Optimized Basis Sets Research Articles

Ballistocardiogram Artifact Reduction in Simultaneous EEG-fMRI Using Deep Learning

The concurrent recording of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) is a technique that has received much attention due to its potential for combined high temporal and spatial resolution. However, the ballistocardiogram (BCG), a large-amplitude artifact caused by cardiac induced movement contaminates the EEG during EEG-fMRI recordings. Removal of BCG in software has generally made use of linear decompositions of the corrupted EEG. This is not ideal as the BCG signal propagates in a manner which is non-linearly dependent on the electrocardiogram (ECG). In this paper, we present a novel method for BCG artifact suppression using recurrent neural networks (RNNs). EEG signals were recovered by training RNNs on the nonlinear mappings between ECG and the BCG corrupted EEG. We evaluated our model's performance against the commonly used Optimal Basis Set (OBS) method at the level of individual subjects, and investigated generalization across subjects. We show that our algorithm can generate larger average power reduction of the BCG at critical frequencies, while simultaneously improving task relevant EEG based classification. The presented deep learning architecture can be used to reduce BCG related artifacts in EEG-fMRI recordings. We present a deep learning approach that can be used to suppress the BCG artifact in EEG-fMRI without the use of additional hardware. This method may have scope to be combined with current hardware methods, operate in real-time and be used for direct modeling of the BCG.

Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets.

We investigate the use of optimized correlation-consistent Gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second-order Møller-Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely, calculations in the Kohn-Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn-Sham basis and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si, and MgO and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for the systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.

Comparison of Density Functional and Correlated Wave Function Methods for the Prediction of Cu(II) Hyperfine Coupling Constants.

The reliable prediction of Cu(II) hyperfine coupling constants remains a challenge for quantum chemistry. Until recently only density functional theory (DFT) could target this property for systems of realistic size. However, wave function based methods become increasingly applicable. In the present work, we define a large set of Cu(II) complexes with experimentally known hyperfine coupling constants and use it to investigate the performance of modern quantum chemical methods for the prediction of this challenging spectroscopic parameter. DFT methods are evaluated against orbital‐optimized second‐order Møller‐Plesset (OO‐MP2) theory and coupled cluster calculations including singles and doubles excitations, driven by the domain‐based local pair natural orbital approach (DLPNO‐CCSD). Special attention is paid to the definition of a basis set that converges adequately toward the basis set limit for the given property for all methods considered in this study, and a specifically optimized basis set is proposed for this purpose. The results suggest that wave function based methods can supplant but do not outcompete DFT for the calculation of Cu(II) hyperfine coupling constants. Mainstream hybrid functionals such as B3PW91 remain on average the best choice.

Ionization energies of hydrogen-bonded dimers with the outer-valence Green’s function method

We investigate the accuracy of the Outer-Valence Green’s Function (OVGF) electron propagator approach for the computation of vertical ionization energies (IEs) of several hydrogen-bonded dimers. The vertical IEs were computed with 10 different basis sets ( i.e. Pople, correlation-consistent and augmented correlation-consistent) and compared with references obtained at the extrapolated equation-of-motion coupled-cluster singles and doubles level. Our study shows that the OVGF method predicts accurately the IEs of hydrogen-bonded clusters. Furthermore, the choice of an optimal basis set is analyzed: our results suggest that the aug-cc-pVDZ basis set provides the best compromise between accuracy and computational costs. The benchmark study provided in this work represents an essential step to investigate molecular ionization, and thus molecular reduction–oxidation properties, in the liquid phase.

One-bond 1 J(15 N,H) coupling constants at sp2 -hybridized nitrogen of Schiff bases, enaminones and similar compounds: A theoretical study.

