The integration of quantum chemical methods with high-performance computing is indispensable for handling large systems with modest accuracy or even small systems but with high accuracy. Continuing with the unified implementation of non-relativistic and relativistic wave functions methods within the MetaWave platform (J. Phys. Chem. A. 2025, 129, 5170), we present here a unified MPI parallelization of the methods by abstracting ever computational step of a method as a dynamically-scheduled loop via ghost process, followed by a global reduction of local results from each node. The algorithmic abstraction enables the use of a single MPI template in various steps of different methods. Taking iCIPT2 [J. Chem. Theory Comput. 2021, 17, 949] as a showcase, the parallel efficiencies achieve 94% and 89% on 16 nodes (1024 cores) for the perturbation and whole calculations, respectively. Further combined with an improved algorithm for the matrix-vector product in the matrix diagonalization and an orbital-configuration-based semi-stochastic estimator for the perturbation correction, this renders large active space calculations possible, so as to obtain benchmarks for the automerization of cyclobutadiene, ground state energy of benzene and potential energy profile of ozone. It is also shown that the error of iCIPT2 follows a power law with respect to the number of configuration state functions.
The integration of quantum chemical methods with high-performance computing is indispensable for handling large systems with modest accuracy or even small systems but with high accuracy. Continuing with the unified implementation of non-relativistic and relativistic wave functions methods within the MetaWave platform (J. Phys. Chem. A. 2025, 129, 5170), we present here a unified MPI parallelization of the methods by abstracting ever computational step of a method as a dynamically-scheduled loop via ghost process, followed by a global reduction of local results from each node. The algorithmic abstraction enables the use of a single MPI template in various steps of different methods. Taking iCIPT2 [J. Chem. Theory Comput. 2021, 17, 949] as a showcase, the parallel efficiencies achieve 94% and 89% on 16 nodes (1024 cores) for the perturbation and whole calculations, respectively. Further combined with an improved algorithm for the matrix-vector product in the matrix diagonalization and an orbital-configuration-based semi-stochastic estimator for the perturbation correction, this renders large active space calculations possible, so as to obtain benchmarks for the automerization of cyclobutadiene, ground state energy of benzene and potential energy profile of ozone. It is also shown that the error of iCIPT2 follows a power law with respect to the number of configuration state functions.
The integration of quantum chemical methods with high-performance computing is indispensable for handling large systems with modest accuracy or even small systems but with high accuracy. Continuing with the unified implementation of nonrelativistic and relativistic wave function methods within the MetaWave platform ( J. Phys. Chem. A 2025, 129, 5170), we present here a unified MPI parallelization of the methods by abstracting every computational step of a method as a dynamically scheduled loop via ghost process, followed by a global reduction of local results from each node. The algorithmic abstraction enables the use of a single MPI template in various steps of different methods. Taking iCIPT2 [ J. Chem. Theory Comput. 2021, 17, 949] as a showcase, the parallel efficiencies achieve 94% and 89% on 16 nodes (1024 cores) for the perturbation and whole calculations, respectively. Further combined with an improved algorithm for the matrix-vector product in the matrix diagonalization and an orbital-configuration-based semistochastic estimator for the perturbation correction, this renders large active space calculations possible, so as to obtain benchmarks for the automerization of cyclobutadiene, ground-state energy of benzene, and potential energy profile of ozone. It is also shown that the error of iCIPT2 follows a power law with respect to the number of configuration state functions.
The physics of strongly correlated materials poses one of the most challenging problems in condensed-matter sciences. Standard approximations applicable to wide classes of materials such as the local density approximation fail, due to the importance of the Coulomb repulsion between localized electrons. Instead, we resort to non-perturbative many-body methods. The calculations are, however, only feasible for rather small model systems. The full Hamiltonian of a real material is approximated by a model Hamiltonian comprising only the most important electronic degrees of freedom, while the effect of all other electrons is included in an average way by renormalizing the parameters. Realistic calculations of strongly correlated materials need to include sufficiently many of these electronic degrees of freedom. The new generation of massively parallel supercomputers allows for these realistic calculations. However, exploiting their computational power requires newly devised algorithms. As a solver we use the Lanczos method, which needs the full many-body state of the correlated system. It is thus limited by the available main memory. The foremost problem for a distributed-memory implementation is that the multiplication of the Hamiltonian to the many-body state leads to highly non-local memory access patterns. A simple yet important observation leads to an efficient solution: in the kinetic term of the Hamiltonian the electron-spin is conserved. Thus, writing the many-body vector as a matrix v(iup,idn), where the indices label spin-configurations, we find that the hopping term only connects vector elements that differ in one index. Hence, storing entire slices v(iup,:) on one node, the kinetic term for the spin-down electrons is local to that process. After transposing v, the same is true for the hopping of the spin-up electrons. With an efficient matrix transpose, implemented via MPI collectives, we thus obtain a version of the Lanczos method that efficiently well on JUBL, Jülich's Blue Gene/L. Using the code we treated two-orbital Hubbard Models which show interesting Mott-band insulator transitions. Kohn's criterium which determines the phase of a system by ground-state properties alone, namely the response of the ground-state energies to a vector potential, was employed. This vector potential can be equivalently regarded as a change in boundary conditions, requiring complex wave vectors. We found that half-filled systems become metallic in the region between a band and Mott insulating phase. To extrapolate to infinite system sizes and therefore getting access to an arbitrarily high resolution in reciprocal space, we use cluster perturbation theory (CPT). It works by diagonalizing a finite cluster exactly and then treating the hopping between identical clusters perturbatively in strong coupling perturbation theory. This leads to an effectively infinite chain. Due to our efficient Lanczos implementation it is possible to calculate relatively large clusters, minimizing finite-size effects. The combination of our Lanczos code and CPT allowed for a treatment of the the organic metal TTF-TCNQ. We were able to solve a long-standing problem in the interpretation of its experimental spectra. Being an interesting one-dimensional metal TTF-TCNQ has been studied thoroughly for more than 30 years. Theoretical estimates as well as experimental measurements suggest values for the parameters of the Hubbard model t and U. With these values Hubbard model calculations show qualitatively the same features as APRES experiments, namely the signatures of spin-charge separation at the Gamma-point. But in order to fit the experimental data to the numerical calculations t has to be doubled, which translates into a broadening of the spectra. This ad-hoc adjustment is not only unsatisfactory but also the temperature dependence of the spectral function is incorrectly reproduced. We resolved this problem by properly including nearest-neighbor Coulomb interactions. Recent DFT calculations show that indeed the commonly used values of t and U are correct. But Coulomb interactions between electrons on neighboring sites are also significant and must not be neglected. Thus, we studied the effect of the next-neighbor interaction parameter V being at about U/2. Including V in our Lanczos calculations for obtaining the angular-integrated spectral function shows that its effect is to broaden the spectra, comparable to increasing the value of t. Moreover, we found that doubling t indeed mimics the effect of Vapprox U/2. Surprisingly, the broadening of the spectrum as a result of V can be understood in first-order Rayleigh-Schrödinger perturbation theory.
