Self-consistent Field Calculations Research Articles

Cluster-Weighting in Bulk Phase Vibrational Circular Dichroism.

We present a cluster-weighting approach for calculating the vibrational circular dichroism (VCD) spectra of bulk phase systems. Based on the quantum cluster equilibrium theory, cluster populations are received via self-consistent field calculations that allow a mixing of differently sized oligomers at the same time. The thereby obtained cluster weights are employed for the weighting of individual cluster VCD spectra in order to calculate an overall gas or bulk phase VCD spectrum. As the mixing of different oligomer sizes is possible, different structural motifs and interactions can be included, and explicit solvation, typically necessary for describing hydrogen bonds, is intrinsically taken care of, however, without neglecting monomeric structures and different conformers. We test the sensitivity of Boltzmann and cluster weights with respect to the level of theory employed and show that cluster weights are less sensitive. By a constant increase of the oligomer sizes included in our cluster sets, combined with a continuous truncation of low populated clusters, we are able to improve the agreement between theory and experiment until we reach an overlap which allows a certain assignment of the absolute configuration based on an experimental bulk phase spectrum. Combined with a computationally cost-efficient level of theory, this approach provides a valuable tool for the fast calculation of VCD spectra for bulk phase systems.

Model Dimeric Manganese(IV) Complexes Featuring Terminal Tris-hydroxotetraazaadamantane and Various Bridging Ligands.

A series of model dinuclear manganese(IV) complexes of the general formula [(H3COH)(L')MnIV(μ-L)2MnIV(L')(HOCH3)] is presented. These compounds feature capping 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands derived from a polydentate oxime compound (L'). The bridging ligands L include azide (1), methoxide (2), and oxalate (3) anions. The magnetic properties and high-field (HF) EPR spectra of 1-3 were studied in detail and revealed varying weak antiferromagnetic coupling and modest zero-field splitting (ZFS) of the local quartet spin sites. Our HF EPR studies provide insight into the dimer ZFS, including determination of the corresponding parameters by giant spin approach for methoxido-bridged complex 2. Furthermore, the physicochemical properties of 1-3 were studied using IR, UV-vis, and electrochemical (cyclic voltammetry) methods. Theoretical exchange coupling constants were obtained using broken-symmetry (BS) density functional theory (DFT). Computational estimates of the local quartet ground spins state ZFSs of 1-3 were obtained using coupled-perturbed (CP) DFT and complete active space self-consistent field (CASSCF) calculations with n-electron valence state perturbation theory (NEVPT2) corrections. We found that the CP DFT calculations which used the B3LYP functional and models derived experimental structures performed best in reproducing both the magnitude and the sign of the experimental D values. Moreover, our computational investigation of 1-3 suggests that we observe metals sites which have an increased +3 character and are supported by redox noninnocent 4,6,10-trihydroxo-3,5,7-trimethyl-1,4,6,10-tetraazaadamantane ligands. The latter conclusion is further corroborated by the observation that the free ligand can be readily oxidized to yield a NO-based radical.

An approximation strategy to compute accurate initial density matrices for repeated self-consistent field calculations at different geometries

ABSTRACT Repeated computations on the same molecular system, but with different geometries, are often performed in quantum chemistry, for instance, in ab-initio molecular dynamics simulations or geometry optimisations. While many efficient strategies exist to provide a good guess for the self-consistent field procedure, little is known on how to efficiently exploit the abundance of information generated during the many computations. In this article, we present a strategy to provide an accurate initial guess for the density matrix, expanded in a set of localised basis functions, within the self-consistent field iterations for parametrised Hartree–Fock problems where the nuclear coordinates are changed along with a few user-specified collective variables, such as the molecule's normal modes. Our approach is based on an offline-stage where the Hartree–Fock eigenvalue problem is solved for some particular parameter values and an online-stage where the initial guess is computed very efficiently for any new parameter value. The method allows nonlinear approximations of density matrices, which belong to a non-linear manifold that is isomorphic to the Grassmann manifold, by mapping such a manifold onto the tangent space. Numerical tests on different amino acids show promising initial results.