1 J(15 N,H) coupling constants for enaminones and NH-forms of intramolecularly hydrogen-bonded Schiff bases as model compounds for sp2 -hybridized nitrogen atoms are evaluated using density functional theory (DFT) to find the optimal functionals and basis sets. Ammonia is used as a test molecule and its one-bond coupling constant is compared with experiment. A methylamine Schiff base of a truncated molecule of gossypol is used for checking the performance of selected B3LYP, O3LYP, PBE, BHandH, and APFD density functionals and standard, modified, and dedicated basis sets for coupling constants. Both in vacuum and in chloroform, modeled by the simple continuum model of solvent, the modified basis sets predict significantly better the 1 J(15 N,H) value in ammonia and in the methylamine Schiff base of a truncated molecule of gossypol than the standard basis sets. This procure is then used on a broad set of intramolecularly hydrogen-bonded molecules, and a good correlation between calculated and experimental one-bond NH coupling constants is obtained. The 1 J(15 N,H) couplings are slightly overestimated. The calculated data show for hydrogen-bonded NH interatomic distances that the calculated values depend on the NH bond lengths. The shorter the bond lengths, the larger the 1 J(15 N,H). A useful correlation between 1 J(15 N,H) and NH bond length is derived that enables realistic predictions of one-bond NH coupling constants. The calculations reproduce experimentally observed trends for the studied molecules.

The role of rotation-vibration coupling in symmetric and asymmetric isotopomers of ozone.

A theoretical framework and a computer code (SpectrumSDT) are developed for accurate calculations of coupled rotational-vibrational states in triatomic molecules using hyper-spherical coordinates and taking into account the Coriolis coupling effect. Concise final formulas are derived for the construction of the Hamiltonian matrix using an efficient combination of the variational basis representation and discrete variable representation methods with locally optimized basis sets and grids. First, the new code is tested by comparing its results with those of the APH3D program of Kendrick et al. [Kendrick, Pack, Walker, and Hayes, J. Chem. Phys. 110, 6673 (1999)]. Then, accurate calculations of the rovibrational spectra are carried out for doubly substituted symmetric (18O16O18O) and asymmetric (18O18O16O) ozone isotopomers for the total angular momentum up to J = 5. Together with similar data recently reported for the singly substituted symmetric (16O18O16O) and asymmetric (16O16O18O) ozone isotopomers, these calculations quantify the role of the Coriolis coupling effect in the large mass-independent isotopic enrichment of ozone, observed in both laboratory experiments and the atmosphere of the Earth. It is found that the Coriolis effect in ozone is relatively small, as evidenced by deviations of its rotational constants from the symmetric-top-rotor behavior, magnitudes of parity splittings (Λ-doubling), and ratios of rovibrational partition functions for asymmetric vs symmetric ozone molecules. It is concluded that all of these characteristics are influenced by the isotopic masses as much as they are influenced by the overall symmetry of the molecule. It is therefore unlikely that the Coriolis coupling effect could be responsible for symmetry-driven mass-independent fractionation of oxygen isotopes in ozone.

Выбор оптимального базисного набора для корректной оценки барьера пирамидальной инверсии триметиламина методом PBE

Выбор оптимального базисного набора для корректной оценки барьера пирамидальной инверсии триметиламина методом PBE

Оценка барьера внутреннего вращения в этане методом PBE. Выбор оптимального базисного набора

Оценка барьера внутреннего вращения в этане методом PBE. Выбор оптимального базисного набора

Выбор оптимального базисного набора для корректной оценки барьера пирамидальной инверсии аммиака методом PBE

Выбор оптимального базисного набора для корректной оценки барьера пирамидальной инверсии аммиака методом PBE

Optimal diffuse augmented atomic basis sets for extrapolation of the correlation energy

AbstractWe seek correlation‐consistent diffuse‐augmented double‐zeta and triple‐zeta basis sets that perform optimally in extrapolating the correlation energy to the one‐electron complete basis set limit, denoted oAVXZ and oAV(X + d)Z. The novel basis sets are method‐dependent in that they are trained to perform optimally for the correlation energy at each specific level of theory. They are shown to yield accurate results in calculating both the energy and tensorial properties such as polarizabilities while not significantly altering the Hartree‐Fock energy. Quantitatively, complete basis set limit (CBS)‐/(oAVdZ,oAVtZ)‐extrapolated correlation energies typically outperform, by 3‐ to 5‐fold, the ones calculated with traditional ansatzes of similar flexibility. Attaining energies of CBS/(AVtZ,AVqZ) type or better accuracy, they frequently outperform expensive raw explicitly correlated ones. Promisingly, a limited test on CBS‐extrapolated energies based on conventional basis sets has shown that they compare well even with extrapolated explicitly correlated ones. Calculated atomization and dissociation energies, molecular geometries, ionization potentials, and electron affinities also tend to outperform the ones obtained with traditional Dunning's ansatzes from which the new basis sets have been determined. The method for basis set generation is simple, and there is no reason of principle why the approach could not be adapted for handling other bases in the literature.

