Self-consistent Field Calculations Research Articles

Magnetic Properties of a Family of [MnIII4LnIII4] Wheel Complexes: An Experimental and Theoretical Study.

The chelating ligand 1,3-bis(tris(hydroxymethyl)methylamino)propane (H6L) has been used to synthesize a family of octanuclear heterometallic complexes with the formula (NMe4)3[Mn4Ln4(H2L)3(H3L)(NO3)12] (Ln = La (1), Ce (2), Pr (3), Nd (4)). Encapsulation by the ligand causes the Mn(III) centers to lie in an unusually distorted (∼C2v) environment, which is shown by density functional theory and complete active space self-consistent field calculations to impact on the magnetic anisotropy of the Mn(III) ion. The theoretical study also supports the experimental observation of a ferromagnetic superexchange interaction between the Mn(III) ions in 1, despite the ions being separated by the diamagnetic La(III) ion. The optical properties of the compounds show that the distortion of the Mn(III) ions leads to three broad absorption bands originating from the transition metal ion, while the Nd(III) containing complex also displays some weak sharp features arising from the lanthanide f-f transitions.

Laser-induced fluorescence and dispersed-fluorescence spectroscopy of the Ã2E-X̃2A1 transition of jet-cooled calcium methoxide (CaOCH3) radicals.

Laser-induced fluorescence (LIF) and dispersed fluorescence (DF) spectra of the Ã2E-X̃2A1 electronic transition of the calcium methoxide (CaOCH3) radical have been obtained under jet-cooled conditions. Complete active space self-consistent field and coupled-cluster calculations on the free radical were performed to aid the assignment of vibronic transitions observed in the LIF/DF spectra. In addition to dominant spectral features that are well reproduced by vibrational frequencies and Franck-Condon (FC) factors calculated ab initio, the FC matrix for the Ã2E-X̃2A1 electronic transition contains considerable off-diagonal elements that connect (i) the CaO-stretch (ν4) mode and non-CaO stretch modes and (ii) the asymmetric CaOC stretch (ν3) and the CaOC bending (ν8) modes. The Jahn-Teller and pseudo-Jahn-Teller interactions involving the Ã2E state as well as the spin-orbit interaction induce additional vibronic transitions that are not allowed under the Born-Oppenheimer approximation. Additionally, anharmonic vibrational terms in the ground state induce transitions that are forbidden in the harmonic-oscillator approximation. Spin-orbit splitting has been observed for several vibrational levels of the Ã2E state, and an essentially constant value was measured at all levels accessed in the LIF experiment. Implications of the present spectroscopic investigation to the proposed schemes of laser-cooling MOCH3 (M = alkaline earth metals) molecules and detection of time-reversal-symmetry-violating interactions are discussed.

Theoretical evaluation of valeraldehyde

The aim of this study was to compute the theoretical (software-based) spectroscopic properties of valeraldehyde as a member of the aldehyde family. The structural, thermochemical, electrical and spectroscopic properties of valeraldehyde were investigated using a quantum calculation approach. The infrared, ultraviolet-visible, Raman, and vibrational self-consistent field calculations and thermochemistry were calculated using the computational software GAMESS (General Atomic and Molecular Electronic Structure System) and the nuclear magnetic resonance predictions were calculated. The calculated energy gap between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) was 164.892.eV, which means valeraldehyde is a poor electrical conductor. The band gap is a non-neglected parameter for optical material. Results of the current computational analysis are useful to predict even a complex aldehyde precursor.
 Significance:
 
 The computational strategy used successfully here could also be useful for investigation of other aldehyde polymers.

Remote Functionalization through Symmetric or Asymmetric Substitutions Control the Pathway of Intermolecular Singlet Fission.

