# Chao Yang

## Short Bio

Chao Yang received his Ph.D. in computational mathematics from Rice University in 1998. He worked at NEC Systems Lab, Inc, a subsidiary of NEC from 1998 to 1999. He was awarded the 1999 Householder fellow in scientific computing by Oak Ridge National Laboratory. He joined Lawrence Berkeley National Laboratory in 2000 and is currently a senior scientist. His research interests include:

- developing numerical algorithms and fast implementation to accelerate scientific simulations
- developing efficient and robust algorithms and implementations for solving inverse problems

His core expertise is in numerical linear algebra, optimization, large-scale data analysis, and high performance computing. Over the last several years, he has successfully used techniques developed in these areas to solve problems in electronic structure calculations, nuclear structure calculations, cavity design for accelerator models, single-particle analysis for cryo-electron microscopy, single molecular diffractive imaging, phase retrieval, ptychography, etc.

## Journal Articles

### Karol Kowalski, Raymond Bair, Nicholas P. Bauman, Jeffery S. Boschen, Eric J. Bylaska, Jeff Daily, Wibe A. de Jong, Thom Dunning, Niranjan Govind, Robert J. Harrison, Murat Keceli, Kristopher Keipert, Sriram Krishnamoorthy, Suraj Kumar, Erdal Mutlu, Bruce Palmer, Ajay Panyala, Bo Peng, Ryan M. Richard, T. P. Straatsma, Peter Sushko, Edward F. Valeev, Marat Valiev, Hubertus J. J. van Dam, Jonathan M. Waldrop, David B. Williams-Young, Chao Yang, Marcin Zalewski, Theresa L. Windus, "From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape", Chemical Reviews, March 31, 2021, doi: 10.1021/acs.chemrev.0c00998

### C. Yang, J. Brabec, L. Veis, D. B. Williams-Young, K. Kolwaski, "Solving Coupled Cluster Equations by the Newton Krylov Method", Frontiers in Chemistr, December 10, 2020, 8:987, doi: 10.3389/fchem.2020.590184

### D. B. Williams-Young, W. A. de Jong, H. J. J. van Dam and C. Yang, "On the Efficient Evaluation of the Exchange Correlation Potential on Graphics Processing Unit Clusters", Frontiers in Chemistry, December 10, 2020, 8:951, doi: 10.3389/fchem.2020.581058

### T. Hernandez, R. Van Beeumen, M. Caprio, C. Yang, "A greedy algorithm for computing eigenvalues of a symmetric matrix with localized eigenvectors", Numerical Linear Algebra and Applications, October 9, 2020, 28:e2341, doi: https://doi.org/10.1002/nla.2341

### D. B. Williams-Young, P. G. Beckman, C. Yang, "A Shift Selection Strategy for Parallel Shift-Invert Spectrum Slicing in Symmetric Self-Consistent Eigenvalue Computatio", ACM Tran. Math Software, October 1, 2020, 46, doi: 10.1145/3409571

### D. Camps, R. Van Beeumen, C. Yang, "Quantum Fourier Transform Revisited", Numerical Linear Algebra and Applications, September 15, 2020, 28:e2331, doi: https://doi.org/10.1002/nla.2331

### Shao-Jun Dong, Chao Wang, Yong-Jian Han, Chao Yang and Lixin He, "Stable diagonal stripes in the t–J model at nhbar = 1/8 doping from fPEPS calculations", npj Quantum Materials, May 8, 2020, 5:28, doi: https://doi.org/10.1038/s41535-020-0226-4

### C. T. Kelley, J. Bernholc, E. L. Briggs, S. Hamilton, L. Lin and C. Yang, "Mesh Independence of the Generalized Davidson Algorithm", Journal of Computational Physics, May 1, 2020, 409:109322, doi: https://doi.org/10.1016/j.jcp.2020.109322

### Kai-Hsin Liou, Chao Yang and James R.Chelikowsky, "Scalable Implementation of Polynomial Filering for Density Functional Theory Calculation in PARSEC", Computer Physics Communications, April 28, 2020, In press, doi: https://doi.org/10.1016/j.cpc.2020.107330

### Li Zhou, Chao Yang, Weiguo Gao, Talita Perciano, Karen M. Davies, Nicholas K. Sauter, "Subcellular structure segmentation from cryo-electron tomograms via machine learning", PLOS Journal of Computational Biology, April 2, 2020, submitte, doi: doi: https://doi.org/10.1101/2020.04.09.034025

