Field Wave Functions Research Articles

Understanding the Optical and Magnetic Properties of Ytterbium(III) Complexes

The absorption and emission spectra of three Yb3+ complexes possessing D3, D2, and C2 symmetries were analyzed with the aid of ab initio calculations based on Complete Active Space (CAS) self-consistent field wave functions (CAS(13,7)). The absorption spectra present contributions from both cold and hot bands, involving thermally populated excited sublevels of the 2F7/2 manifold. The high-resolution emission spectrum of the tris-picolinate complex [Yb(DPA)3]3- recorded at 77 K presents four components, while the complexes with macrocyclic ligands show both cold and hot emission bands, resulting in more than four components for the 2F5/2 → 2F7/2 transition. The combined information provided by the absorption and emission spectra allowed to identify most of the crystal field sublevels of the 2F5/2 and 2F7/2 states. The energies of these crystal field components are well-reproduced by the ab initio calculations, with deviations typically lower than 100 cm-1. The crystal field splitting is very sensitive to subtle changes of the Yb3+ coordination environment. The magnetic anisotropy of [Yb(DPA)3]3- obtained with ab initio calculations was found to be extremely sensitive to changes in the twist angle of the upper and lower faces of the tricapped trigonal prismatic coordination polyhedron. Ab initio ligand field theory provides a straightforward chemical justification for the changes in magnetic anisotropy, which are responsible for the observed pseudocontact shifts in the NMR spectra.

Trends in the Bond Multiplicity of Cr2, Cr3, and Cr2M (M = Zn, Ni, Fe, Mn) Complexes Extracted from Multiconfigurational Wave Functions.

Extended metal atom chains constitute an interesting class of molecules from both theoretical and applied points of view. In the chromium-based series Cr2M(dpa)4X2 (with M = Zn, Ni, Fe, Mn, Cr), the direct metal-metal interactions span a wide range of possibilities and so do their associated properties. The multiplicity and symmetry components of the metal-metal bond are herein analyzed via the effective bond order (EBO) concept using complete active space self-consistent field wave functions and compared with similar bimetallic Cr2L4X2 systems. The bond multiplicity follows a trend dominated by the Cr-Cr distance which, in turn, depends on the nature of the axial ligand (X). Cr2M compounds present asymmetric structures with virtually no interaction between the Cr2 unit and M, whereas fully symmetric structures with delocalized bonding among the three metals are also possible in Cr3 complexes. In such cases, a strategy that involves localization of the molecular orbitals into each Cr-Cr pair is applied to quantify the contribution of each pair to the overall metal-metal bond multiplicity.

Quantum Wave Function Based on String Theory for Frictional Medium to Obtain Collision Probability, Energy Operator and Schrodinger Equation

Schrodinger equation suffer from being not sensitive to the mechanical properties as well as the electric and magnetic properties of matter. This set back can be cured by starting the derivation using the function sensitive to these parameters. Treating particle as vibrating strings a useful expression for the velocity was found using the equation of motion. Then the relation of current density with a velocity and electric field intensity was utilized to obtain the electric field intensity in a frictional medium. Using the analogy of the electric field and quantum wave function, the wave function was obtained and found to give the conventional expression for the collision probability with relaxation time twice the classical one. Another approach was tackled by obtaining a useful expression of the total energy of strings for resistive collisional medium. This expression utilizes the wave function of quantum particle in a frictional medium to obtain collision probability formula. Fortunately this latter approach gives a relaxation time equal to the classical one. The same wave function is used to find Hamiltonian operator for the both steady state and perturbed state by friction. Fortunately both Hamiltonians satisfy hermiticty condition. The hermiticty condition for the perturbed states however needs splitting the Hamiltonian into unpertured and perturbed part.. The perturbed term satisfies uncertainty principle. The energy expression for the resistive medium resembles that of Einstein and RLC circuits. Schrodinger equation for the frictional medium was also found, where it reduces to the ordinary one when friction disappear.

Single-ion anisotropy and exchange coupling in cobalt(ii)-radical complexes: insights from magnetic and ab initio studies.