PWDFT.jl: A Julia package for electronic structure calculation using density functional theory and plane wave basis

We describe the implementation of PWDFT.jl, a package for electronic structure calculations written in Julia programming language using plane wave basis set and pseudopotentials. In this package, a typical Kohn–Sham density functional theory (KSDFT) is divided into three steps: initializing the molecular or crystalline structure, constructing the Kohn–Sham Hamiltonian, and solving the Kohn–Sham problem using self-consistent field (SCF) calculation. To facilitate various tasks involved in these steps, we provide several custom data types which are transparent and easy to be modified. Basic operations such as wave function orthogonalization, action of kinetic and potential operators to wave functions and iterative diagonalization of Hamiltonian have been implemented in pure Julia. Several algorithms to solve the Kohn–Sham problems such as self-consistent field and direct energy minimization have also been implemented in PWDFT.jl. To assess the validity of our implementation, we present the results of total energy calculations against the well-established ABINIT package. We also show how one can use PWDFT.jl to write a simple self-consistent field implementation. Program summaryProgram Title:PWDFT.jlCPC Library link to program files:http://dx.doi.org/10.17632/b87xzmzm2z.1Licensing provisions: GPL-v2Programming language: JuliaNature of problem: Electronic structure of interacting electrons in materialSolution method: Kohn–Sham density functional theory, using plane wave basis set and pseudopotentialsAdditional comments including restrictions and unusual features: Due to the precompilation step, the program may appear to be slow at the first call. Parallelization is not yet considered.

PairDiag: An exact diagonalization program for solving general pairing Hamiltonians

We present a program for solving exactly the general pairing Hamiltonian based on diagonalization. The program generates the seniority-zero shell-model-like basis vectors via the ‘01’ inversion algorithm. The Hamiltonian matrix is constructed in this seniority-zero space. The program evaluates all non-zero elements of the Hamiltonian matrix “on the fly” using the scattering operator and a search algorithm. The matrix is diagonalized by using the iterative Lanczos algorithm. The OpenMP parallel program thus developed, PairDiag, can efficiently calculate the ground-state eigenvalue and eigenvector of the general pairing Hamiltonian for both the even-mass and the odd-mass system. The program is packaged in a Fortran module, which makes it easy to use the program to replace the BCS approximation in standard self-consistent mean field calculations. For systems with dimension around 108, the calculation can be done within hours on standard desktop computers. Program summaryProgram Title: PairDiag.Program Files doi:https://doi.org/10.17632/dzzspfszsh.1Licensing provisions: CC by NC 3.0.Programming language: Fortran 95.Nature of problem: The numerically exact solution of general pairing Hamiltonian can be solved by diagonalization in configuration spaces of fixed seniority.Solution method: The program constructs the seniority-zero space by the ‘01’ inversion algorithm, and diagonalizes the general pairing Hamiltonian by the Lanczos plus QR algorithm.Restrictions: The total number of orbits involved must be less than 63, and the dimension that can be calculated is restricted by the local RAM condition.

Complete active space analysis of a reaction pathway: Investigation of the oxygen-oxygen bond formation.

Water nucleophilic attack is an important step in water oxidation reactions, which have been widely studied using density functional theory (DFT). Nevertheless, a single-determinant DFT picture may be insufficient for a deeper insight into the process, in particular during the oxygen-oxygen bond formation. In this work, we use complete active space self-consistent field calculations and describe an approach for a complete active space analysis along a reaction pathway. This is applied to the water nucleophilic attack at a Ru-based catalyst, which has successfully been used for efficient water oxidation and in silico design of new water oxidation catalysts recently.

Polarized Gaussian basis sets from one-electron ions.