### F. Henneke, L. Lin, C. Vorwerk, C. Draxl, R. Klein and C. Yang, "Fast optical absorption spectra calculations for periodic solid state systems", Communications in Applied Mathematics and Computational Science, March 16, 2020, in press,

### W. Hu, J. Liu, Y. Li, Z. Ding, C. Yang, J. Yang, "Accelerating Excitation Energy Computation in Molecules and Solids within Linear-Response Time-Dependent Density Functional Theory via Interpolative Separable Density Fitting Decomposition", J. Chem. Theory Comput., January 3, 2020, 16:964–973, doi: https://doi.org/10.1021/acs.jctc.9b01019

### L. Yang, Z. Wen, C. Yang and Y. Zhang, "`Block Algorithms with Augmented Rayleigh-Ritz Projections for Large-Scale Eigenpair Computation", Journal of Computational Mathematics, November 1, 2019, 37:889-915, doi: 10.4208/jcm.1910-m2019-0034

### B. Peng, R. Van Beeumen, D.B. Williams-Young, K. Kowalski, C. Yang, "Approximate Green’s function coupled cluster method employing effective dimension reduction", Journal of Chemical Theory and Computation, 2019, 15:3185-3196, doi: 10.1021/acs.jctc.9b00172

### P. Benner, V. Khoromskaia, B. N. Khoromskij and C. Yang, "Computing the density of states for optical spectra of molecules by low-rank and QTT tensor approximation", Journal of Computational Physics, April 1, 2019, 382:221-239, doi: https://doi.org/10.1016/j.jcp.2019.01.011

### Y. Li, Z. Wen, C. Yang, Y. Yuan, "A Semi-smooth Newton Method For semidefinite programs and its applications in electronic structure calculations", SIAM J. Sci. Comput., December 18, 2018, 40:A4131–A415, doi: 10.1137/18M1188069

### R. Van Beeumen, O. Marques, E.G. Ng, C. Yang, Z. Bai, L. Ge, O. Kononenko, Z. Li, C.-K. Ng, L. Xiao, "Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation", Journal of Computational Physics, 2018, 374:1031-1043, doi: 10.1016/j.jcp.2018.08.017

### J. Deusch, M. Shao, C. Yang, M. Gu, "A Robust and Efficient Implementation of LOBPCG", SIAM J. Sc. Comput., October 4, 2018, 40:C655–C676, doi: 10.1137/17M1129830

### M. C. Clement, J. Zhang, C. A. Lewis, C. Yang, Edward F. Valeev, "Optimized Pair Natural Orbitals for the Coupled Cluster Methods", J. Chem. Theory Comput., August 1, 2018, 14:4581–4589, doi: 10.1021/acs.jctc.8b00294

### R. Huang, J. Sun, C. Yang, "Recursive integral method with Cayley transformation", Numerical Linear Algebra with Applications, July 10, 2018, 25:1-12, doi: 10.1002/nla.2199

### Meiyue Shao, Felipe H. da Jornada, Lin Lin, Chao Yang, Jack Deslippe, Steven G. Louie, "A structure preserving Lanczos algorithm for computing the optical absorption spectrum", SIAM Journal on Matrix Analysis and Applications, 2018, 39:683--711, doi: 10.1137/16M1102641

### T. Ke, A. S. Brewster, S. X. Yu, D. Ushizima, C. Yang, N. K. Sauter, "A convolutional neural network-based screening tool for X-ray serial crystallography", JOURNAL OF SYNCHROTRON RADIATION, April 24, 2018, 25:665-670, doi: 10.1107/S1600577518004873

### A. S. Banerjee, L. Lin, P. Suryanarayana, C. Yang, J. E. Pask, "Two-level Chebyshev filter based complementary subspace method for pushing the envelope of large-scale electronic structure calculations", J. Chem. Theory Comput., April 16, 2018, 14:2930–2946, doi: 10.1021/acs.jctc.7b01243

### J. M. Kasper, D. B. Williams-Young, E. Vecharynski, C. Yang, X. Li, "A Well-Tempered Hybrid Method for Solving Challenging Time-Dependent Density Functional Theory (TDDFT) Systems", J. Chem. Theory Comput., March 16, 2018, 14:2034–2041, doi: 10.1021/acs.jctc.8b00141