Singlet fission (SF) produces two coupled triplet excitons from a high energy singlet excitation. The mechanism of SF in a variety of phenyl (-Ph) substituted pentacene is systematically studied through both ab initio and density functional theory calculations. Two classes of substitution to pentacene are considered, namely, symmetric configuration with four Ph groups (TPP) and an asymmetric configuration with two Ph groups (DPP). The positions of the singlet and triplet states are determined by calibrating the active space through state averaged complete active space self-consistent field (SA-CASSCF) calculations. The SF rates are computed based on restricted active space with single and double spin flip wave functions (RAS-SF and RAS-2SF), which are analyzed based on different intermolecular π-stacking patterns of TPP and DPP. The contribution of charge transfer (CT) state near the multiexciton (ME) state plays a significant role for SF efficiency. The role of excimer formation is supportive for ME generation [J. Am. Chem. Soc. 2016, 138, 617], and hence it is critically studied. The ME generation in TPP is a slower process and occurs through an excimer-mediated path with a large coupling between the first singlet excited state and ME state. On the other hand, DPP exhibits a relatively faster SF rate through the formation of a ME state via low-lying CT state, especially the slip-stacked dimers. The present computation elegantly demonstrates the crucial role of functional group substitution in the structure of SF active molecules in determining the efficiency of fission dynamics.

Jahn-Teller effect versus spin-orbit coupling: The structure of the free molybdenum pentafluoride molecule

The complete active space self-consistent field (CASSCF) and multiconfigurational quasi-degenerate second-order perturbation (MCQDPT2) calculations have been used to study the ground and low-lying excited electronic states of MoF5. Scalar-relativistic effects and spin-orbit coupling (SOC) have been taken into account employing the third-order Douglas-Kroll-Hess (DKH) Hamiltonian and full Breit-Pauli operator, respectively. The optimization and the calculation of the Hessian matrix have been performed by non-routine procedure employing the symmetry coordinates for all considered (D3h, C2v and C4v) geometrical configurations. The trigonal bipyramidal D3h structure of molybdenum pentafluoride MoF5 possesses two-fold degenerate ground first excited electronic orbital state and undergoes Jahn-Teller distortion to the C2v configurations. Accounting of SOC quenches the JT effect. As a result the D3h structure of MoF5 is no longer the conical intersection of two adiabatic potential energy surfaces (APES) but two separated APES corresponding to ground (12E1/2) and nearest excited (12E3/2) spin-orbit states are appeared instead. The D3h trigonal bipyramidal structure in the ground spin-orbit state corresponds to the 2-nd order saddle point on APES and lies above the minima (C2v structure, 12E1/2 state) by 244 cm−1. The warping barrier (another C2v structure) in the trough of APES and the Berry pseudorotation barrier (C4v structure, ground spin-orbit state 2E3/2) are 19 and 310 cm−1, respectively. Therefore MoF5 molecule is characterized in the gas phase by a large-amplitude motion of fluorine atoms in the equatorial plane and non-rigid intramolecular rearrangement by Berry mechanism. Despite such non-rigid nuclei dynamic, the calculated harmonic frequencies of MoF5 molecule do not contradict to available experimental IR spectrum. The repeat refinement of MoF5 gas electron diffraction data has been carried out using static and pseudoconformer models based on the SO-MCQDPT2 results. Corresponding to only extreme points on APES the configurations have been included into the pseudoconformer model. The both models have been fitted to the experimental data by the same quality.

Single-Molecule Magnetism in Three Dy2 Complexes from the Use of a Pentadentate Schiff Base Ligand and Different Benzoates.

Three dinuclear dysprosium(III) complexes, [Dy2 L2 (O2 CPh)2 ]⋅2 MeOH (1), [Dy2 L2 {(2-NO2 )O2 CPh}2 ] (2), and [Dy2 L2 {(2-OH)O2 CPh}2 ]⋅MeOH⋅MeCN (3) (H2 L=N1 ,N3 -bis(4-chlorosalicyladehyde)diethylenetriamine), have been synthesized and structurally characterized. Complexes 1-3 possess similar Ln2 cores and differ in substituents at the benzyl rings of benzoates. Direct current (dc) magnetic susceptibility studies in the 2-300 K range showed weak antiferromagnetic interactions between two dysprosium(III) ions in 1-3. The alternating current (ac) magnetic susceptibility measurements indicated that they all exhibited SMM behavior. The strategic attachment of the -NO2 group (in 2) and the -OH functionality (in 3) on the skeleton of the benzoic acid led to subtle variations of the bond lengths and bond angles in the coordination environments of the central dysprosium(III) ions, consequently resulting in the enhancement of the energy barriers for 2 and 3. Complete-active-space self-consistent field (CASSCF) calculations were employed to rationalize the experimental outcomes. Theoretical calculations confirm the existence of antiferromagnetic interactions in 1-3, and the calculated dc magnetic susceptibility data agree well with those obtained experimentally. The computational results reveal more axial g tensors, as well as higher first excited Kramers doublets in 2 and 3; thus resulting in higher energy barriers in compounds 2 and 3.