We demonstrate that basis sets suitable for electronic structure calculations can be obtained from simple accuracy considerations for the hydrogenic one-electron ions Y(Y-1)+ for Y ∈ [1, Z], necessitating no self-consistent field calculations at all. It is shown that even-tempered basis sets with parameters from the commonly used universal Gaussian basis set (UGBS) [E. V. R. de Castro and F. E. Jorge, J. Chem. Phys. 108, 5225 (1998)] reproduce non-relativistic spin-restricted spherical Hartree-Fock total energies from fully numerical calculations to better accuracy than UGBS, which is shown to exhibit huge errors for some elements, e.g., 0.19 Eh for Th+ and 0.13 Eh for Lu, as it has been parameterized for a single atomic configuration. Having shown the feasibility of the one-electron approach, partially energy-optimized basis sets are formed for all atoms in the Periodic Table, 1 ≤ Z ≤ 118, by optimizing the even-tempered parameters for Z(Z-1)+. As the hydrogenic Gaussian basis sets suggested in this work are built strictly from first principles, polarization shells can also be obtained in the same fashion in contrast to previous approaches. The accuracy of the polarized basis sets is demonstrated by calculations on a small set of molecules by comparison to fully numerical reference values, which show that chemical accuracy can be reached even for challenging cases such as SF6. This approach is straightforward to extend to relativistic calculations and could facilitate studies beyond the established Periodic Table.

Divergent Adsorption-Dependent Luminescence of Amino-Functionalized Lanthanide Metal-Organic Frameworks for Highly Sensitive NO2 Sensors.

A novel gas sensing mechanism exploiting lanthanide luminescence modulation upon NO2 adsorption is demonstrated here. Two isostructural lanthanide-based metal-organic frameworks (MOFs) are used, including an amino group as the sensitive recognition center for NO2 molecules. The transfer of energy from the organic ligands to Ln is strongly dependent on the presence of NO2, resulting in an unprecedented photoluminescent sensing scheme. Thereby, NO2 exposition triggers either a reversible enhancement or a decrease in the luminescence intensity, depending on the lanthanide ion (Eu or Tb). Our experimental studies combined with density functional theory and complete active space self-consistent field calculations provide an understanding of the nature and effects of NO2 interactions within the MOFs and the signal transduction mechanism.

Self-Consistent Mean Field Calculations of Polyelectrolyte-Surfactant Mixtures in Solution and upon Adsorption onto Negatively Charged Surfaces.

Self-Consistent Mean-Field Calculations (SCF) have provided a semi-quantitative description of the physico-chemical behavior of six different polyelectrolyte-surfactant mixtures. The SCF calculations performed showed that both the formation of polymer-surfactant in bulk and the adsorption of the formed complexes onto negatively-charged surfaces are strongly affected by the specific nature of the considered systems, with the polymer-surfactant interactions playing a central role in the self-assembly of the complexes that, in turn, affects their adsorption onto interfaces and surfaces. This work evidences that SCF calculations are a valuable tool for deepening on the understanding of the complex physico-chemical behavior of polyelectrolyte-surfactant mixtures. However, it is worth noting that the framework obtained on the basis of an SCF approach considered an equilibrium situation which may, in some cases, be far from the real situation appearing in polyelectrolyte-surfactant systems.

An Overview of Self-Consistent Field Calculations Within Finite Basis Sets.

A uniform derivation of the self-consistent field equations in a finite basis set is presented. Both restricted and unrestricted Hartree–Fock (HF) theory as well as various density functional approximations are considered. The unitary invariance of the HF and density functional models is discussed, paving the way for the use of localized molecular orbitals. The self-consistent field equations are derived in a non-orthogonal basis set, and their solution is discussed also in the presence of linear dependencies in the basis. It is argued why iterative diagonalization of the Kohn–Sham–Fock matrix leads to the minimization of the total energy. Alternative methods for the solution of the self-consistent field equations via direct minimization as well as stability analysis are briefly discussed. Explicit expressions are given for the contributions to the Kohn–Sham–Fock matrix up to meta-GGA functionals. Range-separated hybrids and non-local correlation functionals are summarily reviewed.

Photolysis of 5-Azido-3-Phenylisoxazole at Cryogenic Temperature: Formation and Direct Detection of a Nitrosoalkene.