### P. Benner, H. Fessbender, C. Yang, "Some remarks on the complex J-symmetric eigenproblem", Linear Algebra and its Applications, January 14, 2018, 544:407-442, doi: 10.1016/j.laa.2018.01.014

### Meiyue Shao, Hasan Metin Aktulga, Chao Yang, Esmond G. Ng, Pieter Maris, James P. Vary, "Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver", Computer Physics Communications, 2018, 222:1--13, doi: 10.1016/j.cpc.2017.09.004

### Mathias Jacquelin, Lin Lin, Chao Yang, "PSelInv--A distributed memory parallel algorithm for selected inversion: The non-symmetric case", Parallel Computing, 2018, 74:84--98,

### Victor Wen-zhe Yu, Fabiano Corsetti, Alberto Garcia, William P Huhn, Mathias Jacquelin, Weile Jia, Bjorn Lange, Lin Lin, Jianfeng Lu, Wenhui Mi, others, "ELSI: A unified software interface for Kohn--Sham electronic structure solvers", Computer Physics Communications, 2018, 222:267--285,

### M. Jacquelin, L. Lin and C. Yang, "PSelInv – A distributed memory parallel algorithm for selected inversion : the symmetric case", Parallel Computing, November 9, 2017, 74:84-98, doi: 10.1016/j.parco.2017.11.009

### W. Hu, L. Lin, R. Zhang, C. Yang, J. Yang, "Highly efficient photocatalytic water splitting over edge-modified phosphorene nanoribbons", J. Am. Chem. Soc., October 13, 2017, 139:15429–1543, doi: 10.1021/jacs.7b08474

### W. Hu, L. Lin, C. Yang, "Interpolative Separable Density Fitting Decomposition for Accelerating Hybrid Density Functional Calculations with Applications to Defects in Silicon", J. Chem. Theory Comput., September 29, 2017, 13:5420–5431, doi: 10.1021/acs.jctc.7b00807

### W. Hu, L. Lin, C. Yang, "Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations", J. Chem. Theory Comput, September 22, 2017, 13:5458–5467, doi: 10.1021/acs.jctc.7b00892

### V. Yu. F. Corsetti, A. García, W. P. Huhn, M. Jacquelin, W. Jia, B. Lange, L. Lin, J. Lu, W. Mi, A. Seifitokaldan, Á. Vazquez-Mayagoitia, C. Yang, H. Yang, V. Blum, "ELSI: A unified software interface for Kohn–Sham electronic structure solvers", Computer Physics Communications, September 7, 2017, 222:267-285, doi: 10.1016/j.cpc.2017.09.007

### R. Van Beeumen, D.B. Williams-Young, J.M. Kasper, C. Yang, E.G. Ng, X. Li, "Model order reduction algorithm for estimating the absorption spectrum", Journal of Chemical Theory and Computation, 2017, 13:4950-4961, doi: 10.1021/acs.jctc.7b00402

### E. Vecharynski, J. Brabec, M. Shao, N. Govind, C. Yang, "Efficient Block Preconditioned Eigensolvers for Linear Response Time-dependent Density Functional Theory", Computer Physics Communications, 2017, 221:42-52, doi: https://doi.org/10.1016/j.cpc.2017.07.017

We present two efficient iterative algorithms for solving the linear response eigenvalue problem arising fromthe time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously.The efficiency of the new algorithms is demonstrated by numerical examples.

### W. Hu, L. Lin, A. Banerjee, E. Vecharynski, C. Yang, "Adaptively compressed exchange operator for large scale hybrid density functional calculations with applications to the adsorption of water on silicene", J. Chem. Theory Comput., February 8, 2017, 13:1188–1198,

### E. Vecharynski and C. Yang, "Preconditioned iterative methods for eigenvalue counts", Lecture Notes in Computational Science, January 1, 2017,

### Mathias Jacquelin, Lin Lin, Chao Yang, "PSelInv—A distributed memory parallel algorithm for selected inversion: The symmetric case", ACM Transactions on Mathematical Software (TOMS), 2017, 43:21,

### M. Jacquelin, L. Lin and C. Yang, "A Distributed Memory Parallel Algorithm for Selected Inversion: the non-symmetric case", PMAA, December 30, 2016,

### Hasan Metin Aktulga, Md. Afibuzzaman, Samuel Williams, Aydın Buluc, Meiyue Shao, Chao Yang, Esmond G. Ng, Pieter Maris, James P. Vary, "A High Performance Block Eigensolver for Nuclear Configuration Interaction Calculations", IEEE Transactions on Parallel and Distributed Systems (TPDS), November 2016, doi: 10.1109/TPDS.2016.2630699