The concurrent effects of single-ion anisotropy and exchange interactions on the electronic structure and magnetization dynamics have been analyzed for a cobalt(ii)-semiquinonate complex. Analogs containing diamagnetic catecholate and tropolonate ligands were employed for comparison of the magnetic behavior and zinc congeners assisted with the spectroscopic characterization and assessment of intermolecular interactions in the cobalt(ii) compounds. Low temperature X-band (ν ≈ 9.4 GHz) and W-Band (ν ≈ 94 GHz) electron paramagnetic resonance spectroscopy and static and dynamic magnetic measurements have been used to elucidate the electronic structure of the high spin cobalt(ii) ion in [Co(Me3tpa)(Br4cat)] (1; Me3tpa = tris[(6-methyl-2-pyridyl)methyl]amine, Br4cat2- = tetrabromocatecholate) and [Co(Me3tpa)(trop)](PF6) (2(PF6); trop- = tropolonate), which show slow relaxation of the magnetization in applied field. The cobalt(ii)-semiquinonate exchange interaction in [Co(Me3tpa)(dbsq)](PF6)·tol (3(PF6)·tol; dbsq- = 3,5-di-tert-butylsemiquinonate, tol = toluene) has been determined using an anisotropic exchange Hamiltonian in conjunction with multistate restricted active space self-consistent field ab initio modeling and wavefunction analysis, with comparison to magnetic and inelastic neutron scattering data. Our results demonstrate dominant ferromagnetic exchange for 3+ that is of similar magnitude to the anisotropy parameters of the cobalt(ii) ion and contains a significant contribution from spin-orbit coupling. The nature of the exchange coupling between octahedral high spin cobalt(ii) and semiquinonate ligands is a longstanding question; answering this question for the specific case of 3+ has confirmed the considerable sensitivity of the exchange to the molecular structure. The methodology employed will be generally applicable for elucidating exchange coupling between orbitally-degenerate metal ions and radical ligands and relevant to the development of bistable molecules and their integration into devices.

The symmetry breaking phenomenon in heteronine analogues due to the pseudo Jahn-Teller effect.

The pseudo Jahn-Teller effect (PJTE) is employed in C8AH8 (A = O, S, Se, Te), and C8EH8 + 1 (E = N, P, As, Sb) with planar configurations to show symmetry breaking phenomena (SBP) in heteronine analogues, and to explain why molecules with (C2v) high-symmetry configurations cannot maintain planarity and pucker to their (C2) and (Cs) lower-symmetry structures, respectively. To investigate this phenomenon, geometry optimization and frequency calculations through the density functional B3LYP method using the cc-pVTZ basis set (for Te, and Sb cc-pVTZ-PP) were carried out for all compounds in the series. The state average-complete active space self-consistent field wave-function method was employed to calculate the electronic ground and several low-lying excited states to specify the adiabatic potential energy surface along the a2 and b1 puckering nuclear displacements. The PJTE (A1 + A2 + A1') a2 and (A1 + B1 + A1') b1 problems were formulated as the effects originating via the PJTE theorem. Moreover, replacing hydrogen atoms in C8NH9, a stable planar structure, with fluorine ligands demonstrated that SBP occur from C2v to C2 symmetry. Furthermore, thermochemical calculations via B3LY/cc-pVTZ illustrated that the planarity of the C8E ring is restored in C8EH8- (E = P, As, Sb) anions ,with the change in free energy corresponding to spontaneous deprotonation reactions as 23.67kJmol-1, 21.88kJmol-1, and 16.57kJmol-1, respectively. In fact, despite C8EH8 + 1 having a donor electron-pair and potentially being Lewis base compounds, it acts as a Bronsted-Lowry acid releasing a H+ proton instead in this case.

Embedded Multireference Coupled Cluster Theory.

Internally contracted multireference coupled cluster (icMRCC) theory is embedded within multireference perturbation theory (MRPT) to calculate energy differences in large strongly correlated systems. The embedding scheme is based on partitioning the orbital spaces of a complete active space self-consistent field (CASSCF) wave function, with a truncated virtual space constructed by transforming selected projected atomic orbitals (PAOs). MRPT is applied to the environment using a subtractive embedding approach that also allows for multilayer embedding. Benchmark calculations are presented for biradical bond dissociation, spin splitting in a heterocyclic carbene and hydrated Fe(II), and for the super-exchange coupling constant in solid nickel oxide. The method is further applied to two large transition metal complexes with a triple-ζ basis set: an iron complex with 175 atoms and 2939 basis functions, and a nickel complex with 231 atoms, and 4175 basis functions.

