Lower Level Methods Research Articles

DAPD Set of Pd-Containing Diatomic Molecules: Accurate Molecular Properties and the Great Lengths to Obtain Them.

In the present study, we obtained reliable bond energy, bond length, and zero-point vibrational frequency for a set of diatomic Pd species (the DAPD set). It includes PdH, Pd2, and PdX (X = B, C, N, O, F, Al, Si, P, S, and Cl). Our highest-level protocol (W4X-L) represents scalar and spin-orbit relativistic, valence- and inner-valence correlated, extrapolated CCSDTQ(5) energy. The DAPD set of molecules is challenging for computational chemistry methods in different manners; for Pd2, the spin-orbit contribution to the bond energy is fairly large, whereas for PdC and PdSi, the post-CCSD(T) correlation components are considerable. The diverse range of requirements represents a significant challenge for lower-level methods. While density functional theory (DFT) methods generally yield good agreements for bond lengths and vibrational frequencies, large deviations are found for bond energies. In general, hybrid DFT methods are more accurate than nonhybrid functionals, but the agreement in individual cases varies. This illustrates the critical role that new high-quality reference data would play in the continual development of lower-cost methods.

Complexes of Alkaline and Ammonium Cations with Dopamine and Eumelanin Precursors: Dissecting the Role of Noncovalent Cation-π and Cation-Lone Pair (σ-Type) Interactions.

Cation-π interactions and their possible competition with other noncovalent interactions (NCI) might play a key role in both dopamine- and eumelanin-based bioinspired materials. In this contribution, to unravel the delicate interplay between cation-π interactions and other possible competing forces, the configurational space of noncovalent complexes formed by dopamine or eumelanin precursors (o-benzoquinone, DHI and a semiquinone dimer) and three different cations (Na+, K+, and NH4+) is sampled by means of accurate ab initio calculations. To this end, we resort to the mp2mod method, recently validated by us for benzene-, phenol-, and catechol-cation complexes, whose computational convenience allows for an extensive exploration of the cation-molecule interaction energy surface, by sampling a total of more than 104 arrangements. The mp2mod interaction energy landscapes reveal that, besides the expected cation-π driven arrangements, for all considered molecule-cation pairs the most stable complexes are found when the cation lies within the plane containing the six-membered ring, thus maximizing the σ-type interaction with the oxygen's lone pairs. Due to the loss of aromaticity, the σ-type/cation-π strength ratio is remarkably large in o-benzoquinone, where cation-π complexes seem unlikely to be formed. The above features are shared among all considered cations but are significantly larger when considering the smaller Na+. Besides delivering a deeper insight onto the NCI network established by the considered precursors in the presence of ions, the present results can serve as a reference database to validate or refine lower level methods, as, for instance, the force fields employed in classical simulations.

Recent Advances in First-Principles Based Molecular Dynamics.

First-principles molecular dynamics (FPMD) and its quantum mechanical-molecular mechanical (QM/MM) extensions are powerful tools to follow the real-time dynamics of a broad variety of systems in their ground as well as electronically excited states. The continued advances in computational power have enabled simulations of QM regions of larger sizes for more extended time scales. In addition, development of the parallel algorithms has boosted the performance of QM/MM methods even on existing computer architectures. In the case of density functional-based FPMD, systems of several hundreds to thousands of atoms can now be customarily simulated for tens to hundreds of picoseconds. In spite of this progress, the time scale limitations remain severe, especially when high-rung exchange-correlation functionals or high-level wave function based quantum mechanical methods are used. To ameliorate this, a large number of enhanced sampling methods have been introduced but most of the approaches that have been developed to increase the efficiency of FPMD based simulations sacrifice the real-time dynamics in favor of enhancing sampling. Here, we present some recent advances in boosting the efficiency of FPMD based simulations while keeping the full dynamic information. These include a highly efficient recent implementation of FPMD-based QM/MM simulations that not only enables fully flexible combinations of different electronic structure methods and force fields via a highly efficient communication library, it also fully exploits parallelism for both quantum and classical descriptions. The second type of acceleration methods we discuss is a large family of specially devised multiple-time-step algorithms that make use of suitable breakups of the total nuclear forces into fast components that can be calculated via lower level methods and slowly varying correction forces evaluated with a high-level method at long time intervals. The computational gain of this scheme mostly depends on the cost difference between the two methods and advantageous combinations can yield large speedups without compromising the accuracy of the high-level method. And finally, the third class of FPMD acceleration methods presented here are machine learning models to accelerated FPMD and their powerful combinations with multiple-time-step techniques. The combination of all the approaches enables substantial speedups of FPMD simulations of several orders of magnitude while fully preserving the real-time dynamics and accuracy.