- Download File: ieeetpds-mfdn-lobpcg-rev.pdf (pdf: 889 KB)

### A. S. Banerjee, L. Lin, W. Hu, C. Yang and J. E. Pask, "Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations", Journal of Chemical Physics, October 1, 2016,

### R. Li, Y. Xi, E. Vecharynski, C. Yang, and Y. Saad, "A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems", SIAM Journal on Scientific Computing, Vol. 38, Issue 4, pp. A2512–A2534, 2016, doi: 10.1137/15M1054493

Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a Thick-Restart version of the Lanczos algorithm with deflation ('locking') and a new type of polynomial filters obtained from a least-squares technique. The resulting algorithm can be utilized in a 'spectrum-slicing' approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by extracting eigenpairs located in different sub-intervals independently from one another.

### Fabien Bruneval, Tonatiuh Rangel, Samia M. Hamed, Meiyue Shao, Chao Yang, Jeffrey B. Neaton, "MOLGW 1: many-body perturbation theory software for atoms, molecules, and clusters", Computer Physics Communications, 2016, 208:149–161, doi: 10.1016/j.cpc.2016.06.019

### Meiyue Shao, Lin Lin, Chao Yang, Fang Liu, Felipe H. da Jornada, Jack Deslippe and Steven G. Louie, "Low rank approximation in G0W0 calculations", Science China Mathematics, June 4, 2016, 59:1593–1612, doi: 10.1007/s11425-016-0296-x

### M. Jacquelin, L. Lin, W. Jia, Y. Zhao and C. Yang, "A Left-looking selected inversion algorithm and task parallelism on shared memory systems", April 9, 2016,

### J. R. Jones, F.-H. Rouet, K. V. Lawler, E. Vecharynski, K. Z. Ibrahim, S. Williams, B. Abeln, C. Yang, C. W. McCurdy, D. J. Haxton, X. S. Li, T. N. Rescigno, "An efficient basis set representation for calculating electrons in molecules", Journal of Molecular Physics, 2016, doi: 10.1080/00268976.2016.1176262

The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules. It uses a basis set of product sinc functions arrayed on a Cartesian grid, and yields 1 kcal/mol precision for valence transition energies with a grid resolution of approximately 0.1 bohr. The Coulomb matrix elements are replaced with matrix elements obtained from the kinetic energy operator. A resolution-of-the-identity approximation renders the primitive one- and two-electron matrix elements diagonal; in other words, the Coulomb operator is local with respect to the grid indices. The calculation of contracted two-electron matrix elements among orbitals requires only O(N log(N)) multiplication operations, not O(N^4), where N is the number of basis functions; N = n^3 on cubic grids. The representation not only is numerically expedient, but also produces energies and properties superior to those calculated variationally. Absolute energies, absorption cross sections, transition energies, and ionization potentials are reported for one- (He^+, H_2^+ ), two- (H_2, He), ten- (CH_4) and 56-electron (C_8H_8) systems.

### Z. Wen, C. Yang, X. Liu and Y. Zhang, "A Penalty-based Trace Minimization Method for Large-scale Eigenspace Computation", J. Sci. Comp., March 1, 2016, 66:1175-1203, doi: 10.1007/s10915-015-0061-0

### E. Vecharynski, C. Yang, and F. Xue, "Generalized preconditioned locally harmonic residual method for non-Hermitian eigenproblems", SIAM Journal on Scientific Computing, Vol. 38, No. 1, pp. A500–A527, 2016, doi: 10.1137/15M1027413

We introduce the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly useful for computing a subset of eigenvalues, and their eigen- or Schur vectors, closest to a given shift. The proposed method is based on block iterations and can take advantage of a preconditioner if it is available. It does not need to perform exact shift-and-invert transformation. Standard and generalized eigenproblems are handled in a unified framework. Our numerical experiments demonstrate that GPLHR is generally more robust and efficient than existing methods, especially if the available memory is limited.

