V = 6049(2) 3, Dc = 3.944 g/cm3, Z = 4, GOOF = 1.098, F(000) = 6340, R = 0.0490 and wR = 0.1202. Crystal structure analysis indicates that the Er(Ⅲ) is seven-coordinate with a distorted pentagonal bipyramid and combines to the anion [PW12O40]3- via static electric force.     

Response dynamics of 2-D quantum dots in the presence of time-varying fields: Anharmonicity and pulse shape effects

We explore the pattern of time evolution of different observables in a harmonically confined single carrier 2-D quantum dot when an external time-varying electric field is switched on. A static transverse magnetic field is also present. For given strengths of the confining field, cyclotron frequency, intensity and oscillation frequency of the external field, and pulse shape parameters, the system reveals a long time dynamics that leads to a kind of localization in the unperturbed state space. The presence of cubic anharmonicity in the confining field brings in new features in the dynamics. Frequency dependent linear and non-linear response properties of the dot are analyzed.