There are strong existing limitations on calculations of bound excited states in large molecules, and for resonance states in any polyatomic molecule. These limitations partly reflect deficiencies of existing software and algorithms. But more fundamentally they also reflect limitations of existing methods and models, particularly for resonances, or where multiple electrons are excited, or strong electron correlations are in play. The overall goal of this project is to make meaningful progress by coupling new and improved models for bound and metastable excited states from physical scientists with advances on underlying methodological challenges in applied mathematics, and practical realization via high performance computing.


Physical Sciences Challenges

There are three principal objectives associated with the chemical sciences. First is the development of new methods and associated software implementations for simulating bound excited states of large molecules (up to the 200-500 atom regime), including systems where strong electron correlations are important, as well as dynamic correlation. The potential benefit is that while there are existing methods that can achieve good accuracy for such states of small molecules, these new methods open up a new range of large-molecule applications, which include aspects of the photophysics and chemistry associated with natural and artificial light harvesting that are not yet well understood. The second goal is the adaptation of electronic structure methods to permit the simulation of resonance states of polyatomic molecules, where an electron will autodetach. The potential benefit is that no capability of this type currently exists, despite the fact that interesting systems ranging from radiation-induced damage to DNA, the electron dynamics probed in experiments using new attosecond light sources, and the lowest excited states of various biochromophores involve resonances. The third objective is the development of reduced scaling implementations of existing coupled cluster methods for electronic excited states. The potential benefit is the ability to apply these reliable and proven methods for calculating excited states to larger molecules than was previously possible, and the potential ability to apply the same underlying ideas for reduced scaling to other methods, such as those in the first two objectives.

Computer Science Challenges

There are three principal objectives associated with the computer science that constitutes a complementary, enabling part of this project. The first goal is the development and refinement of an object-oriented tensor library, both for the traditional real matrices associated with theories of bound excited states, and for the complex matrices that naturally arise in treating resonance states. This goal is needed to permit the efficient implementation of the methods discussed in the three chemical sciences objectives, within a unified framework that is immensely easier and more extensible than a procedural approach. The second goal is to exploit this extensibility by parallelizing the tensor library using a distributed hybrid approach (MPI+threads) that is targeted for deployment on leadership class computers (but is also flexible enough to perform well on mid-range clusters). This is necessary to enable achievement of the application goals that are targeted for bound and resonance excited states. The third computer science goal is the distribution and propagation of the software that is developed under this work, both as an open source library for developers, and also as a significant update to a widely used, fully integrated simulation package for end-users of the application.

Applied mathematics challenges

There are also three principal objectives associated with applied mathematics that underpin these excited state methods, and also underpin the tensor libraries used to implement them. First is the exploration and implementation of rank reduction and compression schemes for the tensors that arise in excited state electronic structure calculations, and their use to develop reduced scaling excited state methods. This development in the framework of the tensor library will permit the new implementations that have much lower scaling of computational cost with molecular size, without affecting high-level codes. The second objective is the deployment of optimally efficient eigensolvers for the symmetric real eigenvalue problems that yield bound excited state energies, and the extension and development of eigensolvers for the complex eigenvalue problems that arise in treating resonance states. These developments are needed to permit efficient implementation of both classes of method. The third objective is the deployment and further development of robust linear solvers and effective preconditioners to underpin the iterative eigensolvers discussed above. This development is necessary to ensure overall efficiency of the excited state simulation methods developed here.


Zimmerman PM, Bell F, Goldey M, Bell AT, Head-Gordon M.
Restricted active space spin-flip configuration interaction: Theory and examples for multiple spin flips with odd numbers of electrons.
J Chem Phys. 2012;137(16):164110.

Bell F, Zimmerman PM, Casanova D, Goldey M, Head-Gordon M.
Restricted active space spin-flip (RAS-SF) with arbitrary number of spin-flips.
Phys Chem Chem Phys. 2013;15(1):358-366.

Epifanovsky E, Wormit M, Kus T, Landau A, Zuev D, Khistyaev K, et al.
New implementation of high-level correlated methods using a general block-tensor library for high-performance electronic structure calculations.
J Comp Chem. 2013;34:2293-2309.

Epifanovsky E, Zuev D, Feng X, Khistyaev K, Shao Y, Krylov AI.
General implementation of resolution-of-identity and Cholesky representations of electron-repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks.
J Chem Phys. 2013;139:134105.

Wang S, Li XS, Xia J, Situ Y, de Hoop MV.
Efficient Parallel Algorithms for Solving Linear Systems with Hierarchically Semiseparable Structures.
SIAM J Scientific Computing. 2013;35(6):C519-C544.

Yamazaki I, Li XS, Rouet FH, Uçar B.
On partitioning and reordering problems in a hierarchically parallel hybrid linear solver.
In: Proceedings of IEEE PDSEC Workshop, IPDPS 2013. Boston, MA; 2013. .

Yamazaki I, Li XS. PDSLin: Parallel Domain decomposition Schur complement based Linear solver;.

Ibrahim K, Williams S, Epifanovsky E, Krylov A.
Analysis and Tuning of Libtensor Framework on Multicore Architectures.
In: High Performance Computing Conference (HIPC); 2014. .