All-electron relativistic computations on the low-lying electronic states, bond length, and vibrational frequency of CeF diatomic molecule with spin-orbit coupling effects.

Ab initio all-electron computations have been carried out for Ce+ and CeF, including the electron correlation, scalar relativistic, and spin-orbit coupling effects in a quantitative manner. First, the n-electron valence state second-order multireference perturbation theory (NEVPT2) and spin-orbit configuration interaction (SOCI) based on the state-averaged restricted active space multiconfigurational self-consistent field (SA-RASSCF) and state-averaged complete active space multiconfigurational self-consistent field (SA-CASSCF) wavefunctions have been applied to evaluations of the low-lying energy levels of Ce+ with [Xe]4f1 5d1 6s1 and [Xe]4f1 5d2 configurations, to test the accuracy of several all-electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA-RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(-DKH3)-2012-QZP basis set were carried out to determine the energy levels of the low-lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.

Exploration of H2 binding to the [NiFe]-hydrogenase active site with multiconfigurational density functional theory.

The combination of density functional theory (DFT) with a multiconfigurational wave function is an efficient way to include dynamical correlation in calculations with multiconfiguration self-consistent field wave functions. These methods can potentially be employed to elucidate reaction mechanisms in bio-inorganic chemistry, where many other methods become either too computationally expensive or too inaccurate. In this paper, a complete active space (CAS) short-range DFT (CAS-srDFT) hybrid was employed to investigate a bio-inorganic system, namely H2 binding to the active site of [NiFe] hydrogenase. This system was previously investigated with coupled-cluster (CC) and multiconfigurational methods in the form of cumulant-approximated second-order perturbation theory, based on the density matrix renormalization group (DMRG). We find that it is more favorable for H2 to bind to Ni than to Fe, in agreement with previous CC and DMRG calculations. The accuracy of CAS-srDFT is comparable to both CC and DMRG, despite much smaller active spaces were employed than in the corresponding DMRG calculations. This enhanced efficiency at the smaller active spaces shows that CAS-srDFT can become a useful method for bio-inorganic chemistry.

Molecular structure, nonlinear optical studies and spectroscopic analysis of chalcone derivative (2E)-3-[4-(methylsulfanyl) phenyl]-1-(3-bromophenyl) prop-2-en-1-one by DFT calculations

A collective experimental and theoretical study was conducted on the molecular structure and vibrational spectra of nonlinear optical chalcone derivative (2E)-3-[4-(methylsulfanyl) phenyl]-1-(3-bromophenyl) prop-2-en-1-one (3Br4MSP). The FT-IR and FT-Raman spectra of the molecule in the solid phase have been recorded. Density functional theory (DFT) calculations at B3LYP level with 6–311++G (d,p) basis set have been carried out to derive useful information about the molecular structure and to assign the relevant electronic and vibrational features. These calculations reveal that the optimized geometry closely resembles the experimental XRD data. The vibrational spectra were analyzed on the basis of the potential energy distribution (PED) of each vibrational mode, which allowed us to obtain a quantitative as well as qualitative interpretation of FT-IR and FT-Raman spectra. The UV–vis spectrum was recorded in methanol solution. The excited state properties have been determined by TD-DFT method and the effect of solvent was analyzed by PCM model. The most prominent transition corresponds to π→π∗. The reactivity parameters as chemical potential, global hardness, and electrophilicity index have also been calculated. To provide an explicit assignment and analysis of 13C and 1H NMR spectra, theoretical calculations on chemical shift of the title compound were done through GIAO method at B3LYP/6-311++G (d,p) level. The Mulliken's population analysis shows one of the simplest pictures of charge distribution. The standard statistical thermodynamic functions like heat capacity at constant pressure (Cop,m), entropy (Som) and enthalpy (Hom) were obtained from the theoretical harmonic frequencies for the optimized molecule. The nonlinear optical properties of title molecule are also addressed theoretically. Two contributions, vibrational and electronic, to the electrical properties polarizability and first order hyperpolarizability of 3Br4MSP have been evaluated using the self-consistent field wave functions within the double harmonic oscillator approximation.