To enhance the versatility of organic azides in organic synthesis, a better understanding of their photochemistry is required. Herein, the photoreactivity of azidoisoxazole 1 was characterized in cryogenic matrices with IR and UV-Vis absorption spectroscopy. The irradiation (λ = 254 nm) of azidoisoxazole 1 in an argon matrix at 13 K and in glassy 2-methyltetrahydrofuran (mTHF) at 77 K yielded nitrosoalkene 3. Density functional theory (DFT) and complete active space self-consistent field (CASSCF) calculations were used to aid the characterization of nitrosoalkene 3 and to support the proposed mechanism for its formation. It is likely that nitrosoalkene 3 is formed from the singlet excited state of azidoisoxazole 1 via a concerted mechanism or from cleavage of an intermediate singlet nitrene that does not undergo efficient intersystem crossing to its triplet configuration.

Theoretical Study of Iron Porphyrin Nitrene: Formation Mechanism, Electronic Nature, and Intermolecular C-H Amination.

The formation mechanism and electronic structures of iron porphyrin nitrene intermediates, as well as the nitrene-mediated intermolecular C-H amination, have been studied by performing DFT and ab initio complete active space self-consistent field (CASSCF) calculations. Compared with that of cobalt porphyrin nitrene and iron porphyrin carbene, the formation of iron porphyrin nitrene shows similar but different characteristics. The common feature is that all their formation is required to undergo the "far" or "close" complexes, but these complexes correspond to different energies relative to their respective reactants (isolated metalloporphyrins and azides), which is considered as one main reason to determine the reaction barriers. The overall free energy barrier for the formation of iron porphyrin nitrene was calculated to be 10.6 kcal/mol on a triplet-state surface, which is lower than those of cobalt porphyrin nitrene and iron porphyrin carbene. The departure of N2 from the close complexes formed by iron porphyrin and tosyl azide is nearly barrierless. For iron porphyrin nitrene, both CASSCF and unrestricted DFT calculations revealed that the triplet and open-shell singlet complexes correspond to very similar energies. The triplet nitrene complex can be described as [(por)(-OCH3)FeII═NTs]- ↔ [(por)(-OCH3)FeIII═N•-Ts]- ↔ [(por)(-OCH3)FeIV═N2-Ts]-, while the oss nitrene complex can be described as [(por)(-OCH3)FeIII-N•-Ts]-. Since the N atom bears a similar spin density as in cobalt porphyrin nitrene, the iron porphyrin nitrene exhibits similar activity in hydrogen abstraction. In addition, the intermolecular C-H amination catalyzed by iron porphyrin nitrene follows the hydrogen atom abstraction/radical recombination mechanism with a free energy barrier of 7.1 kcal/mol on the triplet-state surface. In general, the medium reactivity and easily prepared characteristic of iron porphyrin nitrene makes it a potential catalyst for C-H amination.

Lattice self-consistent field calculations of confined symmetric block copolymers of various chain architectures.

The effects of chain architecture and confinement on the structure and orientation of lamellae formed by incompressible and symmetric AB-type block copolymer melts confined between two parallel and identical surfaces are investigated using self-consistent field calculations on a simple cubic lattice. Five systems of various chain architectures (linear, ring, and star) and lengths are studied, with their bulk lamellar period L0 chosen such that they have comparable L0/Rg, where Rg denotes the ideal-chain radius of gyration. For thin films of thickness D = L0 confined between two neutral surfaces, we define the rescaled volume fraction profiles of A, B, chain end, and joint segments in the parallel and perpendicular lamellae such that these profiles can be directly compared among the five systems to quantitatively reveal the interplay between the chain-end enrichment near confining surfaces and the surface-induced A-B compatibilization, and how such interplay is affected by the chain architectures (for example, the chain-crowding effects in the star block copolymers). The effects of D and surface preference for one of the blocks are also investigated.

Dual responsive PMEEECL-PAE block copolymers: a computational self-assembly and doxorubicin uptake study.