Undergraduate Research Across the Psychology Curriculum

Over the past 10 years, the Psychology Department at Indiana University Kokomo has worked to incorporate more opportunities for students to engage in undergraduate research throughout the psychology curriculum. Our previous requirements included a lower level methods course that most students took prior to statistics, with the result that students did not have the opportunity to practice the use of statistics in research contexts unless they completed an independent research project during their senior year. We made several curricular changes to enhance these opportunities to apply statistical knowledge, to increase research literacy and critical analysis, and to better prepare students who go on to complete an independent research project. The lower level methods course was redesigned to explore psychology as a major and career, introduce research concepts, and help students develop critical thinking skills. We also reinstated an upper level methods course with statistics as a prerequisite, allowing better integration of statistics with research methods. Most recently, in fall 2018, we added a lab to the upper level methods course, in which students use computer-based statistical software for data analysis. In addition to these curricular changes, the department has recently been promoting and facilitating more student travel to research conferences throughout the undergraduate program. In this article, we describe the program we designed to scaffold student research and present a six-level framework applicable across a broad range of disciplines. We also present data collected from current students and alumni in psychology to assess their perceptions of the impact of these changes on their research confidence and competence as well as limited results from assessment of student learning. Finally, we provide recommendations for other programs interested in increasing opportunities for student research in their disciplines.

Equation-of-Motion MLCCSD and CCSD-in-HF Oscillator Strengths and Their Application to Core Excitations.

We present an implementation of equation-of-motion oscillator strengths for the multilevel CCSD (MLCCSD) model where CCS is used as the lower level method (CCS/CCSD). In this model, the double excitations of the cluster operator are restricted to an active orbital space, whereas the single excitations are unrestricted. Calculated nitrogen K-edge spectra of adenosine, adenosine triphosphate (ATP), and an ATP-water system are used to demonstrate the performance of the model. Projected atomic orbitals (PAOs) are used to partition the virtual space into active and inactive orbital sets. Cholesky decomposition of the Hartree–Fock density is used to partition the occupied orbitals. This Cholesky-PAO partitioning is cheap, scaling as , and is suitable for the calculation of core excitations, which are localized in character. By restricting the single excitations of the cluster operator to the active space, as well as the double excitations, the CCSD-in-HF model is obtained. A comparison of the two models—MLCCSD and CCSD-in-HF—is presented for the core excitation spectra of the adenosine and ATP systems.

Performance of Localized Coupled Cluster Methods in a Moderately Strong Correlation Regime: Hückel-Möbius Interconversions in Expanded Porphyrins.

Localized orbital coupled cluster theory has recently emerged as a nonempirical alternative to DFT for large systems. Intuitively, one might expect such methods to perform less well for highly delocalized systems. In the present work, we apply both canonical CCSD(T) approximations and a variety of localized approximations to a set of flexible expanded porphyrins—macrocycles that can switch between Hückel, figure-eight, and Möbius topologies under external stimuli. Both minima and isomerization transition states are considered. We find that Möbius(-like) structures have much stronger static correlation character than the remaining structures, and that this causes significant errors in DLPNO-CCSD(T) and even DLPNO-CCSD(T1) approaches, unless TightPNO cutoffs are employed. If sub-kcal mol–1 accuracy with respect to canonical relative energies is required even for Möbius-type systems (or other systems plagued by strong static correlation), then Nagy and Kallay’s LNO-CCSD(T) method with “tight” settings is the suitable localized approach. We propose the present POLYPYR21 data set as a benchmark for localized orbital methods or, more broadly, for the ability of lower-level methods to handle energetics with strongly varying degrees of static correlation.

What Electronic Structure Method Can Be Used in the Global Optimization of Nanoclusters?

