REVIEW 3 major objections 5 minor 300 references
Relativistic Dirac-Coulomb-Breit Four-Component Multireference Perturbation Theory within the Small Tensor Product Distributed Active Space Framework
T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash
Pith's one-line read 4C-MRPT2 gives a working four-component multireference second-order perturbation theory for the Dirac-Coulomb-Breit Hamiltonian, and the benchmark calculations show the Breit contribution reaches about 4% of the total correlation energy…
desk verdict Useful first implementation of four-component MRPT2 with Breit, but the headline 4% Breit share for Xe rests on full-space PT2 energies that have no variational benchmark. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing machinery is the STP-DAS decomposition of the external configuration space, combined with the no-virtual-pair positive-energy spinor basis and the relativistic integral transformation for the DC, DCG, and DCB Hamiltonians. In STP-DAS, each external determinant is represented as a tensor product of sub-determinants from distributed active subspaces, and the Hamiltonian couplings between reference and external spaces are built as a sequence of tensor loops (the $\sigma$-build), so the full external expansion never has to be stored globally. The perturbative step uses an Epstein-Nesbet partitioning in which the zeroth-order Hamiltonian is block-diagonal in the reference space and diagonal on external determinants, giving $E^{(2)}_m = \sum_{K^+ \in Q^+} |\sigma_{m,K^+}|^2 / (E^{(0)}_m - E_{K^+K^+})$. The reference wavefunctions come from four-component CASCI or CASSCF with the positive-energy projection, and the AO-to-MO two-electron integral transformation is the main computational bottleneck once the Hamiltonian is upgraded from DC to DCB.
What would settle it
Run the xenon $^1S_0$ 4C-MRPT2 calculation in progressively larger basis sets (for example Dyall cv3z, cv4z, and beyond) and track the DCB-minus-DC correlation gap of 2.03 eV: if the gap grows by more than a few tenths of an electronvolt as the virtual space expands, the 4% Breit share is not converged. A second check is to compare with a treatment that includes negative-energy pair contributions, since the present method restricts the correlated space to positive-energy spinors.
Extended reading notes
Core claim
The central claim is that a scalable four-component multireference perturbation theory at second order can be built for the Dirac-Coulomb-Breit Hamiltonian, and that including the Breit interaction changes the quantitative picture of relativistic correlation in heavy atoms. Within the no-virtual-pair approximation, the second-order correction is evaluated as a sum over all single and double excitations from the active space into the positive-energy external spinor space, with the Epstein-Nesbet denominator $\Delta E = E^{(0)}_m - E_{K^+K^+}$. The paper reports that the DCB-minus-DC correlation energy difference grows from 0.05 eV for Ne to 2.03 eV for Xe, about 4% of the total correlation energy at this level, and that the Gaunt approximation overestimates this Breit contribution because it omits the partial cancellation from the gauge term. It further finds that the second-order correlation energy depends only weakly on whether the reference orbitals come from 4C-CASCI, 4C-CASSCF+, or 4C-CASSCF$\pm$, and that freezing high-lying virtual spinors is a cheap approximation while freezing the entire 3d core in gallium removes about a third of the correlation.
Load-bearing premise
The load-bearing premise is the no-virtual-pair approximation, namely that excluding negative-energy molecular spinors from both the reference and the perturbation leaves the reported correlation energies and the 4% Breit share essentially unchanged.
Editorial extensions
If this is right
- All-electron four-component correlation calculations for heavy elements become feasible, because the STP-DAS traversal keeps the external-space memory footprint small even when the perturbation runs over hundreds of spinors.
- The Breit interaction should be retained in four-component correlation treatments of heavy atoms: its contribution to the total correlation energy grows with nuclear charge and is roughly 4% for xenon at this level.
- The Gaunt-only approximation overestimates the Breit correlation because it omits the gauge term that cancels part of the Gaunt contribution, so DCB results are the safer benchmark.
- Frozen-virtual and frozen-core approximations are practical: discarding the top 20% of virtual spinors changes the correlation energy by under 1% for Ga and In, although freezing the full 3d core in Ga removes about a third of the correlation.
- Because the PT2 energy depends only weakly on the reference orbital choice, cheaper references such as canonical HF or 4C-CASCI can be used without losing much of the recovered dynamic correlation.
Reading between the lines
- Editorial inference: the observed weak dependence on reference orbitals suggests 4C-MRPT2 may be robust for excited states and bond-breaking regions, where state-specific orbital optimization is difficult; the paper demonstrates only ground states, so this remains to be tested.
- Editorial inference: since the AO-to-MO integral transformation dominates the DCB wall time (roughly 90%), the practical next step is to accelerate that transformation, for example by Cholesky decomposition or local fitting, which would extend the method to molecules containing several heavy centers.
- Editorial inference: extrapolating the reported trend, superheavy elements beyond xenon may show Breit correlation shares of several percent, large enough to affect bond lengths and spin-orbit splittings; this follows from the Z-trend but is not computed in the paper.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript develops a four-component multireference second-order perturbation theory (4C-MRPT2) within the STP-DAS framework for the Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), and Dirac-Coulomb-Breit (DCB) Hamiltonians. The formalism uses an Epstein-Nesbet partitioning with a multiconfigurational reference, a positive-energy (no-virtual-pair) Hilbert space, and STP-DAS tensor structure for the external space. Benchmarks cover computational timings for HBr, positive-negative-energy orbital-rotation effects for He-like ions, all-electron noble-gas correlation energies from Ne to Xe, frozen-core and frozen-virtual approximations for Ga and In, and fine-structure splittings for Ga and In. The paper's headline physical claim is that the Breit contribution to all-electron correlation energy increases rapidly with atomic number and is about 2.03 eV (approximately 4% of the total correlation energy) for Xe; it also reports that the method recovers fine-structure splittings to within a few percent of experiment.