The self-assembly behaviour of dual-responsive block copolymers and their ability to solubilize the anticancer drug doxorubicin (DOX) has been investigated using all-atom molecular dynamics (MD) simulations, MARTINI coarse-grained (CG) force field simulation and Scheutjens–Fleer self-consistent field (SCF) computations. These diblock copolymers, composed of poly{γ-2-[2-(2-methoxyethoxy)ethoxy]ethoxy-ε-caprolactone} (PMEEECL) and poly(β-amino ester) (PAE) are dual-responsive: the PMEEECL block is thermoresponsive (becomes insoluble above a certain temperature), while the PAE block is pH-responsive (becomes soluble below a certain pH). Three MEEECL20–AEM compositions with M = 5, 10, and 15, have been studied. All-atom MD simulations have been performed to calculate the coil-to-globule transition temperature (Tcg) of these copolymers and finding appropriate CG mapping for both PMEEECL–PAE and DOX. The output of the MARTINI CG simulations is in agreement with SCF predictions. The results show that DOX is solubilized with high efficiency (75–80%) at different concentrations inside the PMEEECL–PAE micelles, although, interestingly, the loading efficiency is reduced by increasing the drug concentration. The non-bonded interaction energy and the RDF between DOX and water beads confirm this result. Finally, MD simulations and SCF computations reveal that the responsive behaviour of PMEEECL–PAE self-assembled structures take place at temperature and pH ranges appropriate for drug delivery.

Elucidating the multi-configurational character of the firefly dioxetanone anion and its prototypes in the biradical region using full valence active spaces.

We analyzed the near-degenerate states of the firefly dioxetanone anion (FDO-) and its prototypes, especially in the biradical region, using multi-configurational approaches. The importance of utilizing full valence active spaces by means of density-matrix renormalization group self-consistent field (DMRG-SCF) calculations was described. Our results revealed that the neglect of some valence orbitals can affect the quantitative accuracy in later multi-reference calculations or the qualitative conclusion when optimizing conical intersections. Using all of the relevant valence orbitals of FDO-, we confirmed that there were two conical intersections, as reported in previous work, and that the intersecting states were changed when the active space was enlarged. Beyond these, we found that there were strong interactions between states in the biradical regions, in which the changes in entanglements can be used to visualize the interacting state evolution.

Cyclic (alkyl)(amino)carbenes in organic and organometallic methane C-H activation: a DFT and MCSCF study.

Density functional theory (DFT) and multi-configurational self-consistent field (MCSCF) calculations are used to investigate the electronic and steric properties of cyclic (alkyl)(amino)carbenes (CAACs). Calculations show CAACs' diverse electronic characteristics in terms of its donor and acceptor capabilities. Reactions of CAACs in methane C-H bond activation via insertion and also as a supporting ligand (L) for L(Cp)M (M = Co, Rh, Ir) motifs via C-H oxidative addition are studied. The binding energies and buried volumes are calculated for selected CAACs as ancillary ligands to the L(Cp)Rh motif. Overall, CAACs show highly tunable electronic and steric properties by adjusting their substituents and backbones. Although CAAC may not be viable in activating inert small molecules with low polarity like methane, this class of ligand has great potential as ancillary ligands for transition metal complexes in catalysis. Calculation of C-H activation by L(Cp)Ir and L(Cp)Rh with CAACs as supporting ligands show CAACs can render the reaction more amenable to catalysis by destabilizing the oxidative addition products while keeping the reaction mildly exergonic, and the barriers reasonable.

Brushes and lamellar mesophases of comb-shaped (co)polymers: a self-consistent field theory.

Theory describing equilibrium structural properties of solvent-free brushes formed by comblike polymers tethered by end segment of backbone to planar surface is developed using strong-stretching self-consistent field (SS-SCF) analytical approach and supported by numerical self-consistent field calculations based on the Scheutjens-Fleer (SF-SCF) method. The explicit dependence of self-consistent molecular potential on architectural parameters of comblike polymers is analyzed. It is demonstrated that distribution of local tension in backbones of long comblike polymers approaches that for linear chains. The star-to-comblike transition in solvent-free lamellas which occurs upon increase of backbone length of graft-polymer is analyzed.