### Wei Hu, Lin Lin, Chao Yang, Jun Dai and Jinlong Yang, "Edge-Modied Phosphorene Nano ake Heterojunctions as Highly Efficient Solar Cells", Nano Lett, February 5, 2016, 16:1675–1682, doi: 10.1021/acs.nanolett.5b04593

### L. Lin, Y. Saad and C. Yang, "Approximating spectral densities of large matrices", SIAM Review, February 1, 2016, 58:34–65, doi: 10.1137/130934283

### P. Li, X. Liu, M. Chen, P. Lin, X. Ren, L. Lin, C. Yang, L. He, "Large-scale ab initio simulations based on systematically improvable atomic basis", Computational Materials Science, February 1, 2016, 112:503–517, doi: doi:10.1016/j.commatsci.2015.07.004

### J. Brabec, C. Yang, E. Epifanovsky, A.I. Krylov, and E. Ng, "Reduced-cost sparsity-exploiting algorithm for solving coupled-cluster equations", Journal of Computational Chemistry, January 24, 2016, 37:1059–1067, doi: 10.1002/jcc.24293

### Meiyue Shao, Felipe H. da Jornada, Chao Yang, Jack Deslippe, Steven G. Louie, "Structure preserving parallel algorithms for solving the Bethe–Salpeter eigenvalue problem", Linear Algebra and its Applications, 2016, 488:148–167, doi: 10.1016/j.laa.2015.09.036

### M. van Setten; F. Carouso; S. Sharifzadeh; X. Ren; M. Scheffler; F. Liu; J. Lischner; L. Lin; J. Deslippe; S. Louie; C. Yang; F. Weigend; J. Neaton; F. Evers; P. Rinke, "GW 100: Benchmarking G0W0 for molecular systems", Journal of Chemical Theory and Computation, October 22, 2015,

### Jiri Brabec, Lin Lin, Meiyue Shao, Niranjan Govind, Chao Yang, Yousef Saad, Esmond G. Ng, "Fast Algorithms for Estimating the Absorption Spectrum within Linear Response Time-dependent Density Functional Theory", Journal of Chemical Theory and Computation, 2015, 11:5197–5208, doi: 10.1021/acs.jctc.5b00887

### M. Ulbrich, Z. Wen, C. Yang, D. Klockner, Z. Lu, "A proximal gradient method for ensemble density functional theory", SIAM J. Sci. Comp., June 20, 2015, 37:A1975--A20, doi: 10.1137/14098973X

### Mathias Jacquelin, Lin Lin, Chao Yang, "A Distributed Memory Parallel Algorithm for Selected Inversion : the Symmetric Case", To appear in ACM Transactions on Mathematical Software (TOMS), May 28, 2015,

### Fang Liu, Lin Lin , Derek Vigil-Fowlerd , Johannes Lischnerd, Alexander F. Kemper, , Sahar Sharifzadehe, Felipe H. da Jornadad, Jack Deslippef, Chao Yangc, Jeffrey B. Neaton, Steven G. Louied,, "Numerical integration for ab initio many-electron self energy calculations within the GW approximation", Journal of Computational Physics, April 1, 2015,

### E. Vecharynski, C. Yang, J. E. Pask, "A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix", Journal of Computational Physics, Vol. 290, pp. 73–89, 2015,

We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix *A*. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of *A*. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimal block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer.

### Wei Hu, Lin Lin and Chao Yang, "Edge reconstruction in armchair phosphorene nanoribbons revealed by discontinuous Galerkin density functional theory", Phys. Chem. Chem. Phys., 2015, Advance Article, February 11, 2015, doi: 10.1039/C5CP00333D

With the help of our recently developed massively parallel DGDFT (Discontinuous Galerkin Density Functional Theory) methodology, we perform large-scale Kohn–Sham density functional theory calculations on phosphorene nanoribbons with armchair edges (ACPNRs) containing a few thousands to ten thousand atoms. The use of DGDFT allows us to systematically achieve a conventional plane wave basis set type of accuracy, but with a much smaller number (about 15) of adaptive local basis (ALB) functions per atom for this system. The relatively small number of degrees of freedom required to represent the Kohn–Sham Hamiltonian, together with the use of the pole expansion the selected inversion (PEXSI) technique that circumvents the need to diagonalize the Hamiltonian, results in a highly efficient and scalable computational scheme for analyzing the electronic structures of ACPNRs as well as their dynamics. The total wall clock time for calculating the electronic structures of large-scale ACPNRs containing 1080–10 800 atoms is only 10–25 s per self-consistent field (SCF) iteration, with accuracy fully comparable to that obtained from conventional planewave DFT calculations. For the ACPNR system, we observe that the DGDFT methodology can scale to 5000–50 000 processors. We use DGDFT based ab initio molecular dynamics (AIMD) calculations to study the thermodynamic stability of ACPNRs. Our calculations reveal that a 2 × 1 edge reconstruction appears in ACPNRs at room temperature.