Local Atomic and Electronic Structures of β-Сoooh Nanosheets for the Hydrogen-Release Reaction

The geometric and band structures of cobalt-metahydroxide nanosheets, which are related to a new class of two-dimensional nanocatalysts for the hydrogen-release reaction, are calculated. As a result of improving the procedure, the optimal exchange-correlation functionals, basis sets, and dimensions of the “frozen” core are chosen to calculate the atomic and electronic structures, the density of states, and the width of the forbidden band. The calculated results show a decrease in the forbidden band of the cobalt-metahydroxide nanosheets compared with the crystal phase. The X-ray absorption spectra show a high sensitivity of the method to changes in the local atomic environment, especially in the first coordination sphere of cobalt atoms. The calculated model structure makes it possible to determine the features of the local atomic and electronic structures on a cobalt-metahydrixide nanosheet surface during the hydrogen-release reaction.

Linear-scaling ab initio simulations of spin diffusion in rotating solids.

We investigated the utility of locally restricting the basis sets involved in low-order correlations in Liouville space (LCL) calculations of spin diffusion. Using well-known classical models of spin diffusion, we describe a rationale for selecting the optimal basis set for such calculations. We then show that the use of these locally restricted basis sets provides the same computational accuracy as the full LCL set while reducing the computational time by several orders of magnitude. Speeding up the calculations also enables us to use higher maximum spin orders and increase the computational accuracy. Furthermore, unlike exact and full LCL calculations, locally restricted LCL calculations scale linearly with the system size and should thus enable the ab initio study of spin diffusion in spin systems containing several thousand spins.

Accurate interaction energies by spin component scaled Möller-Plesset second order perturbation theory calculations with optimized basis sets (SCS-MP2mod): Development and application to aromatic heterocycles.

The Spin Component Scaled (SCS) MP2 method using a reduced and optimized basis set (SCS-MP2mod) is employed to compute the interaction energies of nine homodimers, formed by aromatic heterocyclic molecules (pyrrole, furan, thiophene, oxazole, isoxazole, pyridine, pyridazine, pyrimidine, and pyrazine). The coefficients of the same-spin and opposite-spin correlation energies and the Gaussian type orbitals (GTO) polarization exponents of the 6-31G** basis set are simultaneously optimized in order to minimize the energy differences with respect to the coupled-cluster with single, double and perturbative triples excitations [CCSD(T)] reference interaction energies, extrapolated to a complete basis set. It is demonstrated that the optimization of the spin scale factors leads to a noticeable improvement of the accuracy with a root mean square deviation less than 0.1 kcal/mol and a largest unsigned deviation smaller than 0.25 kcal/mol. The pyrrole dimer provides an exception, with a slightly higher deviation from the reference data. Given the high benefit in terms of computational time with respect to the CCSD(T) technique and the small loss of accuracy, the SCS-MP2mod method appears to be particularly suitable for extensive sampling of intermolecular potential energy surfaces at a quantum mechanical level. Within this framework, a transferability test of the SCS-MP2mod parameters to a benchmark set of this class of molecules is very promising as the reference interaction energies of several heterocyclic aromatic heterodimers were reproduced with a standard deviation of 0.30 kcal/mol. The SCS-MP2mod remarkably outperforms the value of 1.95 kcal/mol obtained with standard MP2/6-31G**.

Optimal basis sets for CBS extrapolation of the correlation energy: oV x Z and oV(x+d)Z

We seek correlation consistent double- and triple-zeta basis sets that perform optimally for extrapolating the correlation energy to the one-electron complete basis set limit. Since the methods used are approximate, the novel basis sets become method specific in the sense of performing best for the chosen level of theory. Such basis sets are also shown to perform accurately for tensorial properties and do not significantly alter the Hartree-Fock energy. Quantitatively, the extrapolated correlation energies from (oVdZ, oVtZ) outperform typically by three- to fivefold those obtained from traditional ansatzes with similar flexibility, thus being (VtZ, VqZ) type or even better. They may even outperform explicitly correlated ones. Not surprisingly, the outperformance in relative energies (e.g., atomization and dissociation energies, and ionization potential) is somewhat downscaled, albeit consistently better than with traditional basis sets. As a case study, we also consider the polarizability of p-nitroaniline, a sizeable system for which complete basis set (CBS)(oVdZ, oVtZ) calculations are shown to outperform equally expensive CBS(VdZ, VtZ) results.