The problem of obtaining the spatial structure of nanoclusters is known to be very difficult due to the large number of local minima associated with their potential energy surfaces (isomers). In global optimization approaches, such as basin hopping and genetic algorithms, the problem is normally tackled by first using a low-level and affordable method to evaluate the energy. Afterward, the putative global minimum (and often a few others) is refined with calculations using higher level methods and larger basis sets. There is no guarantee, however, that the structure obtained at the lower level method will be the global minimum at the refined one. In this work, we have performed benchmark coupled cluster calculations at the complete basis set limit for a large number of different isomers of representative clusters of third row elements. Such calculations are then employed to check the hypothesis that lower level methods can be used in the global optimization with reliable results. For this, we have developed a methodology that allows us to compare a large number of minima obtained at different calculation levels. The results indicate that, if the global optimization is capable of reaching not only the global minimum but also a reduced number of low lying structures, most of the tested density functional theory (DFT) functionals are good choices, with emphasis on TPSSh. Besides giving a more solid ground to this commonly used approach, this work helps guiding such global optimizations. The use of the MP2 method and several scaled variants is also assessed, from where it is concluded that the scaled variants yield better results than standard MP2 or DFT approaches, except for one system where a large number of van der Waals structures exist.

What Levels of Coupled Cluster Theory Are Appropriate for Transition Metal Systems? A Study Using Near-Exact Quantum Chemical Values for 3d Transition Metal Binary Compounds.

Transition metal compounds are traditionally considered to be challenging for standard quantum chemistry approximations like coupled cluster (CC) theory, which are usually employed to validate lower level methods like density functional theory (DFT). To explore this issue, we present a database of bond dissociation energies (BDEs) for 74 spin states of 69 diatomic species containing a 3d transition metal atom and a main group element, in the moderately sized def2-SVP basis. The presented BDEs appear to have an (estimated) 3σ error less than 1 kJ/mol relative to the exact solutions to the nonrelativistic Born-Oppenheimer Hamiltonian. These benchmark values were used to assess the performance of a wide range of standard single reference CC models, as the results should be beneficial for understanding the limitations of these models for transition metal systems. We find that interactions between metals and monovalent ligands like hydride and fluoride are well described by CCSDT. Similarly, CCSDTQ appears to be adequate for bonds between metals and nominally divalent ligands like oxide and sulfide. However, interactions with polyvalent ligands like nitride and carbide are more challenging, with even CCSDTQ(P)Λ yielding errors on the scale of a few kJ/mol. We also find that many perturbative and iterative approximations to higher order terms either yield disappointing results or actually worsen the performance relative to the baseline low level CC method, indicating that complexity does not always guarantee accuracy.

What Can We Learn from Multi-Objective Meta-Optimization of Evolutionary Algorithms in Continuous Domains?

Properly configuring Evolutionary Algorithms (EAs) is a challenging task made difficult by many different details that affect EAs’ performance, such as the properties of the fitness function, time and computational constraints, and many others. EAs’ meta-optimization methods, in which a metaheuristic is used to tune the parameters of another (lower-level) metaheuristic which optimizes a given target function, most often rely on the optimization of a single property of the lower-level method. In this paper, we show that by using a multi-objective genetic algorithm to tune an EA, it is possible not only to find good parameter sets considering more objectives at the same time but also to derive generalizable results which can provide guidelines for designing EA-based applications. In particular, we present a general framework for multi-objective meta-optimization, to show that “going multi-objective” allows one to generate configurations that, besides optimally fitting an EA to a given problem, also perform well on previously unseen ones.

Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green's Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy.

We present a detailed discussion of the self-energy embedding theory (SEET), which is a quantum embedding scheme allowing us to describe a chosen subsystem very accurately while keeping the description of the environment at a lower level. We apply SEET to molecular examples where our chosen subsystem is made out of a set of strongly correlated orbitals while the weakly correlated orbitals constitute an environment. Consequently, a highly accurate method is used to calculate the self-energy for the system, while a lower-level method is employed to find the self-energy for the environment. Such a self-energy separation is very general, and to make the SEET procedure applicable to multiple systems, a detailed and practical procedure for the evaluation of the system and environment self-energy is necessary. We list all of the intricacies for one of the possible procedures while focusing our discussion on many practical implementation aspects such as the choice of best orbital basis, impurity solver, and many steps necessary to reach chemical accuracy. Finally, on a set of carefully chosen molecular examples, we demonstrate that SEET, which is a controlled, systematically improvable Green's function method, can be as accurate as established wave function quantum chemistry methods.