Significance. The work is significant for relativistic quantum chemistry if the claims hold. It appears to be the first four-component MRPT2 formulation that treats DCB consistently at the reference and perturbation levels, and the STP-DAS implementation enables external spaces of about 2.17×10^10 determinants. The fine-structure splittings are falsifiable predictions and agree with experiment to within 0.3-4.3%, providing a strong internal check on the method. The formal equations are standard, and no fitted parameters enter the physical claims. However, the headline Breit correlation share is not yet supported by a variational or higher-order benchmark in the full-space regime where it is claimed, and the no-virtual-pair approximation is an acknowledged but unquantified limitation for that specific number.
major comments (3)
- [Section 3.3 (Tables 2 and 4)] The central quantitative claim, that the Breit contribution to the all-electron correlation energy of Xe is about 2.03 eV (~4%), is the difference between full-space 4C-MRPT2 DCB and DC energies in Table 2. The only variational check in the paper, Table 4, uses an identical (18e,58o) space for Xe and shows that 4C-MRPT2 overcorrelates by 1.47 eV (DC) and 1.59 eV (DCB) relative to 4C-MRCISD. In that shared space the Breit correlation difference is +0.15 eV for MRPT2 versus +0.28 eV for MRCISD, whereas the full-space Table 2 value is -2.13 eV. The PT2 error is therefore not a uniform shift: it changes the Breit difference by roughly a factor of two in a space about one-seventh the size of the full space (58 of 406 correlated spinors), and the difference changes sign between the shared and full spaces within MRPT2. Because the full-space calculation extends into high-energy core and virtual excitations, where second-order Epstein-Nesbet perturbation theory is least reliable, the 2.03 eV/4% figure has no demonstrated accuracy. The authors should provide a systematic enlargement benchmark (e.g., MRCI, CC, or higher-order PT in progressively larger spaces) or explicitly reframe the number as an exploratory NVPA estimate that is not yet quantitatively benchmarked.
- [Section 3.2 (No-virtual-pair approximation)] The NVPA is a stated limitation: the positive-energy-only Hilbert space excludes negative-energy dynamic correlation, and the paper acknowledges that the Breit interaction directly couples positive- and negative-energy states and that negative-energy dynamic correlation can only be captured through a QED treatment. This means the reported Breit correlation contribution is, by construction, incomplete. The paper's own Section 3.2 data show that positive-negative orbital-rotation effects grow strongly with Z and are largest for Breit/Gaunt; a similar growth is plausible for the neglected negative-energy dynamic correlation. The manuscript should either provide a quantitative estimate or bound for this omitted contribution (e.g., via two-component or QED-oriented benchmark studies of heavy atoms or ions) or consistently present the 4% claim as an NVPA-limited value.
- [Section 3.3 (Table 2 and surrounding text)] The text in Section 3.3 states that the MRCI correlation energy decreases to -2.35 eV for Xe and that the DC-DCB MRPT2 difference reaches 2.03 eV for Xe. Table 2 lists -2.439 eV for the former; for the latter, the CASSCF+ MRPT2 row gives DCB -55.473 eV and DC -53.343 eV, a difference of 2.130 eV, while the CASCI MRPT2 row gives 1.992 eV. The quoted numbers do not match any row of Table 2, so the discussion should clarify which reference method (CASCI vs CASSCF+) and which row is used for the headline claim, and the numbers must be made internally consistent.
minor comments (5)
- [Section 3.1 (Table 1)] The statement that the σ-build and PT2 steps are 'independent of the underlying Hamiltonian' should be clarified as independence of computational cost; the Hamiltonian enters through the transformed two-electron integrals, which are different for DC, DCG, and DCB.
- [Section 3.2] There is a typo in 'with he Dyall-cv3z basis'; this should read 'with the Dyall-cv3z basis'.
- [Section 2.6] The imaginary level-shift machinery is described but not used in the reported calculations; a sentence explaining why the chosen systems are free of intruder states would help the reader understand the practical need for Section 2.6.
- [Section 2.4 (Eqs. 14-16)] The notation in Eqs. (15)-(16), especially the barred Kronecker deltas and the index domains, is dense and would benefit from a worked example or more explicit definitions; the current presentation makes the implementation difficult for readers to verify.
- [Section 3.4 (Table 5)] The statement that the DC result for In arises from fortuitous cancellation is helpful; it would be useful to quantify the cancellation (e.g., by separating correlation and two-electron spin-orbit contributions) so that readers can assess how robust the agreement is.
Circularity Check
No circularity: the central Breit and fine-structure results are benchmarked independently, and cited prior work is infrastructure only.
full rationale
The paper's derivation chain is self-contained with respect to the claims it actually makes. 4C-MRPT2 is defined through the standard Epstein–Nesbet partitioning (Eqs. 9–12) and the second-order correction in Eq. (17); no parameter is fitted and then renamed as a prediction. The central quantitative claim, that the Breit contribution to the Xe correlation energy reaches about 4%, is computed as a direct DCB-minus-DC difference of independently evaluated full-space MRPT2 correlation energies in Table 2, not as a definitional identity or a fitted constant. The method is checked against an external variational benchmark in Table 4, where 4C-MRPT2 and 4C-MRCISD use identical correlation spaces, and against experimental fine-structure splittings in Table 5. Self-citations to earlier work (STP-DAS, 4C-CASSCF, Breit integral transformation) supply algorithmic and methodological infrastructure, but the physical conclusions do not reduce to those citations: the positive/negative-energy rotation analysis in Section 3.2 is presented as a numerical sensitivity study, and the paper explicitly flags that negative-energy dynamic correlation 'lies beyond the NVPA and can only be captured through a quantum electrodynamics (QED) treatment.' That limitation is a correctness or completeness risk, not circularity. Likewise, the absence of a variational benchmark at the full-space MRPT2 level for the Breit share is an accuracy concern, but it does not make the derivation circular. No step in the paper is equivalent, by construction, to its own inputs.