Determination of the best functional and basis sets for optimization of the structure of hypervalent iodines and calculation of their first and second bond dissociation enthalpies

AbstractHypervalent iodines are widely used in organic chemistry, and their most important feature is the three‐center four‐electron bond. However, there have been few reports on the measurement of their bond dissociation enthalpy (BDE). Therefore, in many cases, BDE is estimated by computational calculations. However, the value of a calculated BDE usually varies depending on the choice of functional and basis set, and the best method for making an accurate evaluation of the three‐center four‐electron bond has not been determined. We succeeded in determining the best functional and basis set to calculate the three‐center four‐electron bond to within 0.79% error and 0.53 standard deviation. Using the optimal functional and basis set, the first and second BDEs of several hypervalent iodines are calculated, and as the effect of benzene substituents was investigated, negative correlation was observed in the Hammett plot. In addition, the effect of ortho‐substituent in cyclic hypervalent iodine was found to be significant. Furthermore, the decomposition route of hypervalent iodine is calculated. The value of a calculated BDE usually varies depending on the choice of functional and basis set. We succeeded in determining the best functional and basis sets to calculate the three‐center four‐electron bond of hypervalent iodine to within 0.79% error and 0.53 standard deviation. Using the optimal functional and basis sets, the first and second BDEs of several hypervalent iodines are calculated, and additionally, the decomposition route of hypervalent iodine is calculated.

SIMPLE code: Optical properties with optimal basis functions

We present SIMPLE, a code developed to calculate optical properties of metallic and insulating extended systems using the optimal basis method originally proposed by E.L. Shirley in 1996. Two different approaches for the evaluation of the complex dielectric function are implemented: (i) the independent-particle approximation considering both interband and intraband contributions for metals and (ii) the Bethe–Salpeter equation for insulators. Since, notably, the optimal basis set is systematically improvable, accurate results can be obtained at a strongly reduced computational cost. Moreover, the simplicity of the method allows for a straightforward use of the code; improvement of the optimal basis and thus the overall precision of the simulations is simply controlled by one (for metals) or two (for insulators) input thresholds. The code is extensively tested, in terms of verification and performance, on bulk silver for metals and on bulk silicon for insulators. Program summaryProgram Title:SIMPLEProgram Files doi:http://dx.doi.org/10.17632/99ps9dz428.1Licensing provisions: GNU General Public License v2Programming language: Fortran 95External routines: Quantum ESPRESSO distribution, BLAS, LAPACK, FFTW, MPI.Nature of problem: First-principles calculations of the optical properties of metals and insulators.Solution method: Shirley’s optimal basis for the complex dielectric function, at the independent-particle level for metals and by solving the Bethe–Salpeter equation for insulators.Restrictions: Norm-conserving pseudopotentials.

Investigating the variability of cardiac pulse artifacts across heartbeats in simultaneous EEG-fMRI recordings: A 7T study

Electroencephalography (EEG) recordings performed in magnetic resonance imaging (MRI) scanners are affected by complex artifacts caused by heart function, often termed pulse artifacts (PAs). PAs can strongly compromise EEG data quality, and remain an open problem for EEG-fMRI. This study investigated the properties and mechanisms of PA variability across heartbeats, which has remained largely unaddressed to date, and evaluated its impact on PA correction approaches. Simultaneous EEG-fMRI was performed at 7T on healthy participants at rest or under visual stimulation, with concurrent recordings of breathing and cardiac activity. PA variability was found to contribute to EEG variance with more than 500 μV2 at 7T, which extrapolates to 92 μV2 at 3T. Clustering analyses revealed that PA variability not only is linked to variations in head position/orientation, as previously hypothesized, but also, and more importantly, to the respiratory cycle and to heart rate fluctuations. The latter mechanisms are associated to short-timescale variability (even across consecutive heartbeats), and their importance varied across EEG channels. In light of this PA variability, three PA correction techniques were compared: average artifact subtraction (AAS), optimal basis sets (OBS), and an approach based on K-means clustering. All methods allowed the recovery of visual evoked potentials from the EEG data; nonetheless, OBS and K-means tended to outperform AAS, likely due to the inability of the latter in modeling short-timescale variability. Altogether, these results offer novel insights into the dynamics and underlying mechanisms of the pulse artifact, with important consequences for its correction, relevant to most EEG-fMRI applications.

