Aza-crown ether structures have been proven to be effective in constructing fluorescent biosensors for selectively detecting and imaging alkali metal ions in biological environments. However, choosing the right aza-crown ether for a specific alkali metal ion remains challenging for synthetic chemists because theoretical guidance on the chelating activities between aza-crown ethers and alkali metal ions has not been available up to now. Predicting the physical properties of the chelator-metal complexations poses a greater challenge due to the numerous quantum mechanical functionals and basis sets to be used in any theoretical investigation. In this study, we report a theoretical investigation of different aza-crown ether structures and their selectivities to alkali metal ions via a novel relationship between the binding energy and charge transfer calculated using twelve different quantum mechanical methods, using a myriad of bases, within the Jacob's Ladder of Chemical Accuracies. Furthermore, this report represents a guide for the synthetic chemist in the selection of aza-crown ethers in the capturing of specific alkali metal ions, primary objectives, while benchmarking different quantum mechanical calculations, as a secondary objective.

The in-medium similarity renormalization group (IMSRG) approach, based on a continuous unitary transformation, has been applied to closed-shell atoms. The flow equation, which is derived for the Hamiltonian, has been solved along with imaginary-time or White generators using the fourth-order Runge-Kutta and Magnus expansion methods. The behavior of the flow as a function of step size was investigated carefully. Our findings for ground state energy for the He $$ \mathrm{He} $$ and Ne $$ \mathrm{Ne} $$ atoms from the IMSRG calculation are close to those obtained with full configuration interaction. Moreover, it has been observed that the IMSRG calculation based on the Magnus expansion approach, coupled with the White generator, requires the fewest steps to converge.

Current challenges in bone regeneration and design of humanoid 3D bone metastases cancer testbeds can be overcome by designing bone-mimetic tissue engineering scaffolds with tunable mechanical and biological properties. This study employs three unnatural amino acids to modify montmorillonite clay (MMT), producing polymer clay nanocomposites (PCNs) to construct 3D bone-mimetic scaffolds. The modification of MMT clay with 5-aminovaleric acid, (+/-)-2-aminopimelic acid, and 4-(4-Aminophenyl) butyric acid is analyzed through xray diffraction (XRD) and fourier-transform infrared spectroscopy (FTIR), revealing changes in the interlayer spacing and functional groups. Molecular modeling elucidates the interaction energies in the amino acid intercalated nanoclays that influence the mechanical properties of the scaffolds. 4-(4-Aminophenyl) butyric acidmodified scaffolds exhibited the highest compressive strength, highlighting the critical influence of molecular interactions on the mechanical properties of the PCN. Despite being a small fraction of the scaffold, the presence and type of amino acids significantly affect the scaffold mechanical properties. Cell viability assays affirm biocompatibility of scaffolds. The amino acids within the nanoclays also impact mineralization on scaffolds seeded with human mesenchymal stem cells (hMSCs). Amino acid type also influences the amount of mineralization in the scaffolds. A sequential culture involving hMSCs and breast cancer cells (MCF-7) on the scaffold mimics breast cancer metastasis to bone. Enhanced mineralization by bone cells in the presence of MCF-7 cells is observed, emphasizing their osteoblastic characteristics. Hence, 3D scaffolds for bone regeneration and bone metastasis cancer testbeds can exhibit tunable mechanical properties and biological responses though a simulation guided choice of unnatural amino acids.

Potential energy curves (PECs) were calculated for 21 and 18 electronic states of NdO and NdS molecules, respectively. In each case, static electron correlation effects were described by incomplete model space multiconfiguration self-consistent field wave functions based on an active space that included the most important valence orbitals. Dynamic electron correlation was included by the multireference second-order generalized Van Vleck perturbation theory method. Scalar-relativistic contributions were included by the effective core potential approach, using def2-TZVPP basis sets. Spin-dependent relativistic corrections were determined to be small and negligible for the Nd atom and so were not included in the calculations. The 21 and 18 electronic states of NdO and NdS were predicted to be in the excitation energy range of similar to 3.2 and similar to 2.7 eV, respectively. The ground electronic states of NdO and NdS were determined as 1(5)H (6s4f(sigma)4f(phi)4f(delta)) and 1(5)H (4f(phi)4f(pi)4f(pi)6s), with spectroscopic constants: bond length R-e = 1.780 and 2.325 & Aring;, and harmonic frequency omega(e) = 891 and 538 cm(-1), respectively.