Assumptions & free parameters
free parameters (4)
- CASSCF active spaces for benchmarks =
6e,8o (noble gases); 2e,10o (He-like ions); 3e,8o (Ga, In)
- Frozen-virtual orbital-energy cutoff =
0.020 E_h
- MRCI correlation spaces =
34 spinors for Ne/Ar; 36 spinors for Kr/Xe
- Shared correlation spaces for Table 4 =
56 spinors (Ne); 58 spinors (Ar, Kr, Xe)
assumptions (5)
- domain assumption No-virtual-pair approximation: only positive-energy molecular spinors are correlated.
- standard math Restricted kinetic balance for the small-component basis.
- domain assumption Finite Gaussian nuclear model.
- domain assumption Epstein-Nesbet partition of the zeroth-order Hamiltonian.
- domain assumption STP-DAS representation of the external space is complete over all single and double excitations.
Cite this review
Pith. "Pith review of Relativistic Dirac-Coulomb-Breit Four-Component Multireference Perturbation Theory within the Small Tensor Product Distributed Active Space Framework." pith.science (2026). https://pith.science/paper/BTKDH5EO
@misc{pith2026260811529,
author = {Pith},
title = {Pith review of: Relativistic Dirac-Coulomb-Breit Four-Component Multireference Perturbation Theory within the Small Tensor Product Distributed Active Space Framework},
year = {2026},
howpublished = {\url{https://pith.science/paper/BTKDH5EO}},
note = {Machine review of arXiv:2608.11529}
}
read the original abstract
We present a four-component multireference second-order perturbation theory (4C-MRPT2) within the small tensor product distributed active space (STP-DAS) framework. The formulation is compatible with the Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG), and Dirac-Coulomb-Breit (DCB) Hamiltonians, and inherits the memory-efficient and massively parallel STP-DAS algorithm, enabling perturbative treatments over very large external spaces. Benchmark calculations on noble-gas and group-13 atoms demonstrate that 4C-MRPT2 efficiently recovers all-electron dynamic correlation while providing new insight into relativistic correlation effects. The calculations show that the Breit contribution to the correlation energy increases rapidly with atomic number and reaches approximately 4% of the total correlation energy for Xe. The method also shows that second-order correlation energies are only weakly dependent on the choice of multiconfigurational reference orbitals, and that frozen-core and frozen-virtual approximations substantially reduce computational cost with minimal loss of accuracy.
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Nonequilibrium Environment Dynamics in a Frequency-Dependent Polarizable Embedding Models , Author =. 2019 , Volume =. doi:10.1021/acs.jctc.8b00836 , Grants=
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2019 , Volume =
Generalized Hartree-Fock with Non-perturbative Treatment of Strong Magnetic Field: Application to Molecular Spin Phase Transition , Author =. 2019 , Volume =. doi:10.1021/acs.jctc.8b01140 , Grants=
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X-ray Absorption Signatures of Hydrogen-bond Structure in Water-Alcohol Solutions , Author=. 2019 , Volume =. doi:10.1002/qua.25802 , Grants=
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2019 , Volume =
On the Efficacy and High-Performance Implementation of Quaternion Matrix Multiplication , Author =. 2019 , Volume =. doi:, Grants=
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2018 , Volume =
Mapping Vibronic Couplings in Intramolecular Charge Transfer of a Solar Cell Dye with Polarization-Selective Two-Dimensional Electronic-Vibrational Spectroscopy , Author =. 2018 , Volume =. doi:10.1021/acs.jpclett.8b02752 , Grants=
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Petrone, A and Beck, R A and Kasper, Joseph M. and Crane, Matthew J. and Pauzauskie, Peter J. and Li, X , Title =. 2018 , doi =
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Huang, Chuyi and Liao, Xunfan and Gao, Ke and Zuo, Lijian and Lin, Francis and Shi, Xueliang and Li, Chang-Zhi and Liu, Hongbin and Li, Xiaosong and Liu, Feng and Chen, Yiwang and Chen, Hongzheng and Jen, Alex K.-Y. , title =. 2018 , doi =
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Zhao, Ting and Liu, Hongbin and Ziffer, Mark E. and Rajagopal, Adharsh and Zuo, Lijian and Ginger, David S. and Li, Xiaosong and Jen, Alex K. Y. , title =. 2018 , doi =
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Liu, Yu and Wolstenholme, Charles H. and Carter, Gregory C. and Liu, Hongbin and Hu, Hang and Grainger, Leeann S. and Miao, Kun and Fares, Matthew and Hoelzel, Conner A. and Yennawar, Hemant P. and Ning, Gang and Du, Manyu and Bai, Lu and Li, Xiaosong and Zhang, Xin , title =....