We present, to the best of our knowledge, the first attempt to exploit the super-computer platform for quantum chemical density matrix renormalization group (QC-DMRG) calculations. We have developed the parallel scheme based on the in-house MPI global memory library, which combines operator and symmetry sector parallelisms, and tested its performance on three different molecules, all typical candidates for QC-DMRG calculations. In case of the largest calculation, which is the nitrogenase FeMo cofactor cluster with the active space comprising 113 electrons in 76 orbitals and bond dimension equal to 6000, our parallel approach scales up to approximately 2000 CPU cores.
With advances in algorithms and growing computing powers, quantum Monte Carlo (QMC) methods have become a leading contender for high accuracy calculations for the electronic structure of realistic systems. The performance gain on recent HPC systems is largely driven by increasing parallelism: the number of compute cores of a SMP and the number of SMPs have been going up, as the Top500 list attests. However, the available memory as well as the communication and memory bandwidth per element has not kept pace with the increasing parallelism. This severely limits the applicability of QMC and the problem size it can handle. OpenMP/MPI hybrid programming provides applications with simple but effective solutions to overcome efficiency and scalability bottlenecks on large-scale clusters based on multi/many-core SMPs. We discuss the design and implementation of hybrid methods in QMCPACK and analyze its performance on current HPC platforms characterized by various memory and communication hierarchies.
Accurate evaluation of electron correlations is essential for the reliable quantitative description of electronic structures in strongly correlated systems, including bond-dissociating molecules, polyradicals, large conjugated molecules, and transition metal complexes. To provide a user-friendly tool for studying such challenging systems, our team developed Kylin 1.0 [J. Comput. Chem. 44, 1316 (2023)], an ab initio quantum chemistry program designed for efficient density matrix renormalization group (DMRG) and post-DMRG methods, enabling high-accuracy calculations with large active spaces. We have now further advanced the software with the release of Kylin 1.3, featuring optimized DMRG algorithms and an improved tensor contraction scheme in the diagonalization step. Benchmark calculations on the Mn4CaO5 cluster demonstrate a remarkable speed-up of up to 16 fater than Kylin 1.0. Moreover, a more user-friendly and efficient algorithm [J. Chem. Theory Comput. 17, 3414 (2021)] for sampling configurations from DMRG wavefunction is implemented as well. Additionally, we have also implemented a spin-adapted version of the externally contracted multi-reference configuration interaction (EC-MRCI) method [J. Phys. Chem. A 128, 958 (2024)], further enhancing the program’s efficiency and accuracy for electron correlation calculations.
Convergent hierarchies of theories for calculating many-body vibrational ground and excited-state wave functions, such as M{o}ller-Plesset perturbation theory or coupled cluster theory, tend to rely on matrix-algebraic manipulations of large, high-dimensional arrays of anharmonic force constants, tasks which require large amounts of computer storage space and which are very difficult to implement in a parallel-scalable fashion. On the other hand, existing quantum Monte Carlo (QMC) methods for vibrational wave functions tend to lack robust techniques for obtaining excited-state energies, especially for large systems. By exploiting analytical identities for matrix elements of position operators in a harmonic oscillator basis, we have developed stochastic implementations of the size-extensive vibrational self-consistent field (MC-XVSCF) and size-extensive vibrational M{o}ller-Plesset second-order perturbation (MC-XVMP2) theories which do not require storing the potential energy surface (PES). The programmable equations of MC-XVSCF and MC-XVMP2 take the form of a small number of high-dimensional integrals evaluated using Metropolis Monte Carlo techniques. The associated integrands require independent evaluations of only the value, not the derivatives, of the PES at many points, a task which is trivial to parallelize. However, unlike existing vibrational QMC methods, MC-XVSCF and MC-XVMP2 can calculate anharmonic frequencies directly, rather than as a small difference between two noisy total energies, and do not require user-selected coordinates or nodal surfaces. MC-XVSCF and MC-XVMP2 can also directly sample the PES in a given approximation without analytical or grid-based approximations, enabling us to quantify the errors induced by such approximations.