Most computational studies of biologically relevant systems have used Molecular Mechanics (MM). While MM is generally reliable for many applications, chemical reactions and bond formations/breakage are not describable in MM. In contrast, Quantum Mechanics (QM) is an approach that utilizes wave functions and/or electron density functions for property and structural analyses and hence does not suffer from such limitations. QM methods can be classified into two main frameworks, ab initio and semi-empirical. Semi-empirical methods utilize experimental or ab initio results to make additional approximations, thereby using a combination of some ab initio calculations and fitted experimental data. Despite the accuracy and general applicability of QM, the major disadvantages are limitations due to the system size. Not surprisingly, hybrid methods that partition the problem at hand into subsystems have been developed. Some of these methods mix QM with MM, and others are strictly QM, but limit the range of interactions. As a result, there exists a plethora of methods, some with fanatical followers, with the result that researchers are often faced with bewildering choices.This review, perhaps more accurately described as a mini-review or perspective, examines recent calculations on biologically relevant (including biomimetic molecules) in which QM is necessary, to a greater or lesser degree, to obtain results that are consistent with the experiment. The review is not an exposition on the theoretical foundations of different methods, but rather a practical guide for the researcher with an interest in using computational methods to produce biologically, or at least biochemically, useful results. Because of our own specific interests, the Arg-Gly-Asp sequence, or so-called RGD, figures prominently in the work, in terms of size, including oligomers of RGD, and strengths of interactions. A key feature of RGD is its role in the binding of cells to the Extra Cellular Matrix (ECM) depending on the cell type and receptor protein on the cell itself. The ECM is comprised of spectra of biological compounds such as proteoglycans and fibrous proteins; RGD is located and found as a motif on these fibrous proteins. The cell bindings to the ECM are done via integrin-RGD binding. Because metal interactions and hydrogen bonding significantly affect integrin-RGD binding, theoretical methodology beyond MM is needed. IntegrinRGD binding affects the adhesion and movement of cells along the ECM. Hence, these interactions are highly relevant to understanding the spread of cancer in an organism.

The importance of localized molecular orbitals (MOs) in correlation treatments beyond mean-field calculation and in the illustration of chemical bonding (and antibonding) can hardly be overstated. However, the generation of orthonormal localized occupied MOs is significantly more straightforward than obtaining orthonormal localized virtual MOs. Orthonormal MOs allow facile use of highly efficient group theoretical methods (e.g., graphical unitary group approach) for calculation of Hamiltonian matrix elements in multireference configuration interaction calculations (such as MRCISD) and in quasi-degenerate perturbation treatments, such as the Generalized Van Vleck Perturbation Theory. Moreover, localized MOs can elucidate qualitative understanding of bonding in molecules, in addition to high-accuracy quantitative descriptions. We adopt the powers of the fourth moment cost function introduced by Jørgensen and coworkers. Because the fourth moment cost functions are prone to having multiple negative Hessian eigenvalues when starting from easily available canonical (or near-canonical) MOs, standard optimization algorithms can fail to obtain the orbitals of the virtual or partially occupied spaces. To overcome this drawback, we applied a trust region algorithm on an orthonormal Riemannian manifold with an approximate retraction from the tangent space built into the first and second derivatives of the cost function. Moreover, the Riemannian trust region outer iterations were coupled to truncated Conjugate Gradient inner loops, which avoided any costly solutions of simultaneous linear equations or eigenvector/eigenvalue solutions. Numerical examples are provided on model systems, including the high-connectivity H10 set in 1-, 2-, and 3-dimensional arrangements, and on a chemically realistic description of cyclobutadiene (c-C4H4) and the propargyl radical (C3H3). In addition to demonstrating the algorithm on occupied and virtual blocks of orbitals, the method is also shown to work on the active space at the MCSCF level of theory.