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Petrone, Alessio and Williams-Young, David B. and Sun, Shichao and Stetina, Torin F. and Li, Xiaosong , title=. 2018 , volume=. doi:10.1140/epjb/e2018-90170-1 , Grants=
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2018 , Volume =
Inverted Solvatochromic Stokes Shift in GFP-like Chromophores with Extended Conjugation , Author=. 2018 , Volume =. doi:10.1063/1674-0068/31/cjcp1806160 , Grants=
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2018 , Volume =
Interplay of Mobile Ions and Injected Carriers Creates Recombination Centers in Metal Halide Perovskites under Bias , Author =. 2018 , Volume =. doi:10.1021/acsenergylett.8b00505 , Grants=
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Computational Simulation of Vibrationally Resolved Spectra for Spin-Forbidden Transitions , Author =. Chirality , Year =. doi:10.1002/chir.22864 , Grants=
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2018 , Volume =
Anisotropic Polarizability-Induced Plasmon Transfer , Author =. 2018 , Volume =. doi:10.1021/acs.jpcc.8b02425 , Grants=
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Brozek, Carl K. and Zhou, Dongming and Liu, Hongbin and Li, Xiaosong and Kittilstved, Kevin R. and Gamelin, Daniel R. , title =. 2018 , doi =
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A. Wildman and E. Martinez-Baez and J. Fulton and G. Schenter and C. Pearce and A. Clark and X. Li , Title =. 2018 , Volume =. doi:10.1021/acs.jpclett.8b00642 , Grants =
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Radler, Joseph J. and Lingerfelt, David B. and Castellano, Felix N. and Chen, Lin X. and Li, Xiaosong , title =. 2018 , doi =
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Beck, Ryan and Petrone, Alessio and Kasper, Joseph M. and Crane, Matthew J. and Pauzauskie, Peter J. and Li, Xiaosong , title =. 2018 , doi =
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Kasper, Joseph M. and Lestrange, Patrick J. and Stetina, Torin F. and Li, Xiaosong , title =. 2018 , doi =
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Kasper, Joseph M. and Williams-Young, David B. and Vecharynski, Eugene and Yang, Chao and Li, Xiaosong , title =. 2018 , doi =
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Duc Nguyen and Joshua J. Goings and Huy A. Nguyen and Joseph Lyding and Xiaosong Li and Martin Gruebele , Title =. 2018 , doi =
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Ju, Dianxing and Dang, Yangyang and Zhu, Zonglong and Liu, Hongbin and Chueh, Chu-Chen and Li, Xiaosong and Wang, Lei and Hu, Xiaobo and Jen, Alex K.-Y. and Tao, Xutang , title =. 2018 , doi =
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Goings, Joshua J. and Lestrange, Patrick J. and Li, Xiaosong , Title =. 2018 , Pages =. doi:10.1002/wcms.1341 , Grants =
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2018 , Volume =
Current Development of Non-collinear Electronic Structure Theory , Author =. 2018 , Volume =. doi:10.1002/qua.25398 , Grants=
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Patrick J. Lestrange and Mark R. Hoffmann and Xiaosong Li , Title =. 2018 , Volume =. doi:10.1016/bs.aiq.2017.06.003 , Grants =
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Gao, Ke and Xu, Bo and Hong, Chaoshen and Shi, Xueliang and Liu, Hongbin and Li, Xiaosong and Xie, Linghai and Jen, Alex K-Y , title =. doi:https://doi.org/10.1002/aenm.201800809 , year =
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Liu, Hongbin and Brozek, Carl K. and Sun, Shichao and Lingerfelt, David B. and Gamelin, Daniel R. and Li, Xiaosong , Title =. 2017 , doi =
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Model Order Reduction Algorithm for Estimating the Absorption Spectrum , Author=. 2017 , Volume =. doi:10.1021/acs.jctc.7b00402 , Grants =
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2017 , Volume =
4-Tert-Butylpyridine Free Organic Hole Transporting Materials for Stable and Efficient Planar Perovskite Solar Cells , Author=. 2017 , Volume =. doi:10.1002/aenm.201700683 , Grants =
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Jennifer L. Stein and Molly I. Steimle and Maxwell W. Terban and Alessio Petrone and Simon J. L. Billinge and Xiaosong Li and Brandi M. Cossairt , Title =. 2017 , Volume =. doi:10.1021/acs.chemmater.7b03075 , Grants =
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2017 , Volume=
Molecular Vibration Induced Plasmon Decay , Author=. 2017 , Volume=. doi:10.1021/acs.jpcc.7b04451 , Grants=
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2017 , Volume =
Two-Component Non-Collinear Time-Dependent Spin Density Functional Theory for Excited State Calculations , Author =. 2017 , Volume =. doi:10.1021/acs.jctc.7b00104 , Grants=
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2017 , Volume =
Effective Inclusion of Mechanical and Electrical Anharmonicity in Excited Electronic States: the VPT2-TDDFT Route , Author =. 2017 , Volume =. doi:10.1021/acs.jctc.7b00218 , Grants=
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Petrone, Alessio and Williams-Young, David B. and Lingerfelt, David B and Li, Xiaosong , Title =. 2017 , Volume =. doi:10.1021/acs.jpca.7b02905 , Grants=
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Heidi D. Nelson and Stijn O. M. Hinterding and Rachel Fainblat and Sidney E. Creutz and Xiaosong Li and Daniel R. Gamelin , Title =. 2017 , Volume =. doi:10.1021/jacs.7b01924 , Grants=
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Lingerfelt, David B. and Lestrange, Patrick J. and Radler, Joseph J. and Brown-Xu, Samantha E. and Kim, Pyosang and Castellano, Felix N. and Chen, Lin X. and Li, Xiaosong , Title =. 2017 , Volume =. doi:10.1021/acs.jpca.6b12099 , Grants =
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2017 , Volume =
Doping Versatile n-Type Organic Semiconductors via Room-Temperature Solution-Processable Anionic Dopants , Author =. 2017 , Volume =. doi:10.1021/acsami.6b14375 , Grants=
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2017 , Volume =
Investigating the Role of Amine in InP Nanocrystal Syntheses: Destabilizing Cluster Intermediates by Z-Type Ligand Displacement , Author=. 2017 , Volume =. doi:10.1039/C6CC07952K , Grants =
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Zhu, Zonglong and Xu, Jing-Qi and Chueh, Chu-Chen and Liu, Hongbin and Li, Zhongan and Li, Xiaosong and Chen, Hongzheng and Jen, Alex K.-Y. , Title =. 2016 , Volume =. doi:10.1002/adma.201601745 , Grants =
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Lingerfelt and David B
Alessio Petrone and David B. Lingerfelt and David B. Williams-Young and Xiaosong Li , Title =. 2016 , Volume =. doi:10.1021/acs.jpclett.6b02292 , Grants =
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Williams-Young, David and Goings, Joshua J and Li, Xiaosong , Title =. 2016 , Volume =. doi:10.1021/acs.jctc.6b00693 , Grants =
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Li, Nan and Zhu, Zonglong and Chueh, Chu-Chen and Liu, Hongbin and Peng, Bo and Petrone, Alessio and Li, Xiaosong and Wang, Liduo and Jen, Alex K.-Y. , Title =. 2016 , doi =
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2016 , doi =
Quantum Confinement Effects on Optical Transitions in Nanodiamonds Containing Nitrogen Vacancies , Author =. 2016 , doi =
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Chen, Lin X. and Shelby, Megan L. and Lestrange, Patrick J. and Jackson, Nicholas E. and Haldrup, Kristoffer and Mara, Michael W. and Stickrath, Andrew B. and Zhu, Diling and Lemke, Henrik and Chollet, Matthieu and Hoffman, Brian M. and Li, Xiaosong , Title =. 2016 , Pages =. ...
