PERFORMANCE PREDICTION OF PARALLEL SELF CONSISTENT FIELD COMPUTATION

A study is made of the vibrational energy levels and the corresponding oscillation dynamics of the clusters Xe4He2, Xe3He2, and I24He. XeHe2 is a representative of the ‘‘three ball’’ clusters, while I2He is a prototype of the ‘‘stick and ball’’ systems. The treatment is based on the vibrational self-consistent field (SCF) method, which introduces an approximate separation of the modes involved. Success of the method depends on an adequate choice of the coordinates that are being mutually separated. We use physical arguments, based on mass ratios and potential function considerations, as well as comparative SCF calculations in different coordinate systems, to determine the appropriate modes for each system. Numerically exact results are also obtained by configuration interaction (CI) calculations using a basis of SCF states. The SCF and CI calculations include all modes and employ realistic potentials. Several states that are both rotationally and vibrationally excited are also calculated. The main conclusions are: (1) Hyperspherical coordinates are the best modes for XeHe2; ellipsoidal coordinates are best for I2He. In each case, the ‘‘good modes’’ SCF gives energies in remarkable agreement with the exact (CI) ones. (2) XeHe2 resembles a quantum liquid drop: Even in the ground state, it is delocalized over and between the (two) classical equilibrium structures. (3) Structural distributions, rather than rigid geometry, are essential for the description of such floppy clusters. The single-mode SCF wave functions offer a highly accurate description of the structural distributions. (4) There is a sequence of bound, excited rotational states of I2He in which the He precesses around the I2 axis. The amplitude of the I2He bending vibrations are very large (θA<20°), but none of the bound states involves a full rotational motion around the I2 stick (with angular momentum normal to the axis). The SCF method with the ‘‘good coordinates’’ proposed here is expected to yield results of similar high accuracy for any cluster of the ‘‘three balls’’ or ‘‘stick and ball’’ types.

To exploit the chemical asymmetry of diblock copolymer chains on the design of high-performance switch sensors, we propose an analytically tractable model system which contains an adsorption-responsive diblock copolymer in an otherwise inert brush, and study its phase transitions by using both analytical theory and self-consistent field calculations. The copolymer chain is chemically asymmetric in the sense that the two blocks assume different adsorption strengths, which is characterized by the defined adsorption ratio. We found that the conformation states, the number of stable phases, and transition types are mainly controlled by the length of each block and the adsorption ratio. In particular, when the length of the ungrafted block is longer than the brush chains, and the adsorption ratio is smaller than a critical value, the copolymer chain shows three thermodynamically stable states, and undergoes two unsynchronous transitions, where the two blocks respond to the adsorption in a different manner, when the adsorption changes from weak to sufficiently strong. For this kind of three-state transition, the transition point, transition barrier, and transition width are evaluated by using the self-consistent field method, and their scaling relationship with respect to the system parameters is extracted, which matches reasonably well with the predictions from the analytical theory. The self-consistent field calculations also indicate that the conformational transitions involved in the three-state transition process are sharp with a low energy barrier, and interestingly, barrier-free transitions are observed. Our finding shows that the three-state transitions not only specify a region where high performance unsynchronous switch sensors can be exploited, but may also provide a useful model understanding the unsynchronous biological processes.

We present an extensive numerical study on the behavior of spherical brushes confined into a spherical cavity. Self-consistent field (SCF) and off-lattice Monte Carlo (MC) techniques are used in order to determine the monomer and end-chain density profiles and the cavity pressure as a function of the brush properties. A comparison of the results obtained via SCF, MC, and the Flory theory for polymer solutions reveals SCF calculations to be a valuable alternative to MC simulations in the case of free and softly compressed brushes, while the Flory's theory accounts remarkably well for the pressure in the strongly compressed regime. In the range of high compressions, we have found the cavity pressure P to follow a scale relationship with the monomer volume fraction v, P approximately v(alpha). SCF calculations give alpha=2.15+/-0.05, whereas MC simulations lead to alpha=2.73+/-0.04. The underestimation of alpha by the SCF method is explained in terms of the inappropriate account of the monomer density correlations when a mean field approach is used.

In this article, two examples have been designed to be used for teaching geometries of coordination compounds by using computational chemistry, including molecular dynamics and quantum chemistry calculations. Specifically, we describe three kinds of software packages, molclus, GFN2-xTB and ORCA, and show how they can be used to predict the geometries of [Zn(NH3)4]2+ and [Cu(NH3)4]2+. All assignments are aimed at helping students gain practice with computational chemistry software while at the same time understanding the differences between tetrahedral and square planar configurations.