We investigated the interaction between biomimetic Fe and Mg co-doped montmorillonite nanoclay and eleven unnatural amino acids. Employing three different functionals (PBE-GGA, PBE-GGA + U, and HSE06), we examined the clay's structural, electronic, and magnetic properties. Our results revealed the necessity of using PBE-GGA + U with U ≥ 4 eV to accurately describe key clay properties. We identified amino acids that strongly interacted with the clay surface, with steric orientation playing a crucial role in facilitating binding. Our DFT calculations highlighted significant electrostatic interactions between the amino acids and the clay slab, with the amino group's predominant role in this interaction. These findings hold promise for designing amino acids for clay-amino acid systems, leading to innovative bio-material composites for various applications. Additionally, our ab-initio molecular dynamics simulations confirmed the stability of clay-amino acid systems under ambient conditions, and the introduction of an implicit water solvent enhanced the binding energy of amino acids on the clay surface.

The generalized Van Vleck second order multireference perturbation theory (GVVPT2) method was used to investigate the low-lying electronic states of Ni2. Because the nickel atom has an excitation energy of only 0.025 eV to its first excited state (the least in the first row of transition elements), Ni2 has a particularly large number of low-lying states. Full potential energy curves (PECs) of more than a dozen low-lying electronic states of Ni2, resulting from the atomic combinations 3F4 + 3F4 and 3D3 + 3D3, were computed. In agreement with previous theoretical studies, we found the lowest lying states of Ni2 to correlate with the 3D3 + 3D3 dissociation limit, and the holes in the d-subshells were in the subspace of delta orbitals (i.e., the so-dubbed δδ-states). In particular, the ground state was determined as X 1Γg and had spectroscopic constants: bond length (Re) = 2.26 Å, harmonic frequency (ωe) = 276.0 cm−1, and binding energy (De) = 1.75 eV; whereas the 1 1Σg+ excited state (with spectroscopic constants: Re = 2.26 Å, ωe = 276.8 cm−1, and De = 1.75) of the 3D3 + 3D3 dissociation channel lay at only 16.4 cm−1 (0.002 eV) above the ground state at the equilibrium geometry. Inclusion of scalar relativistic effects through the spin-free exact two component (sf-X2C) method reduced the bond lengths of both of these two states to 2.20 Å, and increased their binding energies to 1.95 eV and harmonic frequencies to 296.0 cm−1 for X 1Γg and 297.0 cm−1 for 1 1Σg+. These values are in good agreement with experimental values of Re = 2.1545 ± 0.0004 Å, ωe = 280 ± 20 cm−1, and D0 = 2.042 ± 0.002 eV for the ground state. All states considered within the 3F4 + 3F4 dissociation channel proved to be energetically high-lying and van der Waals-like in nature. In contrast to most previous theoretical studies of Ni2, full PECs of all considered electronic states of the molecule were produced.

The propargyl radical, the most stable isomer of neutral C3H3, is important in combustion reactions, and a number of spectroscopic and reaction dynamics studies have been performed over the years. However, theoretical calculations have never been able to find a state that can generate strong absorption around 242 nm as seen in experiments. In this study, we calculated the low-lying electronic energy levels of the propargyl radical using the highly accurate multireference configuration interaction singles and doubles method with triples and quadruples treated perturbatively [denoted as MRCISD(TQ)]. Calculations indicate that this absorption can be attributed to a Franck-Condon-allowed electronic transition from the ground 2B1 state to the Rydberg-like excited state 12A1. Further insight into the behavior of the multireference perturbative theory methods, GVVPT2 and GVVPT3, on a very challenging system are also obtained.

The efficiency of the recently proposed iCIPT2 [iterative configuration interaction (iCI) with selection and second-order perturbation theory (PT2); J. Chem. Theory Comput. 2020, 16, 2296] for strongly correlated electrons is further enhanced (by up to 20×) by using (1) a new ranking criterion for configuration selection, (2) a new particle-hole algorithm for Hamiltonian construction over randomly selected configuration state functions (CSF), and (3) a new data structure for the quick sorting of the variational and first-order interaction spaces. Meanwhile, the memory requirement is also significantly reduced. As a result, this improved implementation of iCIPT2 can handle 1 order of magnitude more CSFs than the previous version, as revealed by taking the chromium dimer and an iron-sulfur cluster, [Fe2S2(SCH3)]42-, as examples.