Physical properties of the candidate quantum spin-ice systemPr2Hf2O7

Physical properties of a pyrohafnate compound Pr2Hf2O7 have been investigated by ac magnetic susceptibility \chi_ ac(T), dc magnetic susceptibility \chi(T), isothermal magnetization M(H) and heat capacity C_p(T) measurements on polycrystalline as well as single crystal samples combined with high-resolution synchrotron x-ray diffraction (XRD) for structural characterization and inelastic neutron scattering (INS) to determine the crystal field energy level scheme and wave functions. Synchrotron XRD data confirm the ordered cubic pyrochlore (Fd-3m) structure without any noticeable site mixing or oxygen deficiency. No clear evidence of long range magnetic ordering is observed down to 90 mK, however the \chi_ac(T) evinces slow spin dynamics revealed by a frequency dependent broad peak associated with spin freezing. The INS data reveal the expected five well defined magnetic excitations due to crystal field splitting of the J = 4 ground state multiplet of the Pr^3+. The crystal field parameters and ground state wavefunction of Pr^3+ have been determined. The Ising anisotropic nature of magnetic ground state is inferred from the INS as well as \chi(T) and M(H) data. Together these properties make Pr2Hf2O7 a candidate compound for quantum spin-ice behavior.

Multiconfigurational and DFT analyses of the electromeric formulation and UV–vis absorption spectra of the superoxide adduct of ferrous superoxide reductase

The putative initial adduct of ferrous superoxide reductase (SOR) with superoxide has been alternatively formulated as ferric-peroxo or ferrous-superoxo. The ~600-nm UV–vis absorption band proposed to be assigned to this adduct (either as sole intermediate in the SOR catalytic cycle, or as one of the two intermediates) has recently been interpreted as due to a ligand-to-metal charge transfer, involving thiolate and superoxide in a ferrous complex, contrary to an alternative assignment as a predominantly cysteine thiolate-to-ferric charge transfer in a ferric-peroxo electromer. In an attempt to clarify the electromeric formulation of this adduct, we report a computational study using a multiconfigurational complete active space self-consistent field (MC-CASSCF) wave function approach as well as modelling the UV–vis absorption spectra with time-dependent density functional theory (TD-DFT). The MC-CASSCF calculations disclose a weak interaction between iron and the dioxygenic ligand and a dominant configuration with an essentially ferrous-superoxo character. The computed UV–vis absorption spectra reveal a marked dependence on the choice of density functional – both in terms of location of bands and in terms of orbital contributors. For the main band in the visible region, besides the recently reported thiolate-to-superoxide charge transfer, a more salient, and less functional-dependent, feature is a thiolate-to-ferric iron charge transfer, consistent with a ferric-peroxo electromer. By contrast, the computed UV–vis spectra of a ferric-hydroperoxo SOR model match distinctly better (and with no qualitative dependence on the DFT methodology) the 600-nm band as due to a mainly thiolate-to-ferric character – supporting the assignment of the SOR “600-nm intermediate” as a S=5/2 ferric-hydroperoxo species.

Enhancement of octupole strength in near spherical nuclei

The validity of the rotational formula used to compute E1 and E3 transition strengths in even-even nuclei is analyzed within the Generator Coordinate Method framework based on mean field wave functions. It turns out that those nuclei with spherical or near spherical shapes the E1 and E3 strengths computed with this formula are strongly underestimated and a sound evaluation of them requires angular momentum projected wave functions. Results for several isotopic chains with proton number equal or near magic numbers are analyzed and compared with experimental data. The use of angular momentum projected wave functions greatly improves the agreement with the scarce experimental data.