We introduce PSCF+, an extended and improved open-source software package for polymer self-consistent field (SCF) calculations of block copolymer self-assembly. PSCF+ supports various chain models (including the continuous Gaussian chains, discrete Gaussian chains, and freely jointed chains), nonbonded isotropic pair repulsions (including the Dirac δ-function, Gaussian, soft-sphere, and dissipative particle dynamics potentials), and system compressibility (compressible vs incompressible), thus enabling direct comparisons with molecular simulations and field-theoretic simulations based on the same model system without any parameter-fitting. Several recently proposed algorithms are implemented in PSCF+ to greatly reduce the GPU memory usage and speed-up the SCF calculations, including the Richardson-extrapolated pseudospectral methods for solving the modified diffusion equations, the crystallographic discrete cosine transforms taking advantage of the partial symmetry of some ordered phases, and the "slice" algorithm for storing chain propagators. It also avoids redundant calculations and storage of propagators for chain architectures such as bottlebrush block copolymers, and uses an improved iterative scheme for solving SCF equations in athermal solvent conditions. Last but not least, it implements the automated calculation along a path to efficiently calculate free-energy curves and phase boundaries. PSCF+ is freely available and remains under active development, with further extensions planned to broaden its applicability to more complex polymeric systems.

A hybrid analytical-numerical integration scheme is introduced to accelerate the Fock build in self-consistent field (SCF) and time-dependent density functional theory (TDDFT) calculations. To evaluate the Coulomb matrix J[D], the density matrix D is first decomposed into two parts, the superposition of atomic density matrices D⊕A and the rest DR = D-D⊕A. While J[D⊕A] is evaluated analytically, J[DR] is evaluated fully numerically [with the multipole expansion of the Coulomb potential (MECP)] during the SCF iterations. Upon convergence, DR is further split into those of near (DRC) and distant (DRL) atomic orbital (AO) pairs, such that J[DRC] and J[DRL] are evaluated seminumerically and fully numerically (with MECP). Such a hybrid J-build is dubbed "analytic-MECP" (aMECP). Likewise, the analytic evaluation of K[D⊕A] and seminumerical evaluation of K[DR] are also invoked for the construction of the exchange matrix K[D] during the SCF iterations. The chain-of-spheres (COSX) algorithm [Chem. Phys. 356, 98 (2009]) is employed for K[DR] but with a revised construction of the S-junctions for overlap AO pairs. To distinguish from the original COSX algorithm (which does not involve the partition of the density matrix D), we denote the presently revised variant as COSx. Upon convergence, DR is further split into those of near (DRC) and distant (DRL) AO pairs followed by a rescaling, leading to and , respectively. and are then evaluated analytically and seminumerically (with COSx), respectively. Such a hybrid K-build is dubbed "analytic-COSx" (aCOSx). Extensive numerical experimentations reveal that the combination of aMECP and aCOSx is highly accurate for ground state SCF calculations ( error in energy) and is particularly efficient for calculations of large molecules with extended basis sets. As for TDDFT excitation energies, a medium grid for MECP and a coarse grid for COSx are already sufficient.

Optical properties can be determined by either the transverse dielectric function ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\perp}}}$(q,\ensuremath{\omega}) or the longitudinal dielectric function ${\mathrm{\ensuremath{\epsilon}}}_{\mathcal{n}}$(q,\ensuremath{\omega}) in the long wavelength limit, i.e., q\ensuremath{\rightarrow}0. By expressing ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\perp}}}$(q\ensuremath{\rightarrow}0,\ensuremath{\omega}) in terms of density response functions, we calculate the third, fifth, and seventh frequency moments of Im${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\perp}}}$(q\ensuremath{\rightarrow}0,\ensuremath{\omega}) in addition to the first frequency moment, the well-known conductivity sum rule. While the third and fifth moments reflect the inhomogeneity of the system, correlation effects contribute explicitly to the seventh moment. In addition, the frequency moments of Im[-1/${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\parallel}}}$(q\ensuremath{\rightarrow}0,\ensuremath{\omega})] can be constructed from these moments. The dielectric functions evaluated in a self-consistent field (SCF) approximation, such as the random phase approximation (RPA) or the adiabatic local density approximation (ALDA), satisfy the first three odd frequency moments provided the single particle states on which the SCF calculation is based are calculated in the corresponding SCF approximation. The seventh frequency moment constitutes a severe requirement that ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\perp}}}$(q\ensuremath{\rightarrow}0,\ensuremath{\omega}) evaluated in the RPA or the ALDA cannot satisfy. This is demonstrated for nearly free electron systems.