Algorithms, and pilot implementations, of multi-CPU parallel versions of the second-order Generalized Van Vleck Perturbation Theory method for molecular electronic structure (GVVPT2) and of the perturbatively corrected multireference configuration interaction method including single and double electron replacements [nR-MRCISD(TQ)] are presented and analyzed. It is shown that a cornerstone of the organization of the original, serial methods, macroconfigurations, is also effective for organizing parallel versions. In fact, the use of macroconfigurations, and specifically pairs of macroconfigurations between interacting subspaces, suggests a natural framework that allows optimization of the parallel algorithms. As with the earlier serial versions, a graphical implementation of orbital configurations, which in turn allows efficient use of unitary group approach coupling coefficients, runs below organization at the macroconfiguration level. Consequently, resulting wave functions are rigorously spin adapted, and spatial symmetry has also been implemented at the level of Abelian point groups. Numerical results are presented and analyzed for illumination of future directions for improvement. The parallelization scheme is oriented to departmental and university class computer clusters (or supercomputers) and is expected to facilitate the effective use of GVVPT2 for many molecules of interest to computational chemistry, and shows that the highly accurate nR-MRCISD(TQ) can now be considered as available for investigating problematic molecules outside the applicability of more commonly available methods.

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground-state energy of the benzene molecule in a standard correlation-consistent basis set of double-ζ quality. As a broad international endeavor, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around -863 mEH. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 mEH), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

Even when starting with very poor initial guess, the iterative configuration interaction (iCI) approach [J. Chem. Theory Comput. 12, 1169 (2016)] for strongly correlated electrons can converge from above to full CI (FCI) very quickly by constructing and diagonalizing a very small Hamiltonian matrix at each macro/micro-iteration. However, as a direct solver of the FCI problem, iCI is computationally very expensive. The problem can be mitigated by observing that a vast number of configurations have little weights in the wave function and hence do not contribute discernibly to the correlation energy. The real questions are as follows: (a) how to identify those important configurations as early as possible in the calculation and (b) how to account for the residual contributions of those unimportant configurations. It is generally true that if a high-quality yet compact variational space can be determined for describing static correlation, a low-order treatment of the residual dynamic correlation would then be sufficient. While this is common to all selected CI schemes, the "iCI with selection" scheme presented here has the following distinctive features: (1) the full spin symmetry is always maintained by taking configuration state functions (CSF) as the many-electron basis. (2) Although the selection is performed on individual CSFs, it is orbital configurations (oCFGs) that are used as the organizing units. (3) Given a coefficient pruning-threshold Cmin (which determines the size of the variational space for static correlation), the selection of important oCFGs/CSFs is performed iteratively until convergence. (4) At each iteration, for the growth of the wave function, the first-order interacting space is decomposed into disjoint subspaces so as to reduce memory requirement on the one hand and facilitate parallelization on the other hand. (5) Upper bounds (which involve only two-electron integrals) for the interactions between doubly connected oCFG pairs are used to screen each first-order interacting subspace before the first-order coefficients of individual CSFs are evaluated. (6) Upon convergence of the static correlation for a given Cmin, dynamic correlation is estimated using the state-specific Epstein-Nesbet second-order perturbation theory (PT2). The efficacy of the iCIPT2 scheme is demonstrated numerically using benchmark examples, including C2, O2, Cr2, and C6H6.

Dynamic electric properties are most commonly determined by applying linear and nonlinear response theory. This is often a sequential process as each order of response depends on the solution for the previous lower order. Response theory is a perturbative approach and is not directly amenable to modeling time-resolved spectroscopies or experiments involving exotic pulse shapes. Nonperturbative interaction between a system and an electric field can be modeled explicitly in time. This makes it possible to more easily resolve higher-order properties and highly nonlinear processes. Time-dependent configuration interaction has asserted itself as a powerful tool for accurately modeling electronic dynamics. We have implemented time-dependent configuration interaction using the graphical unitary group approach in order to study the dynamics of open-shell systems while retaining spin as a good quantum number. This approach has been used to resolve linear and nonlinear electric properties of molecular systems. Important considerations when modeling dynamic electric properties in the time-domain are presented as well as comparisons to properties of broken symmetry solutions.