BOLD hemodynamic response function changes significantly with healthy aging

Functional magnetic resonance imaging (fMRI) has been used to infer age-differences in neural activity from the hemodynamic response function (HRF) that characterizes the blood-oxygen-level-dependent (BOLD) signal over time. BOLD literature in healthy aging lacks consensus in age-related HRF changes, the nature of those changes, and their implications for measurement of age differences in brain function. Between-study discrepancies could be due to small sample sizes, analysis techniques, and/or physiologic mechanisms. We hypothesize that, with large sample sizes and minimal analysis assumptions, age-related changes in HRF parameters could reflect alterations in one or more components of the neural-vascular coupling system. To assess HRF changes in healthy aging, we analyzed the large population-derived dataset from the Cambridge Center for Aging and Neuroscience (CamCAN) study (Shafto et al., 2014). During scanning, 74 younger (18–30 years of age) and 173 older participants (54–74 years of age) viewed two checkerboards to the left and right of a central fixation point, simultaneously heard a binaural tone, and responded via right index finger button-press. To assess differences in the shape of the HRF between younger and older groups, HRFs were estimated using FMRIB's Linear Optimal Basis Sets (FLOBS) to minimize a priori shape assumptions. Group mean HRFs were different between younger and older groups in auditory, visual, and motor cortices. Specifically, we observed increased time-to-peak and decreased peak amplitude in older compared to younger adults in auditory, visual, and motor cortices. Changes in the shape and timing of the HRF in healthy aging, in the absence of performance differences, support our hypothesis of age-related changes in the neural-vascular coupling system beyond neural activity alone. More precise interpretations of HRF age-differences can be formulated once these physiologic factors are disentangled and measured separately.

Machine Learning Adaptive Basis Sets for Efficient Large Scale Density Functional Theory Simulation.

It is chemically intuitive that an optimal atom centered basis set must adapt to its atomic environment, for example by polarizing toward nearby atoms. Adaptive basis sets of small size can be significantly more accurate than traditional atom centered basis sets of the same size. The small size and well conditioned nature of these basis sets leads to large saving in computational cost, in particular in a linear scaling framework. Here, it is shown that machine learning can be used to predict such adaptive basis sets using local geometrical information only. As a result, various properties of standard DFT calculations can be easily obtained at much lower costs, including nuclear gradients. In our approach, a rotationally invariant parametrization of the basis is obtained by employing a potential anchored on neighboring atoms to ultimately construct a rotation matrix that turns a traditional atom centered basis set into a suitable adaptive basis set. The method is demonstrated using MD simulations of liquid water, where it is shown that minimal basis sets yield structural properties in fair agreement with basis set converged results, while reducing the computational cost in the best case by a factor of 200 and the required flops by 4 orders of magnitude. Already a very small training set yields satisfactory results as the variational nature of the method provides robustness.

Adaptive optimal basis set for BCG artifact removal in simultaneous EEG-fMRI

Electroencephalography (EEG) signals recorded during simultaneous functional magnetic resonance imaging (fMRI) are contaminated by strong artifacts. Among these, the ballistocardiographic (BCG) artifact is the most challenging, due to its complex spatio-temporal dynamics associated with ongoing cardiac activity. The presence of BCG residuals in EEG data may hide true, or generate spurious correlations between EEG and fMRI time-courses. Here, we propose an adaptive Optimal Basis Set (aOBS) method for BCG artifact removal. Our method is adaptive, as it can estimate the delay between cardiac activity and BCG occurrence on a beat-to-beat basis. The effective creation of an optimal basis set by principal component analysis (PCA) is therefore ensured by a more accurate alignment of BCG occurrences. Furthermore, aOBS can automatically estimate which components produced by PCA are likely to be BCG artifact-related and therefore need to be removed. The aOBS performance was evaluated on high-density EEG data acquired with simultaneous fMRI in healthy subjects during visual stimulation. As aOBS enables effective reduction of BCG residuals while preserving brain signals, we suggest it may find wide application in simultaneous EEG-fMRI studies.