PICVib: an accurate, fast and simple procedure to investigate selected vibrational modes at high theoretical levels and evaluate Raman intensities

Raman intensities and depolarization ratios are important properties to assign the vibrational spectrum and thus to characterize substances and materials. Practical and reliable computational methods are relevant to guide and aid the assignment and interpretation of Raman spectra. The procedure for investigating categories of vibrations (PICVib) approach is generalized for the Raman intensity calculations, and it is shown to be successful and to preserve all interesting features of the procedure such as easiness of implementation, parallelization, flexibility and treatment of large systems at high theoretical levels. The PICVib method involves calculations of the polarizability tensors at the displaced structures to provide the Raman intensities of selected normal modes, in addition to their vibrational wavenumbers and infrared intensities. It was validated for very diverse molecular systems: XH3 (D3h), YH4 (D4h), conformers of 1,3,5-trinitro-1,3,5-triazacyclohexane, SN2 and E2 product complexes, fullerene C60, lanthanide ion aquo complexes and hydrogen-bonded complexes (water–water, water–methanol and methanol–methanol) including the guanine-cytosine pair. This assessment shows an excellent overall performance of the PICVib method for calculating Raman intensities of localized normal modes and even mixed vibrations. For vibrations involving intermolecular complexes, the choice of the lower level method (e.g. density functionals and semiempiricals) is crucial. This makes the PICVib procedure practically complete for vibrational analysis of molecular systems and should now be generalized for extended and periodic systems. Copyright © 2016 John Wiley & Sons, Ltd.

11,11-dimethyl-1,6-methano[10]annulene--an annulene with an ultralong CC bond or a fluxional molecule?

Extensive quantum chemical calculations involving more than 20 different methods and including vibrational, temperature, entropic, and environmental corrections suggest that 11,11-dimethyl-1,6-methano[10]annulene (1) is characterized by a broad, asymmetric single well potential minimum in which the molecule can carry out a large-amplitude vibration. This result is obtained by using CASPT2(14,14) and CCSD(T) together with a VTZ basis set. The average R(C1C6) distance of 1 is close to 1.8 Å, in agreement with X-ray diffraction measurements. Lower level methods fail because a reliable account of the electronic structure of bridged annulenes requires a balanced description of nondynamical and dynamical electron correlation effects as well as a correct assessment of bridge-annulene interactions. An independent determination of the distance R using the mean deviation between the calculated and measured (13)C NMR chemical shifts of 1 leads to a value of 1.79 Å. By using electron density, energy density, and the local C1C6 stretching mode, it is demonstrated that the covalent bond ceases to exist at 1.695 Å and that for larger R values through-space homoaromatic interactions lead to some stabilization. The peculiar potential of 1 is shown to be a result of the interaction of the methyl groups with the perimeter CC bonds bisected by the symmetry plane of the molecule. CASPT2(14,14), CASPT2(10,10), CCSD(T), and BD(T) calculations were also used to provide for the first time reliable descriptions of the valence tautomeric potentials for the parent molecule, 1,6-methano[10]annulene (2), and the system 1,3,5-cycloheptatriene-norcardiene (3). In the latter case, calculations confirm a previous kinetic measurement of the free activation energy but correct NMR-based estimates. The methodology described can be applied to other annulenes and fullerenes.

