Conspectus 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.

The calculation of electron correlation is vital for the description of atomistic phenomena in physics, chemistry, and biology. However, accurate wavefunction-based methods exhibit steep scaling and often sluggish convergence with respect to the basis set at hand. Because of their delocalization and ease of extrapolation to the basis-set limit, plane waves would be ideally suited for the calculation of basis-set limit correlation energies. However, the routine use of correlated wavefunction approaches in a plane-wave basis set is hampered by prohibitive scaling due to a large number of virtual continuum states and has not been feasible for all but the smallest systems, even if substantial computational resources are available and methods with comparably beneficial scaling, such as the Møller–Plesset perturbation theory to second order (MP2), are used. Here, we introduce a stochastic sampling of the MP2 integrand based on Monte Carlo summation over continuum orbitals, which allows for speedups of up to a factor of 1000. Given a fixed number of sampling points, the resulting algorithm is dominated by a flat scaling of . Absolute correlation energies are accurate to <0.1 kcal/mol with respect to conventional calculations for several hundreds of electrons. This allows for the calculation of unbiased basis-set limit correlation energies for systems containing hundreds of electrons with unprecedented efficiency gains based on a straightforward treatment of continuum contributions.

Identification of the most stable structure(s) of a system is a prerequisite for the calculation of any of its properties from first-principles. However, even for relatively small molecules, exhaustive explorations of the potential energy surface (PES) are severely hampered by the dimensionality bottleneck. In this work, we address the challenging task of efficiently sampling realistic lowlying peptide coordinates by resorting to a surrogate based genetic algorithm (GA)/density functional theory (DFT) approach (sGADFT) in which promising candidates provided by the GA are ultimately optimized with DFT. We provide a benchmark of several computational methods (GAFF, AMOEBApro13, PM6, PM7, DFTB3-D3(BJ)) as possible prescanning surrogates and apply sGADFT to two test case systems that are (i) two isomer families of the protonated Gly-Pro-Gly-Gly tetrapeptide (Masson, A.; et al.

Identification of the most stable structure(s) of a system is a prerequisite for the calculation of any of its properties from first-principles. However, even for relatively small molecules, exhaustive explorations of the potential energy surface (PES) are severely hampered by the dimensionality bottleneck. In this work, we address the challenging task of efficiently sampling realistic low-lying peptide coordinates by resorting to a surrogate based genetic algorithm (GA)/density functional theory (DFT) approach (sGADFT) in which promising candidates provided by the GA are ultimately optimized with DFT. We provide a benchmark of several computational methods (GAFF, AMOEBApro13, PM6, PM7, DFTB3-D3(BJ)) as possible prescanning surrogates and apply sGADFT to two test case systems that are (i) two isomer families of the protonated Gly-Pro-Gly-Gly tetrapeptide, and (ii) the doubly-protonated cyclic decapeptide gramicidin S. We show that our GA procedure can correctly identify low-energy minima in as little as a few hours. Subsequent refinement of surrogate low-energy structures within a given energy threshold (≤ 10 kcal/mol (i), ≤ 5 kcal/mol (ii)) via DFT relaxation invariably led to the identification of the most stable structures as determined from high-resolution infrared (IR) spectroscopy at low temperature. The sGADFT method therefore constitutes a highly efficient route for the screening of realistic low-lying peptide structures in the gas phase as needed for instance for the interpretation and assignment of experimental IR spectra.

Second-order Møller Plesset perturbation theory (MP2) is the most expedient wavefunction-based method for considering electron correlation in quantum chemical calculations and as such provides a cost-effective framework to assess the effects of basis sets on correlation energies, for which the complete basis set (CBS) limit can commonly only be obtained via extrapolation techniques. Software packages providing MP2 energies are commonly based on atom-centered bases with innate issues related to possible basis set superposition errors (BSSE), especially in the case of weakly-bonded systems. Here, we present non-covalent interaction energies in the CBS limit, free of BSSE, for 20 dimer systems of the S22 dataset obtained via a highly-parallelized MP2 implementation in the plane-wave pseudopotential molecular dynamics package CPMD. The specificities related to plane waves for accurate and efficient calculations of gas-phase energies are discussed, and results compared to the localized (aug-)cc-pV[D,T,Q,5]Z correlation-consistent bases as well as their extrapolated CBS estimates. We find that the BSSE-corrected aug-cc-pV5Z basis can provide MP2 energies highly consistent with the CBS plane wave values with a minimum mean absolute deviation of ~0.05 kcal/mol without the application of any extrapolation scheme. In addition, we tested the performance of 13 different extrapolation schemes and found that the $X^{-3}$ expression applied to the (aug-)cc-pVXZ bases provides the smallest deviations against CBS plane wave values if the extrapolation sequence is composed of points D and T, while $(X + \frac{1}{2})^{-4}$ performs slightly better for TQ and Q5 extrapolations. Also, we propose $A (X-\frac{1}{2})^{-3} + B (X+\frac{1}{2})^{-4}$ as a reliable alternative to extrapolate total energies from the DTQ, TQ5 or DTQ5 data points. In spite of the general good agreement between the values obtained from the two types of basis set, it is noticed that differences between plane waves and (aug-)cc-pVXZ basis sets, extrapolated or not, tend to increase with the number of electrons, thus raising the question whether these discrepancies could indeed limit the attainable accuracy for localized bases in the limit of large systems.