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2016 , Volume =
``Watching'' Polaron Pair Formation from First-Principles Electron-Nuclear Dynamics , Author =. 2016 , Volume =. doi:10.1021/acs.jpca.6b06419 , Grants =
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Goings and Joseph M
Joshua J. Goings and Joseph M. Kasper and Franco Egidi and Shichao Sun and Xiaosong Li , Title =. 2016 , doi =
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Chong, Erica Q. and Lingerfelt, David B. and Petrone, Alessio and Li, Xiaosong , Title =. 2016 , doi =
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2016 , doi =
Weller, Caroline E and Dhall, Abhinav and Ding, Feizhi and Linares, Edlaine and Whedon, Samuel D and Senger, Nicholas A and Tyson, Elizabeth L and Bagert, John D and Li, Xiaosong and Augusto, Ohara and Chatterjee, Champak , Title =. 2016 , doi =
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Pepin, Robert and Petrone, Alessio and Laszlo, Kenneth J. and Bush, Matthew F. and Li, Xiaosong and Ture. Does Thermal Breathing Affect Collision Cross Sections of Gas-Phase Peptide Ions? An Ab Initio Molecular Dynamics Study , Journal = JPCL, Volume =. 2016 , doi =
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Egidi, Franco and Goings, Joshua J. and Frisch, Michael J. and Li, Xiaosong , Title =. 2016 , doi =
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Goings, Joshua J. and Li, Xiaosong , Title =. 2016 , Volume =. doi:10.1063/1.4953668 , Grants =
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Shelby, Megan L. and Lestrange, Patrick J. and Jackson, Nicholas E. and Haldrup, Kristoffer and Mara, Michael W. and Stickrath, Andrew B. and Zhu, Diling and Lemke, Henrik T. and Chollet, Matthieu and Hoffman, Brian M. and Li, Xiaosong and Chen, Lin X. , Title =. 2016 , doi =
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2016 , Volume =
Highly Sensitive Built-In Strain Sensors for Polymer Composites: Fluorescence Turn-On Response through Mechanochemical Activation , Author=. 2016 , Volume =. doi:10.1002/adma.201600589 , Grants =
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2016 , Volume=
Computational Studies of the Electronic Structures of Copper-Doped CdSe Nanocrystals: Oxidation States, Jahn--Teller Distortions, Vibronic Bandshapes, and Singlet--Triplet Splittings , Author=. 2016 , Volume=. doi:10.1021/acs.jpcc.5b11319 , Grants =
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2016 , Pages=
Single-Crystal and Electronic Structure of a 1.3 nm Indium Phosphide Nanocluster , Author=. 2016 , Pages=. doi:10.1021/jacs.5b13214 , Grants =
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2016 , Pages =
Direct Ab Initio (Meta-)Surface-Hopping Dynamics , Author =. 2016 , Pages =. doi:10.1021/acs.jctc.5b00697 , Grants =
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[222]
Lestrange and Franco Egidi and Xiaosong Li , Journal = JCP, Grants =
Patrick J. Lestrange and Franco Egidi and Xiaosong Li , Journal = JCP, Grants =. The Consequences of Improperly Describing Oscillator Strengths Beyond the Electric Dipole Approximation , DOI =
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[223]
Imaging Excited Orbitals of Quantum Dots: Experiment and Electronic Structure Theory , DOI =
Nienhaus, Lea and Goings, Joshua J and Nguyen, Duc and Wieghold, Sarah and Lyding, Joseph and Li, Xiaosong and Gruebele, Martin , Journal = JACS, Grants =. Imaging Excited Orbitals of Quantum Dots: Experiment and Electronic Structure Theory , DOI =
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[224]
Goings and Feizhi Ding and Ernest R
Joshua J. Goings and Feizhi Ding and Ernest R. Davidson and Xiaosong Li , Journal = JCP, Grants =. Approximate Singly Excited States from a Two-Component Hartree Fock Reference , DOI =
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[225]
and Liu, Hongbin and Lingerfelt, David B
Ding, Feizhi and Goings, Joshua J. and Liu, Hongbin and Lingerfelt, David B. and Li, Xiaosong , Journal = JCP, Grants =. Ab Initio Two-Component Ehrenfest Dynamics , DOI =
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[226]
Energy-Specific Equation-of-Motion Coupled-Cluster Methods for High-Energy Excited States: Application to K-Edge X-Ray Absorption Spectroscopy , DOI =
Bo Peng and Patrick J Lestrange and Joshua J Goings and Marco Caricato and Xiaosong Li , Journal = JCTC, Grants=. Energy-Specific Equation-of-Motion Coupled-Cluster Methods for High-Energy Excited States: Application to K-Edge X-Ray Absorption Spectroscopy , DOI =
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[227]
Intemann and Kai Yao and Feizhi Ding and Yunxiang Xu and Xukai Xin and Xiaosong Li and Alex K.-Y
Jeremy J. Intemann and Kai Yao and Feizhi Ding and Yunxiang Xu and Xukai Xin and Xiaosong Li and Alex K.-Y. Jen , Journal = AFM, Grants =. Enhanced Performance of Organic Solar Cells with Increased End Group Dipole Moment in Indacenodithieno[3,2-b]thiophene-Based Molecules , DOI =
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[228]
Lestrange and Phu D
Patrick J. Lestrange and Phu D. Nguyen and Xiaosong Li , Journal = JCTC, Grants =. Calibration of Energy-Specific TDDFT for Modeling K-Edge XAS Spectra of Light Elements , DOI =
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[229]
and Nguyen, Phu D
Li, Chang-Zhi and Liang, Po-Wei and Sulas, Dana B. and Nguyen, Phu D. and Li, Xiaosong and Ginger, David S. and Schlenker, Cody W. and Jen, Alex K.-Y. , Issue =. Modulation of Hybrid Organic-Perovskite Photovoltaic Performance by Controlling the Excited Dynamics of Fullerenes , DOI =
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doi:10.1063/1.4918561 , Volume =
Goings, Joshua J and Ding, Feizhi and Frisch, Michael J and Li, Xiaosong , Journal = JCP, Grants =. doi:10.1063/1.4918561 , Volume =