### D. Zuev, E. Vecharynski, C. Yang, N. Orms, and A.I. Krylov, "New algorithms for iterative matrix-free eigensolvers in quantum chemistry", Journal of Computational Chemistry, Vol. 36, Issue 5, pp. 273–284, 2015,

New algorithms for iterative diagonalization procedures that solve for a small set of eigen-states of a large matrix are described. The performance of the algorithms is illustrated by calculations of low and high-lying ionized and electronically excited states using equation-of-motion coupled-cluster methods with single and double substitutions (EOM-IP-CCSD and EOM-EE-CCSD). We present two algorithms suitable for calculating excited states that are close to a specified energy shift (interior eigenvalues). One solver is based on the Davidson algorithm, a diagonalization procedure commonly used in quantum-chemical calculations. The second is a recently developed solver, called the “Generalized Preconditioned Locally Harmonic Residual (GPLHR) method.” We also present a modification of the Davidson procedure that allows one to solve for a specific transition. The details of the algorithms, their computational scaling, and memory requirements are described. The new algorithms are implemented within the EOM-CC suite of methods in the Q-Chem electronic structure program.

### Wei Hu, Lin Lin, Chao Yang and Jinlong Yang, "Electronic structure and aromaticity of large-scale hexagonal graphene nanoflakes", J. Chem. Phys. 141, 214704 (2014), December 2, 2014, 141:214704, doi: 10.1063/1.4902806

- Download File: JCPGNFs.pdf (pdf: 3.7 MB)

With the help of the recently developed SIESTA-PEXSI method [L. Lin, A. García, G. Huhs, and C. Yang, J. Phys.: Condens. Matter26, 305503 (2014)], we perform Kohn-Sham density functional theory calculations to study the stability and electronic structure of hydrogen passivated hexagonal graphene nanoflakes (GNFs) with up to 11 700 atoms. We find the electronic properties of GNFs, including their cohesive energy, edge formation energy, highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap, edge states, and aromaticity, depend sensitively on the type of edges (armchair graphene nanoflakes (ACGNFs) and zigzag graphene nanoflakes (ZZGNFs)), size and the number of electrons. We observe that, due to the edge-induced strain effect in ACGNFs, large-scale ACGNFs’ edge formation energydecreases as their size increases. This trend does not hold for ZZGNFs due to the presence of many edge states in ZZGNFs. We find that the energy gaps E g of GNFs all decay with respect to 1/L, where L is the size of the GNF, in a linear fashion. But as their size increases, ZZGNFs exhibit more localized edge states. We believe the presence of these states makes their gap decrease more rapidly. In particular, when L is larger than 6.40 nm, we find that ZZGNFs exhibit metallic characteristics. Furthermore, we find that the aromatic structures of GNFs appear to depend only on whether the system has 4N or 4N + 2 electrons, where N is an integer.

### J. Kaye, L. Lin and C. Yang, "A posteriori error estimator for adaptive local basis functions to solve Kohn-Sham density functional theory", Comm. Math. Sci., January 5, 2014, 13:1741--1740, doi: http://dx.doi.org/10.4310/CMS.2015.v13.n7.a5

### H. M. Aktulga, L. Lin, C. Haine, E. G. Ng, C. Yang, "Parallel Eigenvalue Calculation based on Multiple Shift-invert Lanczos and Contour Integral based Spectral Projection Method", Parallel Computing, December 6, 2013, in press,

### H. M. Aktulga, C. Yang, E. G. Ng, P. Maris, J. P. Vary, "Improving the Scalability of a Symmetric Iterative Eigensolver for Multi-core Platforms", Concurrency and Computation: Practice & Experience, September 12, 2013, online, doi: 10.1002/cpe.3129

### L. Lin, M. Chen, C. Yang, L. He, "Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion", J Phsy: Condens Matter, 2013,

### L. Lin, C. Yang, "Elliptic preconditioner for accelerating the self-consistent field iteration in Kohn-Sham Density Functional Theory", SIAM J. Sci. Comp., 2013,

### H. Hu, C. Yang, K. Zhao, "Absorption correction A* for cylindrical and spherical crystals with extended range and high accuracy calculated by Thorkildsen & Larsen analytical method", in press Acta Crystallographica, A, 2012,