Multireference Ab Initio Studies of Magnetic Properties of Terbium-Based Single-Molecule Magnets.

We investigate how different chemical environments influence magnetic properties of terbium(III) (Tb)-based single-molecule magnets (SMMs), using first-principles relativistic multireference methods. Recent experiments showed that Tb-based SMMs can have exceptionally large magnetic anisotropy and that they can be used for experimental realization of quantum information applications, with a judicious choice of chemical environment. Here, we perform complete active space self-consistent field calculations including relativistic spin-orbit interaction for representative Tb-based SMMs such as TbPc2 and TbPcNc in three charge states. We calculate the low-energy electronic structure from which we compute the Tb crystal-field (CF) parameters and construct an effective pseudospin Hamiltonian. Our calculations show that the ligand type and fine points of molecular geometry do not affect the gap between the ground-state and first-excited doublets, whereas the latter varies weakly with oxidation number. On the other hand, higher-energy levels have a strong dependence on all these characteristics. For neutral TbPc2 and TbPcNc molecules, the Tb magnetic moment and ligand spin are parallel to each other and the coupling strength between them does not depend much on the ligand type and details of the atomic structure. However, ligand distortion and molecular symmetry play a crucial role in transverse CF parameters which lead to tunnel splitting. The tunnel splitting induces quantum tunneling of magnetization by itself or by combining with other processes. Our results provide insights into the mechanisms of magnetization relaxation in the representative Tb-based SMMs.

Repulsion between Colloidal Particles Mediated by Nonadsorbing Polymers: Lattice Monte Carlo Simulations and the Corresponding Self-Consistent Field Calculations

Using a lattice self-consistent field (SCF) theory and the corresponding lattice Monte Carlo (MC) simulations combined with our recently proposed Z method [Zhang, P.; Wang, Q. Soft Matter 2015, 11,...

Car-Parrinello Monitor for More Robust Born-Oppenheimer Molecular Dynamics.

Born-Oppenheimer molecular dynamics (BOMD) is a promising simulation method for exploring the possible reaction pathways of a chemical system, but one significant challenge is the increased difficulty of converging the self-consistent field (SCF) calculation that often accompanies the breaking and forming of chemical bonds. To address this challenge, we developed an enhancement to the BOMD simulation method called the Car-Parrinello monitor (CPMonitor) that uses Car-Parrinello molecular dynamics (CPMD) to recover from SCF convergence failures. CPMonitor works by detecting SCF convergence failures in BOMD and switching to a CPMD Hamiltonian to propagate through the region of configuration space where the SCF calculation is unable to converge, then switching back to BOMD when good convergence behavior is re-established. We present a series of simulation studies that use CPMonitor, including detailed studies of the thermodynamic and dynamical properties of simple systems, as well as ab initio nanoreactor simulations containing transition metal atoms that were previously not possible to simulate using standard BOMD methods. Our studies show that CPMonitor can make BOMD simulations robust to SCF convergence difficulties and improve simulation performance and stability in reaction discovery applications.