Relative energies, structures, vibrational frequencies, and electronic spectra of pyrylium cation, an oxygen-containing carbocyclic ring isoelectronic with benzene, and its isomers

We have studied relative energies, structures, rotational, vibrational, and electronic spectra of the pyrylium cation, an oxygen-containing six-membered carbocyclic ring, and its six isomers, using ab initio quantum chemical methods. Isoelectronic with benzene, the pyrylium cation has a benzenoid structure and is the global minimum on the singlet potential energy surface of C5H5O(+). The second lowest energy isomer, the furfuryl cation, has a five membered backbone akin to a sugar, and is only 16 kcal mol(-1) above the global minimum computed using coupled cluster theory with singles, doubles, and perturbative triple excitations (CCSD(T)) with the correlation consistent cc-pVTZ basis set. Other isomers are 25, 26, 37, 60, and 65 kcal mol(-1) above the global minimum, respectively, at the same level of theory. Lower level methods such as density functional theory (B3LYP) and second order Møller-Plesset perturbation theory performed well when tested against the CCSD(T) results. The pyrylium and furfuryl cations, although separated by only 16 kcal mol(-1), are not easily interconverted, as multiple bonds must be broken and formed, and the existence of more than one transition state is likely. Additionally, we have also investigated the asymptotes for the barrierless ion-molecule association of molecules known to exist in the interstellar medium that may lead to formation of the pyrylium cation.

Formal equivalence verification and debugging techniques with auto-correction mechanism for RTL designs

By increasing the complexity of system on chip (SoC) designs formal equivalence verification and debugging have become more and more important. Lower level methods such as BDDs and SAT solvers suffer from space and time explosion problems to match sizes of industrial designs in formal equivalence verification and debugging. This paper proposes techniques to verify and debug datapath intensive designs based on a canonical decision diagram called Horner Expansion Diagram (HED). It allows us to check the equivalence between two models in different levels of abstraction, e.g., a Register Transfer Level (RTL) implementation and a non-cycle-accurate specification. In order to reduce the complexity of equivalence checking problem, we tackle the exponential path enumeration problem by automatically identifying internal equivalent conditional expressions as well as suitable merge points. Our debugging technique is based on introducing mutations into the buggy implementation and then observing if the specification is capable of detecting these changes. We make use of a simple heuristic to reduce the number of mutants when dealing with multiple errors. We report the results of deploying our equivalence verification technique on several industrial designs which show 16.8× average memory usage reduction and 8.0× speedup due to merge-point detection. Furthermore, our debugging technique shows 13.7× average memory usage reduction and 4.6× speedup due to using SMT solvers to find equivalent conditions. In addition, the proposed debugging technique can avoid the computation of unnecessary mutants so that the results show 2.9× average reduction of the number of mutants to be processed.

Electron-Nuclear Motion in the Cope Rearrangement of Semibullvalene: Ever Synchronous?

The effect of nuclear motion on the synchronicity of the pincer motion type electronic rearrangement associated with bond making and bond breaking and vice versa is investigated for the degenerate Cope rearrangement of semibullvalene using a time-independent quantum chemical approach. We find that distinct paths along the potential energy surface corresponding to synchronous nuclear rearrangement involve asynchronous electronic fluxes out of the old and into the new bond while synchronous electronic fluxes entail asynchronous nuclear rearrangement. In order to demonstrate the robustness of the results, various high-level quantum chemical methods including full structure optimizations up to second order multireference perturbation theory using triple-ζ basis sets (RS2/cc-pVTZ), which are subsequently refined at the RS3/cc-pVTZ and MRCI+Dav/cc-pVTZ levels of theory, are used for solving the electronic Schrödinger equation. These benchmark results extend previous quantum chemical data for the degenerate Cope rearrangement of semibullvalene and are tested against lower level methods (e.g., density functional theory calculations using the B3LYP and B3PW91 functionals).

Accurate Determination of the Reaction Course in HY2 ⇌ Y + YH (Y = O, S): Detailed Analysis of the Covalent- to Hydrogen-Bonding Transition

The accurate prediction of a bond-breaking/bond-forming reaction course is useful but very difficult. Toward this goal, a cost-effective multireference scheme (A. J. C. Varandas, J. Chem. Theory Comput. 2012, 8, 428) is tested that provides a generalization of the Hartree-Fock plus dispersion model for closed-shell interactions, and hence is based on the popular but largely untested idea of performing single point calculations with a high-level method at stationary points or along paths located using a lower level method. The energetics so calculated for the reaction HO2 <−> O + OH is predicted in excellent agreement with the experimental data, whereas the reaction path shows a scar at the onset of hydrogen-bonding: a weak van der Waals type minimum separated from the deep covalent well by a small barrier, all below the O + OH asymptote. The O-OH long-range interaction potential is also examined and possible implications in reaction dynamics discussed. Corresponding attributes for the reaction HS2 <−> S + SH are predicted, in good agreement with the best theoretical and experimental results. A perspective on the general utility of the approach is presented.