### D. Y. Parkinson, C. Yang, C. Knoechel, C. A. Larabell, M. Le Gros, "Automatic alignment and reconstruction of images for soft X-ray tomography", J Struct Biol, February 2012, 177:259--266, doi: 10.1016/j.jsb.2011.11.027

### Zaiwen Wen, Chao Yang, Xin Liu, Stefano Marchesini, "Alternating direction methods for classical and ptychographic phase retrieval", Inverse Problems, January 2012, 28:115010,

### L. Lin, C. Yang, J. Lu, L. Ying, W. E, "A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations", SIAM J. Sci. Comput., 2011, 33:1329,

### L. Lin, C. Yang, J. Meza, J. Lu, L. Ying, W. E, "SelInv -- An algorithm for selected inversion of a sparse symmetric matrix", ACM Trans. Math. Software, 2011, 37:40,

### Filipe RNC Maia, Chao Yang, Stefano Marchesini, "Compressive auto-indexing in femtosecond nanocrystallography", Ultramicroscopy, 2011, 111:807--811, LBNL 4598E,

## Conference Papers

### D. B. Williams-Young, C. Yang, "Parallel Shift-Invert Spectrum Slicing on Distributed Architectures with GPU Accelerators", ICPP20, ACM, August 1, 2020, 1-11, doi: https://doi.org/10.1145/3404397.3404416

### R. Van Beeumen, G. D. Kahanamoku-Meyer, N. Y. Yao and C. Yang, "A scalable matrix-free iterative eigensolver for studying many-body localization", HPCAsia2020: Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region, ACM, January 7, 2020, 179-187, doi: 10.1145/3368474.3368497

### Gianina Alina Negoita, James P. Vary, Glenn R. Luecke, Pieter Maris, Andrey M. Shirokov, Ik Jae Shin, Youngman Kim, Esmond G. Ng, Chao Yang, Matthew Lockner, Gurpur M. Prabhu, "Deep Learning: Extrapolation Tool for Ab Initio Nuclear Theory", CoRR, November 10, 2018,

### W. Hu, M. Shao, A. Cepelloti, F. H. Jornada, L. Lin, K. Thicke, C. Yang, S. Louie, "Accelerating Optical Absorption Spectra and Exciton Energy Computation via Interpolative Separable Density Fitting", International Conference on Computational Science (ICCS2018), Lecture Notes in Computer Science, Springer, Cham, June 12, 2018, 10861:604-617, doi: 10.1007/978-3-319-93701-4_48

### Mathias Jacquelin, Lin Lin, Weile Jia, Yonghua Zhao, Chao Yang, "A Left-Looking Selected Inversion Algorithm and Task Parallelism on Shared Memory Systems", Proceedings of the International Conference on High Performance Computing in Asia-Pacific Region, January 1, 2018, 54--63,

### William Huhn, Alberto Garcia, Luigi Genovese, Ville Havu, Mathias Jacquelin, Weile Jia, Murat Keceli, Raul Laasner, Yingzhou Li, Lin Lin, others, "Unified Access To Kohn-Sham DFT Solvers for Different Scales and HPC: The ELSI Project", Bulletin of the American Physical Society, American Physical Society, 2018,

### Meiyue Shao and Chao Yang, "Properties of Definite Bethe--Salpeter Eigenvalue Problems", Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing. EPASA 2015. Lecture Notes in Computational Science and Engineering, vol 117., 2017, 91--105, doi: 10.1007/978-3-319-62426-6_7

### E. Vecharynski and C. Yang, "Preconditioned iterative methods for eigenvalue counts", to appear in Proceedings of International Workshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, in Lecture Notes in Computational Science and Engineering, Springer, 2016,

We describe preconditioned iterative methods for estimating the number of eigenvalues of a Hermitian matrix within a given interval. Such estimation is useful in a number of applications.In particular, it can be used to develop an efficient spectrum-slicing strategy to compute many eigenpairs of a Hermitian matrix. Our method is based on the Lanczos- and Arnoldi-type of iterations. We show that with a properly defined preconditioner, only a few iterations may be needed to obtain a good estimate of the number of eigenvalues within a prescribed interval. We also demonstrate that the number of iterations required by the proposed preconditioned schemes is independent of the size and condition number of the matrix. The efficiency of the methods is illustrated on several problems arising from density functional theory based electronic structure calculations.