Ab initio study of electronic structure properties of CaAFe4As4 (A = K, Rb and Cs) superconductors

The electronic and magnetic structures of CaAFe4As4 where A = K, Rb, Cs (denoted as Ca-1144) were investigated through the full-potential augmented plane wave method and the generalized gradient approximation. The Self-consistent Field calculations for several magnetic configurations revealed a nonmagnetic to be the ground state of the studied superconductors. A comparison of Density of States, DOS, of the Ca-1144 to those of their parent compounds (Ca, K, Cs and Rb) Fe2As2 (denoted as 122) (in both orthorhombic and tetragonal phase) suggested that the high DOS at Fermi level and the presence of Van Hove singularities in Ca-1144 are not different enough from the 122 compounds to explain the Tc enhancement in the Ca-1144 superconductors. However, there is pronounced dissimilarity in the Electronic Band Structures between the Ca-1144 and 122 materials, namely, the chemical A-doping increases the number of bands crossing EF and forms hole-type pockets around the Γ point as well as electron-type ones at the corners of Brillouin zone. This observed distinction implies a close correlation with the enhanced Tc values. It is worth pointing out that the Fermi surface of the CaCsFe4As4 is found to reminiscence the structure of nodal gap. The Electron Localization Function discloses an anisotropic behaviour and the presence of both valence and metallic bonds in all studied compounds but the weaker covalent bonding is the necessary adjunct to the Tc enlargement in the Ca-1144 superconductors.

On the Origin of Seemingly Nonsurface-Active Particles Partitioning between Phase-Separated Solutions of Incompatible Nonadsorbing Polymers and Their Adsorption at the Phase Boundary.

We have computed the free energy per unit area (i.e., interfacial tension) between a solid surface and two coexisting polymer solutions, where there is no specific interaction between the particles and either polymer, via self-consistent field calculations. Several different systems have been studied, including those where the two polymers differ in molecular weight (Mw) by a factor of ∼2 or where the polymers have the same Mw, but one set of chains is branched with the other linear. In the absence of any enthalpic contribution resulting from adsorption on the solid particle surface, the differences in the free energy per unit area resulting from the polymer-depleted regions around the particles in the two coexisting phases are found to be ∼1 μN m-1. Although this value may seem rather small, this difference is more than capable of inducing the partitioning of particles of 100 nm in size (or larger) into the phase with the lower interfacial free energy at the solid surface. By examining the density profile variation of the polymers close to the surface, we can also infer information about the wettability and contact angle (θ) of solid particles at the interface between the two coexisting phases. This leads to the conclusion that for all systems of this type, when the incompatibility between the two polymers is sufficiently large, θ will be close to 90°.

The red bands of TaH: Identification of the ground and low-lying electronic states

Doppler-limited laser excitation spectra were recorded for 12 bands of the molecule tantalum hydride (TaH) in the red region, covering the wavelengths 605–665 nm. These excitation bands originate from three different lower electronic states. Dispersed fluorescence experiments revealed three additional low-lying electronic states of the molecule. The identities and energies of these six states are found to be in good agreement with the multiconfiguration self-consistent field calculations of Koseki et al. (2004). The ground state is X3Φ2, with the [0.1]0+ state lying only 76 ± 6 cm−1 above it. The upper states display energy shifts caused by numerous local perturbations with other dark states.

Tuning the Magnetization Dynamic Properties of Nd⋅⋅⋅Fe and Nd⋅⋅⋅Co Single-Molecular Magnets by Introducing 3 d-4 f Magnetic Interactions.

By using paramagnetic [Fe(CN)6 ]3- anions in place of diamagnetic [Co(CN)6 ]3- anions, two field-induced mononuclear single-molecular magnets, [Nd(18-crown-6)(H2 O)4 ][Co(CN)6 ]⋅2 H2 O (1) and [Nd(18-crown-6)(H2 O)4 ][Fe(CN)6 ]⋅2 H2 O (2), have been synthesized and characterized. Single-crystal X-ray diffraction analysis revealed that compounds 1 and 2 were ionic complexes. The NdIII ions were located inside the cavities of the 18-crown-6 ligands and were each bound by four water molecules on either side of the crown ether. Magnetic investigations showed that these compounds were both field-induced single-molecular magnets. By comparing the slow relaxation behaviors of compounds 1 and 2, we found significant differences between the direct and Raman processes for these two complexes, with a stronger direct process in compound 2 at low temperatures. Complete active space self-consistent field (CASSCF) calculations were also performed on two [Nd(18-crown-6)(H2 O)4 ]3+ fragments of compounds 1 and 2. Ab initio calculations showed that the magnetic anisotropies of the NdIII centers in complexes 1 and 2 were similar to each other, which indicated that the difference in relaxation behavior was not owing to the magnetic anisotropy of NdIII . Our analysis showed that the magnetic interaction between the NdIII ion and the low-spin FeIII ion in complex 2 played an important role in enhancing the direct process and suppressing the Raman process of the single-molecular magnet.