Benchmark Studies on the Building Blocks of DNA. 3. Watson–Crick and Stacked Base Pairs

Excited states of stacked adenine-thymine and guanine-cytosine pairs as well as the Watson-Crick pair of guanine-thymine have been investigated using the equation of motion coupled-cluster (EOM-CC) method with single and double as well as approximate triple excitations. Transitions have been assigned, and the form of the excitations has been analyzed. The majority of the excitations could be classified as localized on the nucleobases, but for all three studied systems, charge-transfer (CT) transitions could also be identified. The main aim of this study was to compare the performance of lower-level methods (ADC(2) and TDDFT) to the high-level EOM-CC ones. It was shown that both ADC(2) and TDDFT with long-range correction have nonsystematic error in excitation energies, causing alternation of the energetic ordering of the excitations. Considering the high costs of the EOM-CC calculations, there is a need for reliable new approximate methods.

Electronically Excited States in Poly(p-phenylenevinylene): Vertical Excitations and Torsional Potentials from High-Level Ab Initio Calculations

Ab initio second-order algebraic diagrammatic construction (ADC(2)) calculations using the resolution of the identity (RI) method have been performed on poly-(p-phenylenevinylene) (PPV) oligomers with chain lengths up to eight phenyl rings. Vertical excitation energies for the four lowest π–π* excitations and geometry relaxation effects for the lowest excited state (S1) are reported. Extrapolation to infinite chain length shows good agreement with analogous data derived from experiment. Analysis of the bond length alternation (BLA) based on the optimized S1 geometry provides conclusive evidence for the localization of the defect in the center of the oligomer chain. Torsional potentials have been computed for the four excited states investigated and the transition densities divided into fragment contributions have been used to identify excitonic interactions. The present investigation provides benchmark results, which can be used (i) as reference for lower level methods and (ii) give the possibility to parametrize an effective Frenkel exciton Hamiltonian for quantum dynamical simulations of ultrafast exciton transfer dynamics in PPV type systems.

Incremental Scheme for Intermolecular Interactions: Benchmarking the Accuracy and the Efficiency.

In this work, we introduce a method to automatically compute the basis set superposition error (BSSE) for large clusters and introduce a correction scheme to improve the accuracy of incrementally expanded coupled cluster energies (CCSD(T)) using the domain-specific basis set approach. The key step for the automatic BSSE computation is the automated partitioning of the system. With the proposed scheme, one can compute the BSSE of large clusters or complexes with different fragments and different charges fully automatic. The second proposal is to use the error from an incrementally expanded MP2 calculation to reduce the error in the corresponding incremental CCSD(T) calculation (CCSD(T)|MP2). This scheme improves the accuracy of incremental CCSD(T) expansions using the domain-specific basis set significantly. The performance of the method is analyzed for intermolecular interactions of H2 and H2O clusters and for the adiabatic interaction energy of Zn(H2O)62+. The errors of the expansion are compared to basis set errors and errors introduced by a cheap lower level method, MP2. Using the proposed CCSD(T)|MP2 scheme, the largest error to the exact CCSD(T) calculation is found to be 0.14 kcal/mol for Zn(H2O)62+. With the incremental scheme, it was possible to increase the basis set of the CCSD(T) calculation for (H2O)10 to quintuple-ζ level with 2370 basis functions.

Tuning metal hydride thermodynamics via size and composition: Li–H, Mg–H, Al–H, and Mg–Al–H nanoclusters for hydrogen storage

Nanoscale Li and intermetallic Al-Mg metal hydride clusters are investigated as a possible hydrogen storage material using the high-level quantum Monte Carlo computational method. Lower level methods such as density functional theory are qualitatively, not quantitatively accurate for the calculation of the enthalpy of absorption of H(2). At sizes around 1 nm, it is predicted that Al/Mg alloyed nanoparticles are stable relative to the pure compositions and the metal composition can be tuned in tandem with the size to tune the hydrogen absorption energy, making this a promising route to a rechargeable hydrogen storage material.