Short-time dynamics and decay mechanism of E,E-2,4-hexadienal in the first light-absorbing S2(ππ*) state.

The initial nonadiabatic decay dynamics of E,E-2,4-hexadienal (HAL) in the light absorbing S2(ππ*) state were studied using resonance Raman spectroscopy and complete-active space self-consistent field (CASSCF) calculations. The UV and vibrational spectra were assigned on the basis of the UV absorption, Fourier transform (FT)-Raman and FT-infrared measurements, the density-functional theory computations, and the normal mode analysis. The A-band resonance Raman spectra in cyclohexane and acetonitrile were obtained at 282.4, 273.9, 266.0, 252.7, and 245.9 nm excitation wavelengths, respectively, to probe the corresponding structural dynamics of HAL. The A-band absorption cross section and the corresponding absolute resonance Raman cross sections were simulated using a simple model based on the time-dependent wave-packet theory in a Brownian oscillator model. The geometric structures of the singlet electronic excited states and their curve-crossing points were optimized at the CASSCF level of theory. The obtained short-time structural dynamics in easy-to-visualize internal coordinates were then compared with the CASSCF-predicted structural-parameter changes of S2(ππ*)S1(nπ*)-n (n = 1-4). Our results indicate that the initial population of HAL in the S2 state ramifies in or nearby the Franck-Condon (FC) region, leading to five S2(ππ*) → S1(nπ*) internal conversion pathways due to the flexibility of the molecular chain and the different electronic resonant structures formed nearby FC of the S2 state. Then, the formed S1 transient species, which have different geometric structures and different energy partitions, undergo different photophysical processes, such as S1 → S0 internal conversion, S1 → T1 intersystem crossing, and the S1 → S'1 photoisomerization reaction. The substitution effect on the S2(ππ*) → S1(nπ*) internal conversion dynamics and the trans-cis photoisomerization reaction is proposed in terms of the p-π conjugation interaction or the p-σ superconjugation interaction.

The interplay of VSCF/VCI calculations and matrix-isolation IR spectroscopy – Mid infrared spectrum of CH3CH2F and CD3CD2F

We present the first matrix-isolation infrared (MI-IR) spectra of CH3CH2F and its isotopologue CD3CD2F in Neon and Argon matrix, together with new gas-phase IR spectra. Extensive vibrational self-consistent field and configuration interaction (VSCF/VCI) calculations are performed, based on an ab initio potential energy surface at ae-CCSD(T)-F12a/cc-pCVTZ-F12 level of electronic structure theory. We encounter an excellent agreement between VCI calculated transitions and the experimental MI-IR and gas-phase IR spectra. Mean absolute deviations are scattering between 1 and 4 cm−1. The interplay of accurate vibrational structure calculations and high-resolution infrared experiments enables unprecedented insights in the CH respectively CD stretch region, providing the first rigorous assignment of the energetically very close ν1,ν12 and ν13 fundamental transitions.

Novel implementation of seniority number truncated valence bond methods with applications to H22 chain.

Both the efficiency and capability of the seniority number truncated valence bond (VB) methods are highly improved by using our recently proposed extension of Malmqvist's algorithm for the reciprocal transformation of many-electron bases constructed by nonorthogonal orbitals [Zhou, Chen, and Wu, J. Chem. Phys. 149(4), 044111 (2018)] and by the adoption of the direct technique in solving the generalized eigenvalue problem. Due to the compactness of the wave function that benefited from seniority number restriction, the memory need and computational cost for energy evaluation and orbital optimization in valence bond self-consistent field calculation are largely reduced. The last obstacle in nonorthogonal orbital based ab initio VB calculation is thus removed. Consequently, we can accomplish seniority number truncated VB calculation at the same computational scaling as that of the most general configuration selected multiconfigurational self-consistent field with a memory cost much less than the corresponding complete active space self-consistent field (CASSCF). Test on Hn string molecules shows that the seniority number truncated VB calculation maintains the majority of static correlation by using a more compact wave function than CASSCF.