Active Space Selection Based on Natural Orbital Occupation Numbers from n-Electron Valence Perturbation Theory.

Efficient and robust approximations to the full configuration interaction (full-CI) method such as the density matrix renormalization group (DMRG) and the full-CI quantum Monte Carlo (FCIQMC) algorithm allow for multiconfigurational self-consistent field (MC-SCF) calculations of molecules with many strongly correlated electrons. This opens up the possibility to treat large and complex systems that were previously untractable, but at the same time it calls for an efficient and reliable active space selection as the choice of how many electrons and orbitals enter the active space is critical for any multireference calculation. In this work we propose an Active Space Selection based on 1st order perturbation theory (ASS1ST) that follows a "bottom-up" strategy and utilizes a set of quasi-natural orbitals together with sensible thresholds for their occupation numbers. The required quasi-natural orbitals are generated by diagonalizing the virtual and internal part of the one-electron reduced density matrix that is obtained from strongly contracted n-electron valence perturbation theory (SC-NEVPT) on top of a minimal active space calculation. Self-consistent results can be obtained when the proposed selection scheme is applied iteratively. Initial applications on four chemically relevant benchmark systems indicate the capabilities of ASS1ST. Eventually, the strengths and limitations are critically discussed.

Halide Perovskite-Derived Compounds Rb2TeX6 (X = Cl, Br, and I): Electronic Structure of the Ground and First Excited States.

Herein, we report a study of the electronic structure of the ground and first excited states of Rb2TeCl6, Rb2TeBr6, and Rb2TeI6 halide-perovskite-derived crystals. Using X-ray photoelectron spectroscopy (XPS) measurements and density functional theory and multiconfiguration self-consistent field (MCSCF) calculations, the experimental and theoretical XPS spectra of the valence region were obtained. In addition, the effects of the cations and halogen atoms on the electronic structure were determined, and the classification of the excited states in double point group representation was carried out. Furthermore, a possible reason for the luminescence quenching in an isostructural series of crystals containing the [TeI6]2- anions was determined.

The multiplet electronic structure of UO+ ion: Relativistic two-component ab initio approach

The relativistic two-component ab initio calculations have been carried out to calculate the electronic structure and spectroscopic properties of UO+ ion. The State-Averaged Restricted Active Space Self-Consistent Field (SA-RASSCF) calculations have been performed with spin-orbit effects. The ground state along with a manifold of low-lying spin-orbit states below 12 600 cm−1 have been reported and compared with available results from experiment, Ligand Field Theory (LFT) and previous theoretical results. The configurational assignments along with spectroscopic properties at equilibrium bond distances and also the nature of the potential energy curves have been reported. The ground state Ω = 9/2 at R = 1.790 Å is found to be ionic in nature, U3+(5f3(4I))O2−(1S), with a vibrational frequency of 962 cm−1. The computed excitation energies compare reasonably well with the available experimental counterpart.

Symmetry-Projected Jastrow Mean-Field Wave Function in Variational Monte Carlo.

We extend our low-scaling variational Monte Carlo (VMC) algorithm to optimize the symmetry-projected Jastrow mean-field (SJMF) wave functions. These wave functions consist of a symmetry-projected product of a Jastrow and a general broken-symmetry mean-field reference. Examples include Jastrow antisymmetrized geminal power, Jastrow-Pfaffians, and resonating valence bond states, among others, all of which can be treated with our algorithm. We will demonstrate using benchmark systems including the nitrogen molecule, a chain of hydrogen atoms, and 2-D Hubbard model that a significant amount of correlation can be obtained by optimizing the energy of the SJMF wave function. This can be achieved at a relatively small cost when multiple symmetries including spin, particle number, and complex conjugation are simultaneously broken and projected. We also show that reduced density matrices can be calculated using the optimized wave functions, which allows us to calculate other observables such as correlation functions and will enable us to embed the VMC algorithm in a complete active-space self-consistent field calculation.