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doi:10.1021/acs.jpcc.5b00263 , Volume =
Peng, Bo and Lingerfelt, David B and Ding, Feizhi and Aikens, Christine M and Li, Xiaosong , Journal = JPCC, Grants =. doi:10.1021/acs.jpcc.5b00263 , Volume =
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[232]
Richards and Chu-Chen Chueh and Feizhi Ding and Lilo D
Bin Zhao and Chang-Zhi Li and Sheng-Qiang Liu and Jeffrey J. Richards and Chu-Chen Chueh and Feizhi Ding and Lilo D. Pozzo and Xiaosong Li and Alex K.-Y. Jen , Journal = JMCA, Grants =. A Conductive Liquid Crystal via Facile Doping of an n-type Benzodifurandione Derivative , DOI =
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[233]
and Mennucci, Benedetta and Li, Xiaosong , Journal = JCP, Grants =
Ding, Feizhi and Lingerfelt, David B. and Mennucci, Benedetta and Li, Xiaosong , Journal = JCP, Grants =. doi:10.1063/1.4906083 , Volume =
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[234]
and Frisch, Michael J
Ding, Feizhi and Goings, Joshua J. and Frisch, Michael J. and Li, Xiaosong , Journal = JCP, Grants =. Ab Initio Non-Relativistic Spin Dynamics , DOI =
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[235]
and Schimpf, Alina M
Goings, Joshua J. and Schimpf, Alina M. and May, Joseph W. and Johns, Robert W. and Gamelin, Daniel R. and Li, Xiaosong , Journal = JPCC, Grants =. Theoretical Characterization of Conduction-Band Electrons in Photodoped and Aluminum-Doped Zinc Oxide (AZO) Quantum Dots , DOI =
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[236]
and Caricato, Marco and Frisch, Michael J
Goings, Joshua J. and Caricato, Marco and Frisch, Michael J. and Li, Xiaosong , Journal = JCP, Grants =. doi:10.1063/1.4898709 , Volume =
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[237]
Lingerfelt and Nadia Rega and Xiaosong Li , Journal = PCCP, Grants =
Alessio Petrone and David B. Lingerfelt and Nadia Rega and Xiaosong Li , Journal = PCCP, Grants =. From Charge-Transfer to a Charge-Separated State: A Perspective from the Real-Time TDDFT Excitonic Dynamics , DOI =
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[238]
and Lingerfelt, David B
Fischer, Sean A. and Lingerfelt, David B. and May, Joseph W. and Li, Xiaosong , Journal = PCCP, Grants =. Non-Adiabatic Molecular Dynamics Investigation of Photoionization State Formation and Lifetime in Mn ^. doi:10.1039/C4CP01683A , Volume =
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[239]
Guidez and Christine M
Feizhi Ding and Emilie B. Guidez and Christine M. Aikens and Xiaosong Li , Journal = JCP, Grants =. Quantum Coherent Plasmon in Silver Nanowires: A Real-Time TDDFT Study , DOI =
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[240]
May and Jiao Ma and Ekaterina Badaeva and Xiaosong Li , Journal = JPCC, Grants =
Joseph W. May and Jiao Ma and Ekaterina Badaeva and Xiaosong Li , Journal = JPCC, Grants =. Effect of Excited-State Structural Relaxation on Midgap Excitations in Co ^. doi:10.1021/jp501360d , Volume =
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[241]
Lestrange and Bo Peng and Feizhi Ding and Gary W
Patrick J. Lestrange and Bo Peng and Feizhi Ding and Gary W. Trucks and Michael J. Frisch and Xiaosong Li , Journal = JCTC, Grants =. Density of States Guided M\"oller-Plesset Perturbation Theory , DOI =
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[242]
May and Daniel R
Bo Peng and Joseph W. May and Daniel R. Gamelin and Xiaosong Li , Journal = JPCC, Grants =. Effects of Crystallographic and Shape Anisotropies on Dopant-Carrier Exchange Interactions in Magnetic Semiconductor Quantum Dots , DOI =
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[243]
Bradshaw and Joseph W
Liam R. Bradshaw and Joseph W. May and Jillian L. Dempsey and Xiaosong Li and Daniel R. Gamelin , Journal = PRB, Grants =. Ferromagnetic Excited-State Mn ^. doi:10.1103/PhysRevB.89.115312 , Volume =
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[244]
deQuilettes and Phu D
Matthew Gliboff and Dana Sulas and Dennis Nordlund and Dane W. deQuilettes and Phu D. Nguyen and Gerald T. Seidler and Xiaosong Li and David S. Ginger , Journal = JPCC, Grants =. Direct Measurement of Acceptor Group Localization on Donor-Acceptor Polymers Using Resonant Auger ...
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[245]
Lingerfelt and Sean A
David B. Lingerfelt and Sean A. Fischer and Joseph W. May and Xiaosong Li , Journal = JPCC, Grants =. Dynamical Investigations of Inhomogenous Vibrational Broadening in Diluted Magnetic Semiconductor Nanocrystals , DOI =
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[246]
Goings and Feizhi Ding and Xiaosong Li , Journal = AQC, Grants =
Joshua J. Goings and Feizhi Ding and Xiaosong Li , Journal = AQC, Grants =. Self-Consistent Field Using Direct Inversion in Iterative Subspace Method and Quasi-Newton Vectors , Volume =. doi:10.1016/B978-0-12-800536-1.00004-6 , Year =
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[247]
A Guided Self-Consistent-Field Method for Excited State Wave Function Optimization: Applications to Ligand Field Transitions in Transition Metal Complexes , DOI =
Bo Peng and Benjamin E. A Guided Self-Consistent-Field Method for Excited State Wave Function Optimization: Applications to Ligand Field Transitions in Transition Metal Complexes , DOI =
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[248]
Jen , Journal = AM, Grants =
Chang-Zhi Li and Chu-Chen Chueh and Feizhi Ding and Hin-Lap Yip and Po-Wei Liang and Xiaosong Li and Alex K.-Y. Jen , Journal = AM, Grants =. Doping of Fullerenes via Anion-Induced Electron Transfer and Its Implication for Surfactant Facilitated High Performance Polymer Solar ...