Mayhall NJ, Goldey M, Head-Gordon M.
A quasidegenerate second order perturbation theory approximation to the restricted active space spin flip method for excited states and strong correlations.
J Chem Theor Comput. 2014;10:589-599.

Mayhall NJ, Head-Gordon M.
Increasing spin-flips and decreasing cost: Perturbative corrections for external singles to the complete active space spin flip model for low-lying excited states and strong correlation.
J Chem Phys. 2014;141:044112.

Mayhall NJ, Horn PR, Sundstrom EJ, Head-Gordon M.
Spin-flip non-orthogonal configuration interaction: a variational and almost black-box method for describing strongly correlated molecules.
Phys Chem Chem Phys. 2014;16(41):22694-22705.

Mayhall NJ, Head-Gordon M.
Computational quantum chemistry for single Heisenberg spin couplings made simple: Just one spin flip required.
J Chem Phys. 2014;141(13):134111.

Napov A, Li XS.
An Algebraic Multifrontal Preconditioner That Exploits the Low-rank Property.
Numer Lin Alg Appl. 2014;Submitted.

Baboulin M, Li XS, Rouet FH.
Using Random Butterfly Transformations to Avoid Pivoting in Sparse Direct Methods.
In: Proc. of VECPAR’14 11th International Meeting High Performance Computing for Computational Science. Eugene, Oregon; 2014. .

Wang S, Li XS, Rouet FH, Xia J, de Hoop MV.
A Parallel Geometric Multifrontal Solver Using Hierarchically Semiseparable Structures.
ACM Trans Math Software. 2013;(revised).

Sao P, Vuduc R, Li XS.
A distributed CPU-GPU sparse direct solver.
In: Proceedings of Euro-Par 2014 Parallel Processing, submitted. Porto, Portugal; 2014. .

Zuev D, Jagau TC, Bravaya KB, Epifanovsky E, Shao Y, Sundstrom E, et al.
Complex absorbing potentials within EOM-CC family of methods: Theory, Implementation, and Benchmarks.
J Chem Phys. 2014;141(2):024102.

Shao Y, Gan Z, Epifanovsky E, Gilbert ATB, Wormit M, Kussmann J, et al.
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package.
Mol. 2015;113:184-215.

White AF, Head-Gordon M, McCurdy CW.
Complex basis functions revisited: Implementation with applications to carbon tetrafluoride and aromatic N-containing heterocycles within the static-exchange approximation.
J Chem Phys. 2015;142(5):054103.

Zuev D, Vecharynski E, Yang C, Orms N, Krylov AI.
New algorithms for iterative matrix-free eigensolvers in quantum chemistry.
J Comput Chem. 2015;36:273-284.

Manzer SF, Epifanovsky E, Head-Gordon M.
Efficient Implementation of the Pair Atomic Resolution of the Identity Approximation for Exact Exchange for Hybrid and Range- Separated Density Functionals.
J Chem Theor Comput. 2015;11:518-527.

Ghysels P, Rouet FH, Li XS, Williams S, Ghysels P.
An efficient multicore implementation of a novel HSS-structured multifrontal solver using randomized sampling.
SIAM J Scientific Computing. 2015;(submitted).

STRUMPACK: STRUctured Matrices PACKages;.

Rouet FH, Li XS, Ghysels P.
A distributed-memory package for dense hierarchically semi-separable matrix computations using randomization.
ACM TransSoftware. 2014;(submitted).

Brabec J, Yang C, Epifanovsky E, Krylov AI, Ng E.
Reduced-cost sparsity-exploiting algorithm for solving coupled-cluster equations.
J Chem Phys. 2015;(submitted).

Sao P, Liu X, Vuduc R, Li XS.
A Sparse Direct Solver for Distributed Memory Xeon Phi-accelerated Systems.
In: 29th IEEE International Parallel & Distributed Processing Symposium (IPDPS). Hyderabad, India; 2015. .


MEE SciDAC kickoff meeting presentation


MEE SciDAC early progress presentation


MEE SciDAC 2014 progress presentation



Tensor algebra library for computational chemistry. The library is a set of performance linear tensor algebra routines for large tensors found in post-Hartree-Fock methods. The routines are able to dynamically balance the use of physical memory (RAM) and disk and perform computations on multiple CPUs or CPU cores in a shared-memory environment.
Download Libtensor 2.2 (BSD License)
If used, please cite J. Comput. Chem. 2013, 34, 2293.

Q-Chem is a comprehensive ab initio quantum chemistry package for accurate predictions of molecular structures, reactivities, and vibrational, electronic and NMR spectra. With Q-Chem as the development platform for the new electronic structure codes, we have developed and implemented the following methods:
• RAS-SF : Variational method for describing excited states and strongly correlated molecules
• SF-CAS(h,p), SF-CAS(S) : Perturbative methods for describing excited states and strongly correlated molecules, including the possibility for including dynamical correlation.
• SF-NOCI : Variational method which uses non-orthogonal orbitals to achieve a more compact wavefunction, which still includes orbital relaxation.
• Complex Basis-Functions : An open-ended and efficient implementation of complex basis functions for describing low energy shape resonances in unbound systems.

STRUctured Matrices PACKages - is a package for computations with sparse and dense structured matrices, i.e., matrices that exhibit some kind of low-rank property. STRUMPACK uses Hierarchical Semi-Separable representations (HSS) and Randomized Sampling techniques.