Synthesis, Structures, and Single-Molecule Magnetic Properties of Three Dy2 Complexes.

To explore the influences of the subtle structural variations in the ligand backbones on the single-molecule magnetic properties of dinuclear dysprosium(III) complexes, three ligands-H2 L1 (H2 L1 =N1 ,N3 -bis(salicylaldehyde)diethylenetriamine), H2 L2 (H2 L2 =N1 ,N3 -bis(3-methoxysalicylidene)diethylenetriamine), and H2 L3 (H2 L3 =N1 ,N3 -bis(5-chlorosalicyladehyde)diethylenetriamine)-were synthesized and employed to prepare the expected dinuclear dysprosium(III) complexes. The three ligands differ in terms of the substituents at the benzene rings of the salicylaldehyde moieties. The reactions of Dy(NO3 )3 ⋅6 H2 O, pivalic acid, and the ligands H2 L1 , H2 L2 , and H2 L3 generated complexes with the formulae [Dy2 (L1 )2 (piv)2 ] (1), [Dy2 (L2 )2 (piv)2 ] (2), and [Dy2 (L3 )2 (piv)2 ]⋅ 2 MeCN (3), respectively. The purposeful attachment of the functional groups with varied sizes at the benzene rings of the salicylaldehyde backbones resulted in slight differences in the Dy-O-Dy bond angles and the Dy⋅⋅⋅Dy bond lengths in 1-3; consequently, the three complexes exhibited distinct magnetic properties. They all showed slow magnetization relaxation with energy barriers of 40.32 (1), 31.67 (2), and 33.53 K (3). Complete active space self-consistent field (CASSCF) calculations were performed on complexes 1-3 to rationalize the slight discrepancy observed in the magnetic behavior. The calculated results satisfactorily explained the experimental outcomes.

Liquid-liquid phase separation during amphiphilic self-assembly.

The self-assembly of amphiphilic molecules in solution is a ubiquitous process in both natural and synthetic systems. The ability to effectively control the structure and properties of these systems is essential for tuning the quality of their functionality, yet the underlying mechanisms governing the transition from molecules to assemblies have not been fully resolved. Here we describe how amphiphilic self-assembly can be preceded by liquid-liquid phase separation. The assembly of a model block co-polymer system into vesicular structures was probed through a combination of liquid-phase electron microscopy, self-consistent field computations and Gibbs free energy calculations. This analysis shows the formation of polymer-rich liquid droplets that act as a precursor in the bottom-up formation of spherical micelles, which then evolve into vesicles. The liquid-liquid phase separation plays a role in determining the resulting vesicles' structural properties, such as their size and membrane thickness, and the onset of kinetic traps during self-assembly.

How ill-defined constituents produce well-defined nanoparticles: Effect of polymer dispersity on the uniformity of copolymeric micelles

This paper addresses an important question in nanoparticle assembly: whether one needs to use uniform constituents in order to make uniform nanoparticles. Intuitively, one would expect that well-defined batches are necessary to create well-defined assemblies, but the practical laboratory experience is often different. This observation is poorly understood and usually not reported in the final publications. The authors study the problem theoretically, using the example of polymeric nanoparticles made of polydisperse polymers. Their theoretical approach, the self-consistent field (SCF) theory, is well-established and known to be reliable far from critical points. The results show that monodisperse diblock copolymers in solution self assemble to micellar nanoparticles of different sizes, whereas diblock copolymers with moderate dispersity self-assemble to micellar nanoparticles of nearly uniform size. Based on the SCF calculations, the authors can analyze the reasons for this unexpected behavior. Their findings send out a clear message to the scientific community: monodisperse constituents will not necessarily produce monodisperse nanoparticles. Based on the presented calculations it is likely that monodisperse polymers are by no means a requirement for the synthesis of monodisperse micellar nanoparticles; in fact, such systems result in more polydisperse micellar nanoparticles.