The modeling of physical phenomena in computational fracture mechanics, computational fluid dynamics and other fields is based on solving systems of partial differential equations (PDEs). When PDEs are defined over geometrically complex domains, they often do not admit closed form solutions. In such cases, they are solved approximately using discretizations of domains into simple elements like triangles and quadrilaterals in two dimensions (2D), and tetrahedra and hexahedra in three dimensions (3D). These discretizations are called finite element meshes. Many applications, for example, real-time computer assisted surgery, or crack propagation from fracture mechanics, impose time and/or mesh size constraints that cannot be met on a single sequential machine. As a result, the development of parallel mesh generation algorithms is required. In this dissertation, we describe a complete solution for both sequential and parallel construction of guaranteed quality Delaunay meshes for 2D and 3D geometries. First, we generalize the existing 2D and 3D Delaunay refinement algorithms along with theoretical proofs of mesh quality in terms of element shape and mesh gradation. Existing algorithms are constrained by just one or two specific positions for the insertion of a Steiner point inside a circumscribed disk of a poorly shaped element. We derive an entire 2D or 3D region for the selection of a Steiner point (i.e., infinitely many choices) inside the circumscribed disk. Second, we develop a novel theory which extends both the 2D and the 3D Generalized Delaunay Refinement methods for the concurrent and mathematically guaranteed independent insertion of Steiner points. Previous parallel algorithms are either reactive relying on implementation heuristics to resolve dependencies in parallel mesh generation computations or require the solution of a very difficult geometric optimization problem (the domain decomposition problem) which is still open for general 3D geometries. Our theory solves both of these drawbacks. Third, using our generalization of both the sequential and the parallel algorithms we implemented prototypes of practical and efficient parallel generalized guaranteed quality Delaunay refinement codes for both 2D and 3D geometries using existing state-of-the-art sequential codes for traditional Delaunay refinement methods. On a heterogeneous cluster of more than 100 processors our implementation can generate a uniform mesh with about a billion elements in less than 5 minutes. Even on a workstation with a few cores, we achieve a significant performance improvement over the corresponding state-of-the-art sequential 3D code, for graded meshes.

Parallelization of an existing sequential application to achieve a good speed-up on a data-parallel infrastructure is quite difficult and time consuming effort. One of the important steps towards this is to assess whether the existing application in its current form can be parallelized to get the desired speedup. In this paper, we propose a method of analyzing an existing sequential source code that contains data-parallel loops, and give a reasonably accurate prediction of the extent of speedup possible from this algorithm. The proposed method performs static and dynamic analysis of the sequential source code to determine the time required by various portions of the code, including the data-parallel portions. Subsequently, it uses a set of novel invariants to calculate various bottlenecks that exists if the program is to be transferred to a GPGPU platform and predicts the extent of parallelization necessary by the GPU in order to achieve the desired end-to-end speedup. Our approach does not require creation of GPU code skeletons of the data parallel portions in the sequential code, thereby reducing the performance prediction effort. We observed a reasonably accurate speedup prediction when we tested our approach on multiple well-known Rodinia benchmark applications, a popular matrix multiplication program and a fast Walsh transform program.

The symmetry orbital-symmetry orbital tensor method is applied to the evaluation of molecular integrals (one-electron and two-electron integrals) and the symmetry-orbital-tensor and self-consistent-field (SOT-SCF) calculations. A calculation scheme is proposed to simplify the evaluation of integrals and a key equation is derived to reduce the computation efforts in SCF iterations. According to the key equation, compared with the traditional SCF method, the computation efficiencies including CPU timing and external disk (or internal memory) requirement increase in the magnitude of the square of the order of a point group. The new SOT method is expected to be useful in the theoretical calculations of large molecular systems of high point group symmetries.