Assessment of oscillator strengths with multiconfigurational short-range density functional theory for electronic excitations in organic molecules

ABSTRACTWe have in a series of recent papers investigated electronic excited states with a hybrid between a complete active space self-consistent field (CASSCF) wave function and density functional theory (DFT). This method has been dubbed the CAS short-range DFT method (CAS–srDFT). The previous papers have primarily focused on the excitation energies, and not on the oscillator strengths, although they comprise an important part of the absorption spectrum. In this study, we have carried out a quantitative analysis of oscillator strengths obtained with CAS–srDFT. As target molecules, we have considered the large collection of organic molecules whose excited states were investigated with a range of electronic structure methods by Thiel et al. As a by-product of our calculations of oscillator strengths, we also obtain electronic excitation energies, which enable us to compare the performance of CAS–srPBE for excitation energies, using a larger set of chromophores compared to previous studies.

Communication: An efficient approach to compute state-specific nuclear gradients for a generic state-averaged multi-configuration self consistent field wavefunction

We present a new, very efficient semi-numerical approach for the computation of state-specific nuclear gradients of a generic state-averaged multi-configuration self consistent field wavefunction. Our approach eliminates the costly coupled-perturbed multi-configuration Hartree-Fock step as well as the associated integral transformation stage. The details of the implementation within the Firefly quantum chemistry package are discussed and several sample applications are given. The new approach is routinely applicable to geometry optimization of molecular systems with 1000+ basis functions using a standalone multi-core workstation.

Chemical bonding: the orthogonal valence-bond view.

Chemical bonding is the stabilization of a molecular system by charge- and spin-reorganization processes in chemical reactions. These processes are said to be local, because the number of atoms involved is very small. With multi-configurational self-consistent field (MCSCF) wave functions, these processes can be calculated, but the local information is hidden by the delocalized molecular orbitals (MO) used to construct the wave functions. The transformation of such wave functions into valence bond (VB) wave functions, which are based on localized orbitals, reveals the hidden information; this transformation is called a VB reading of MCSCF wave functions. The two-electron VB wave functions describing the Lewis electron pair that connects two atoms are frequently called covalent or neutral, suggesting that these wave functions describe an electronic situation where two electrons are never located at the same atom; such electronic situations and the wave functions describing them are called ionic. When the distance between two atoms decreases, however, every covalent VB wave function composed of non-orthogonal atomic orbitals changes its character from neutral to ionic. However, this change in the character of conventional VB wave functions is hidden by its mathematical form. Orthogonal VB wave functions composed of orthonormalized orbitals never change their character. When localized fragment orbitals are used instead of atomic orbitals, one can decide which local information is revealed and which remains hidden. In this paper, we analyze four chemical reactions by transforming the MCSCF wave functions into orthogonal VB wave functions; we show how the reactions are influenced by changing the atoms involved or by changing their local symmetry. Using orthogonal instead of non-orthogonal orbitals is not just a technical issue; it also changes the interpretation, revealing the properties of wave functions that remain otherwise undetected.

¹H Chemical Shifts in Paramagnetic Co(II) Pyrazolylborate Complexes: A First-Principles Study.

We apply the theory of the nuclear magnetic resonance (NMR) chemical shift for paramagnetic systems to demanding cobalt(II) complexes. Paramagnetic NMR (pNMR) chemical shift results by density-functional theory (DFT) can be very far from the experimental values. Therefore, it is of interest to investigate the applicability of electron-correlated ab initio computational methods to achieve useful accuracy. Here, we use ab initio wave function based electronic structure methods to calculate the pNMR chemical shift within the theoretical framework established recently. We applied the N-electron valence-state perturbation theory (NEVPT2) on three Co(II) systems, where the active space of the underlying complete active space self-consistent field (CASSCF) wave function consists of seven electrons in the five metal 3d orbitals. These complexes have the S = 3/2 electronic ground state consisting of two doublets separated by zero-field splitting (ZFS). To calculate the hyperfine coupling tensor A, DFT was used, while the g- and ZFS-tensors were calculated using the ab initio CASSCF and NEVPT2 methods. These results were combined to obtain the total chemical shifts. The shifts obtained from these calculations are in generally good agreement with the experimental results, in some cases suggesting a reassignment of the signals. The accuracy of this mixed ab initio/DFT approach is very promising for further applications to demanding pNMR problems involving transition metals.