In this study, we investigated physical and electronic properties of possible two-dimensional structures formed by Si (silicon) and Ir (iridium). To this end, different plausible structures were modeled by using density functional theory and the cohesive energies calculated for the geometry of optimized structures, with the lowest equilibrium lattice constants. Among several candidate structures, we identified three mechanically (via elastic constants and Young's modulus), dynamically (via phonon calculations), and thermodynamically stable iridium silicide monolayer structures. The lowest energy structure has a chemical formula of Ir2Si4 (called r-IrSi2), with a rectangular lattice (Pmmn space group). Its cohesive energy was calculated to be −0.248 eV (per IrSi2 unit) with respect to bulk Ir and bulk Si. The band structure indicates that the Ir2Si4 monolayer exhibits metallic properties. Other stable structures have hexagonal (P-3m1) and tetragonal (P4/nmm) cell structures with 0.12 and 0.20 eV/f.u. higher cohesive energies, respectively. Our calculations showed that Ir-Si monolayers are reactive. Although O2 molecules exothermically dissociate on the surface of the free-standing iridium silicide monolayers with large binding energies, H2O molecules bind to the monolayers with a rather weak interaction.

Sparse matrix-vector multiplication (SpMV) can be used to solve diverse-scaled linear systems and eigenvalue problems that exist in numerous, and varying scientific applications. One of the scientific applications that SpMV is involved in is known as Configuration Interaction (CI). CI is a linear method for solving the nonrelativistic Schrödinger equation for quantum chemical multi-electron systems, and it can deal with the ground state as well as multiple excited states. In this paper, we have developed a hybrid approach in order to deal with CI sparse matrices. The proposed model includes a newly-developed hybrid format for storing CI sparse matrices on the Graphics Processing Unit (GPU). In addition to the new developed format, the proposed model includes the SpMV kernel for multiplying the CI matrix (proposed format) by a vector using the C language and the Compute Unified Device Architecture (CUDA) platform. The proposed SpMV kernel is a vector kernel that uses the warp approach. We have gauged the newly developed model in terms of two primary factors, memory usage and performance. Our proposed kernel was compared to the cuSPARSE library and the CSR5 (Compressed Sparse Row 5) format and already outperformed both.

Sparse matrix-vector multiplication (SpMV) can be used to solve diverse-scaled linear systems and eigenvalue problems that exist in numerous and varying scientific applications. One of the scientific applications that SpMV is known as Configuration Interaction (CI). CI is a linear method for solving the nonrelativistic Schrödinger equation for quantum chemical multi-electron systems and it can deal with the ground state as well as multiple excited states. A typical CI sparse matrix requires a significant large matrix for detecting and capturing more electron correlation. In this paper, we have developed a hybrid approach to reduce the space requirement of CI sparse matrices. The proposed model includes a newly-developed hybrid format for storing CI sparse matrices on the CPU/GPU. In addition to the new developed format, the proposed model includes the SpMV kernel for multiplying the CI matrix by vector using the C language and the Compute Unified Device Architecture (CUDA) platform. We have gauged the newly developed model in terms of two primary factors, memory usage and performance.

The footnotes in Table 3 are improper and should therefore be revised as The research of this work was supported by the National Key R&D Program of China (Project No. 2017YFB0203402) and the National Natural Science Foundation of China (Project Nos. 21290192 and 21473002).

Based on the generic “static‐dynamic‐static” framework for strongly coupled basis vectors (Liu and Hoffman, Theor. Chem. Acc. 2014, 133, 1481), an iterative Vector Interaction (iVI) method is proposed for computing multiple exterior or interior eigenpairs of large symmetric/Hermitian matrices. Although it works with a fixed‐dimensional search subspace, iVI can converge quickly and monotonically from above to the exact exterior/interior roots. The efficacy of iVI is demonstrated by taking both mathematical and physical matrices as examples. © 2017 Wiley Periodicals, Inc.