The transformative impact of modern computational paradigms and technologies, such as high-performance computing (HPC), quantum computing, and cloud computing, has opened up profound new opportunities for scientific simulations. Scalable computational chemistry is one beneficiary of this technological progress. The main focus of this paper is on the performance of various quantum chemical formulations, ranging from low-order methods to high-accuracy approaches, implemented in different computational chemistry packages and libraries, such as NWChem, NWChemEx, Scalable Predictive Methods for Excitations and Correlated Phenomena, ExaChem, and Fermi-Löwdin orbital self-interaction correction on Azure Quantum Elements, Microsoft's cloud services platform for scientific discovery. We pay particular attention to the intricate workflows for performing complex chemistry simulations, associated data curation, and mechanisms for accuracy assessment, which is demonstrated with the Arrows automated workflow for high throughput simulations. Finally, we provide a perspective on the role of cloud computing in supporting the mission of leadership computational facilities.

Molecular visualization software has the common objective of manipulation and interpretation of data from numerical simulations. They visualize many complicated molecular structures with personal computer and workstation, to help analyze a large quantity of data produced by various computational methods. However, users are often discouraged from using these tools for visualization and analysis due to the difficult and complicated user interface. In this regard, we have developed an easy-to-use three-dimensional molecular visualization and analysis program named POSMOL. This has been developed on the Microsoft Windows platform for the easy and convenient user environment, as a compact program which reads outputs from various computational chemistry software without editing or changing data. The program animates vibration modes which are needed for locating minima and transition states in computational chemistry, draws two and three dimensional (2D and 3D) views of molecular orbitals (including their atomic orbital components and these partial sums) together with molecular systems, measur es various geometrical parameters, and edits molecules and molecular structures.

A novel method is presented that significantly reduces the computational bottleneck of executing high-level, electronic structure calculations of the energies and their gradients for a large database that adequately samples the configuration space of importance for systems containing more than four atoms that are undergoing multiple, simultaneous reactions in several energetically open channels. The basis of the method is the high-degree of correlation that generally exists between the Hartree-Fock (HF) and higher-level electronic structure energies. It is shown that if the input vector to a neural network (NN) includes both the configuration coordinates and the HF energies of a small subset of the database, MP4(SDQ) energies with the same basis set can be predicted for the entire database using only the HF and MP4(SDQ) energies for the small subset and the HF energies for the remainder of the database. The predictive error is shown to be less than or equal to the NN fitting error if a NN is fitted to the entire database of higher-level electronic structure energies. The general method is applied to the computation of MP4(SDQ) energies of 68,308 configurations that comprise the database for the simultaneous, unimolecular decomposition of vinyl bromide into six different reaction channels. The predictive accuracy of the method is investigated by employing successively smaller subsets of the database to train the NN to predict the MP4(SDQ) energies of the remaining configurations of the database. The results indicate that for this system, the subset can be as small as 8% of the total number of configurations in the database without loss of accuracy beyond that expected if a NN is employed to fit the higher-level energies for the entire database. The utilization of this procedure is shown to save about 78% of the total computational time required for the execution of the MP4(SDQ) calculations. The sampling error involved with selection of the subset is shown to be about 10% of the predictive error for the higher-level energies. A practical procedure for utilization of the method is outlined. It is suggested that the method will be equally applicable to the prediction of electronic structure energies computed using even higher-level methods than MP4(SDQ).

We investigate interfacial properties between two highly incompatible polymers of different stiffness. The extensive Monte Carlo simulations of the binary polymer melt yield detailed interfacial profiles and the interfacial tension via an analysis of capillary fluctuations. We extract an effective Flory–Huggins parameter from the simulations, which is used in self-consistent field calculations. These take due account of the chain architecture via a partial enumeration of the single chain partition function, using chain conformations obtained by Monte Carlo simulations of the pure phases. The agreement between the simulations and self-consistent field calculations is almost quantitative, however, we find deviations from the predictions of the Gaussian chain model for high incompatibilities or large stiffnesses. The interfacial width at very high incompatibilities is smaller than the prediction of the Gaussian chain model, and decreases upon increasing the statistical segment length of the semiflexible component.

Ion pair interactions in aqueous solution and the role of explicit water molecules have been investigated using ab initio self-consistent reaction field (SCRF) calculations with and without some explicit water molecules. Both the Polarizable Continuum Model (PCM) and the Self-Consistent Isodensity surface Polarizable Continuum Model (SCIPCM) were used for this study. The results suggest that the inclusion of explicit water molecules on hydrogen bonding sites on a solute and the use of a continuum model to complete the hydration environment is more accurate than a continuum model alone. This procedure is also computationally more economical than an explicit bulk water model to represent ion pair interactions in aqueous solution. The results also demonstrate that the SCIPCM method is superior to the PCM method for the interaction of ion pairs, and that the PCM method should not be used for oppositely charged ion pairs until further improvements are introduced.