Molecular g-tensors from analytical response theory and quasi-degenerate perturbation theory in the framework of complete active space self-consistent field method

The molecular g-tensor is an important spectroscopic parameter provided by electron para magnetic resonance (EPR) measurement and often needs to be interpreted using computational methods. Here, we present two new implementations based on the first-order and second-order perturbation theories to calculate the g-tensors within the complete-active space self-consistent field (CASSCF) wave function model. In the first-order method, the quasi-degenerate perturbation theory (QDPT) is employed for constructing relativistic CASSCF states perturbed with the spin–orbit coupling operator, which is described effectively in one-electron form with the flexible nuclear screening spin–orbit approximation introduced recently by us. The second-order method is a newly reported approach built upon the linear response theory which accounts for the perturbation with respect to external magnetic field. It is implemented with the coupled–perturbed CASSCF (CP-CASSCF) approach, which provides an equivalent of untruncated sum-over-states expansion. The comparison of the performances between the first-order and second-order methods is shown for various molecules containing light to heavy elements, highlighting their relative strength and weakness. The formulations of QDPT and CP-CASSCF approaches as well as the derivation of the second-order Douglas–Kroll–Hess picture change of Zeeman operators are given in detail.

Energy level structure and optical dephasing under magnetic field in Er3+:LiYF4 at 1.5 μm

Er3+:LiYF4 is a material where optical inhomogeneous linewidths are smaller than hyperfine splittings, which could be advantageous for quantum information processing protocols. We investigated the Zeeman and hyperfine structures under magnetic field by optical spectroscopy at 1.5μm and found a good agreement with calculations based on crystal field wavefunctions. Since Zeeman splittings have a non-linear dependance on the magnetic field, this calculations could be useful to estimate energy level structures for arbitrary field strengths and orientations. Coherence lifetimes have been measured on a 100ppm erbium doped sample under a 2.2T magnetic field. Values up to 4.7μs have been observed, with an exponential decay of the echo intensity as a function the pulse delay.

The externally corrected coupled cluster approach with four- and five-body clusters from the CASSCF wave function.

An externally corrected CCSDt (coupled cluster with singles, doubles, and active triples) approach employing four- and five-body clusters from the complete active space self-consistent field (CASSCF) wave function (denoted as ecCCSDt-CASSCF) is presented. The quadruple and quintuple excitation amplitudes within the active space are extracted from the CASSCF wave function and then fed into the CCSDt-like equations, which can be solved in an iterative way as the standard CCSDt equations. With a size-extensive CASSCF reference function, the ecCCSDt-CASSCF method is size-extensive. When the CASSCF wave function is readily available, the computational cost of the ecCCSDt-CASSCF method scales as the popular CCSD method (if the number of active orbitals is small compared to the total number of orbitals). The ecCCSDt-CASSCF approach has been applied to investigate the potential energy surface for the simultaneous dissociation of two O-H bonds in H2O, the equilibrium distances and spectroscopic constants of 4 diatomic molecules (F2(+), O2(+), Be2, and NiC), and the reaction barriers for the automerization reaction of cyclobutadiene and the Cl + O3 → ClO + O2 reaction. In most cases, the ecCCSDt-CASSCF approach can provide better results than the CASPT2 (second order perturbation theory with a CASSCF reference function) and CCSDT methods.

Systematic theoretical investigation of the zero-field splitting in Gd(III) complexes: wave function and density functional approaches.

The zero-field splitting (ZFS) of the electronic ground state in paramagnetic ions is a sensitive probe of the variations in the electronic and molecular structure with an impact on fields ranging from fundamental physical chemistry to medical applications. A detailed analysis of the ZFS in a series of symmetric Gd(III) complexes is presented in order to establish the applicability and accuracy of computational methods using multiconfigurational complete-active-space self-consistent field wave functions and of density functional theory calculations. The various computational schemes are then applied to larger complexes Gd(III)DOTA(H2O)(-), Gd(III)DTPA(H2O)(2-), and Gd(III)(H2O)8(3+) in order to analyze how the theoretical results compare to experimentally derived parameters. In contrast to approximations based on density functional theory, the multiconfigurational methods produce results for the ZFS of Gd(III) complexes on the correct order of magnitude.