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[249]
Chapman and Wenkel Liang and Xiaosong Li , Journal = JPCA, Grants =
Craig T. Chapman and Wenkel Liang and Xiaosong Li , Journal = JPCA, Grants =. Solvent Effects on Intramolecular Charge Transfer Dynamics in a Fullerene Derivative , DOI =
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[250]
Jen , Journal = AM, Pages =
Chang-Zhi Li and Chu-Chen Chueh and Hin-Lap Yip and Feizhi Ding and Xiaosong Li and Alex K.-Y. Jen , Journal = AM, Pages =. Solution-Processable Highly Conducting Fullerenes , DOI =
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[251]
An Efficient Method for Calculating Dynamical Hyperpolarizabilities Using Real-Time Time-Dependent Density Functional Theory , DOI =
Feizhi Ding and Benjamin E. An Efficient Method for Calculating Dynamical Hyperpolarizabilities Using Real-Time Time-Dependent Density Functional Theory , DOI =
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[252]
Hratchian and Xiaosong Li , Journal = JCTC, Pages =
Hrant P. Hratchian and Xiaosong Li , Journal = JCTC, Pages =. Thirty Years of Geometry Optimization in Quantum Chemistry and Beyond: A Tribute to Berny Schlegel , Volume =
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[253]
Schlenker and Kung-Shih Chen and Hin-Lap Yip and Chang-Zhi Li and Liam R
Cody W. Schlenker and Kung-Shih Chen and Hin-Lap Yip and Chang-Zhi Li and Liam R. Bradshaw and Stefan T. Ochsenbein and Feizhi Ding and Xiaosong Li and Daniel R. Gamelin and Alex K.-Y. Jen and David S. Ginger , Journal = JACS, Pages =. Polymer Triplet Energy Levels Need Not Li...
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[254]
Jen , Journal = AM, Pages =
Yun-Xiang Xu and Chu-Chen Chueh and Hin-Lap Yip and Fei-Zhi Ding and Yong-Xi Li and Chang-Zhi Li and Xiaosong Li and Wen-Chang Chen and Alex K.-Y. Jen , Journal = AM, Pages =. Improved Charge Transport and Absorption Coefficient in Indacenodithieno[3,2-b]thiophene-Based Ladder...
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[255]
Fischer and Wenkel Liang and Xiaosong Li , Journal = JPCL, Pages =
Phu Nguyen and Feizhi Ding and Sean A. Fischer and Wenkel Liang and Xiaosong Li , Journal = JPCL, Pages =. Solvated First-Principles Excited State Charge Transfer Dynamics with Time-Dependent Polarizable Continuum Model and Solvent Dielectric Relaxation , DOI =. 2012 , Grants=
2012
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May and Jeremy D
Joseph W. May and Jeremy D. Lehner and Michael J. Frisch and Xiaosong Li , Journal = JCTC, Pages =. Transition State Search Using a Guided Direct Inversion in the Iterative Subspace Method , Volume =. 2012 , DOI =
2012
-
[257]
Chapman and Wenkel Liang and Xiaosong Li , Journal = JCP, Pages =
Feizhi Ding and Craig T. Chapman and Wenkel Liang and Xiaosong Li , Journal = JCP, Pages =. Mechanisms of Bridge-Mediated Electron Transfer: A TDDFT Electronic Dynamics Study , DOI =. 2012 , Grants=
2012
-
[258]
May and Ryan J
Joseph W. May and Ryan J. McMorris and Xiaosong Li , Journal = JPCL, Pages =. Ferromagnetism in p -Type Manganese-Doped Zinc Oxide Quantum Dots , Volume =. 2012 , DOI =
2012
-
[259]
White and Daniel R
Bo Peng and Wenkel Liang and Michael A. White and Daniel R. Gamelin and Xiaosong Li , Journal = JPCC, Number =. Theoretical Evaluation of Spin-Dependent Auger De-Excitation in Mn ^. 2012 , DOI =
2012
-
[260]
Chapman and Feizhi Ding and Xiaosong Li , Journal = JPCA, Number =
Wenkel Liang and Craig T. Chapman and Feizhi Ding and Xiaosong Li , Journal = JPCA, Number =. Modeling Ultrafast Solvated Electronic Dynamics Using Time-Dependent Density Functional Theory and Polarizable Continuum Model , DOI =. 2012 , Grants=
2012
-
[261]
The Early Life of a Peptide Cation-Radical
Christopher Moss and Wenkel Liang and Xiaosong Li and Franti. The Early Life of a Peptide Cation-Radical. Ground and Excited-State Trajectories of Electron-Based Peptide Dissociations During the First 330 Femtoseconds , DOI =. 2012 , Grants=
2012
-
[262]
Orbital Pathways for Mn
R\'. Orbital Pathways for Mn. 2011 , DOI =
2011
-
[263]
Chapman and Christine M
Feizhi Ding and Wenkel Liang and Craig T. Chapman and Christine M. Isborn and Xiaosong Li , Journal = JCP, Number =. On the Gauge Invariance of Nonperturbative Electronic Dynamics Using the Time-Dependent Hartree-Fock and Time-Dependent Kohn-Sham , DOI =. 2011 , Grants=
2011
-
[264]
Fischer and Craig T
Sean A. Fischer and Craig T. Chapman and Xiaosong Li , Journal = JCP, Number =. Surface Hopping with Ehrenfest Excited Potential , DOI =. 2011 , Grants=
2011
-
[265]
Fischer and Michael J
Wenkel Liang and Sean A. Fischer and Michael J. Frisch and Xiaosong Li , Journal = JCTC, Number =. Energy-Specific Linear Response TDHF/TDDFT for Calculating High-Energy Excited States , DOI =. 2011 , Grants=
2011
-
[266]
May and Jiao Ma and Daniel R
Ekaterina Badaeva and Joseph W. May and Jiao Ma and Daniel R. Gamelin and Xiaosong Li , Journal = JPCC, Number =. Characterization of Excited-State Magnetic Exchange in Mn ^. 2011 , DOI =
2011
-
[267]
Dalton and Bruce H
Wenkel Liang and Xiaosong Li and Larry R. Dalton and Bruce H. Robinson and Bruce E. Eichinger , Journal = JPCB, Number =. Solvents Level Dipole Moments , Volume =. 2011 , DOI =
2011
-
[268]
Chapman and Xiaosong Li , Journal = JCP, Number =
Wenkel Liang and Craig T. Chapman and Xiaosong Li , Journal = JCP, Number =. Efficient First-Principles Electronic Dynamics , DOI =. 2011 , Grants=
2011
-
[269]
Chapman and Wenkel Liang and Xiaosong Li , Journal = JPCL, Number =
Craig T. Chapman and Wenkel Liang and Xiaosong Li , Journal = JPCL, Number =. Ultrafast Coherent Electron-Hole Separation Dynamics in a Fullerene Derivative , Volume =. 2011 , DOI =
2011
-
[270]
Bale and Bruce E
Denise H. Bale and Bruce E. Eichinger and Wenkel Liang and Xiaosong Li and Larry R. Dalton and Bruce H. Robinson and Philip J. Reid , Journal = JPCB, Number =. Dielectric Dependence of the First Molecular Hyperpolarizability for Electro-Optic Chromophores , Volume =. 2011 , DOI =
2011
-
[271]
Chapman and Wenkel Liang and Xiaosong Li , Journal = JCP, Number =
Craig T. Chapman and Wenkel Liang and Xiaosong Li , Journal = JCP, Number =. Open-System Electronic Dynamics and Thermalized Electronic Structure , DOI =. 2011 , Grants =
2011
-
[272]
Chapman and Michael J
Wenkel Liang and Craig T. Chapman and Michael J. Frisch and Xiaosong Li , Journal = JCTC, Number =. Geometry Optimization with Multilayer Methods Using Least-Squares Minimization , Volume =. 2010 , DOI =
2010
-
[273]
Jen and Xiaosong Li , Journal = JPCC, Number =
Jane Hung and Wenkel Liang and Jingdong Luo and Zhengwei Shi and Alex K.-Y. Jen and Xiaosong Li , Journal = JPCC, Number =. Rational Design Using Dewar's Rules for Enhancing the First Hyperpolarizability of Nonlinear Optical Chromophores , Volume =. 2010 , DOI =
2010
-
[274]
Frisch , Journal = JCTC, Number =
Wenkel Liang and Haitao Wang and Jane Hung and Xiaosong Li and Michael J. Frisch , Journal = JCTC, Number =. Eigenspace Update for Molecular Geometry Optimization in Nonredundant Internal Coordinate , Volume =. 2010 , DOI =
2010
-
[275]
Polishak and Xiaosong Li and Todd R
Zhengwei Shi and Wenkel Liang and Jingdong Luo and Su Huang and Brent M. Polishak and Xiaosong Li and Todd R. Younkin and Bruce A. Block and Alex K.-Y. Jen , Journal = CM, Number =. Tuning the Kinetics and Energetics of Diels-Alder Cycloaddition Reactions to Improve Poling Eff...
2010
-
[276]
Isborn and Alex Lindsay and Xiaosong Li and Stanley M
Wenkel Liang and Christine M. Isborn and Alex Lindsay and Xiaosong Li and Stanley M. Smith and Robert J. Levis , Journal = JPCA, Number =. Time-Dependent Density Functional Theory Calculations of Ehrenfest Dynamics of Laser Controlled Dissociation of NO ^. 2010 , Grants =. doi...
2010 doi
-
[277]
Gamelin and Xiaosong Li , Journal = JPCL, Number =
Yong Feng and Ekaterina Badaeva and Daniel R. Gamelin and Xiaosong Li , Journal = JPCL, Number =. Excited-State Double Exchange in Manganese-Doped ZnO Quantum Dots: A Time-Dependent Density-Functional Study , Volume =. 2010 , DOI =
2010
-
[278]
Smith and Dmitri A
Stanley M. Smith and Dmitri A. Romanov and Xiaosong Li and Jason A. Sonk and H. Bernhard Schlegel and Robert J. Levis , Journal = JPCA, Number =. Numerical Bound State Electron Dynamics of Carbon Dioxide in the Strong-Field Regime , Volume =. 2010 , DOI =
2010
-
[279]
Isborn and Xiaosong Li , Journal = JCP, Number =
Wenkel Liang and Christine M. Isborn and Xiaosong Li , Journal = JCP, Number =. Obtaining Hartree-Fock and Density Functional Theory Doubly Excited States with Car-Parrinello Density Matrix Search , DOI =
-
[280]
Ochsenbein and Yong Feng and Kelly M
Stefan T. Ochsenbein and Yong Feng and Kelly M. Whitaker and Ekaterina Badaeva and William K. Liu and Xiaosong Li and Daniel R. Gamelin , Journal = NN, Pages =. Charge-Controlled Magnetism in Colloidal Doped Semiconductor Nanocrystals , Volume =. doi:10.1038/nnano.2009.221 , Year =
-
[281]
Isborn and Xiaosong Li , Journal = JCTC, Number =
Christine M. Isborn and Xiaosong Li , Journal = JCTC, Number =. Singlet-Triplet Transitions in Real-Time Time-Dependent Hartree-Fock/Density Functional Theory , Volume =. 2009 , DOI =
2009
-
[282]
Moss and Christine M
Christopher L. Moss and Christine M. Isborn and Xiaosong Li , Journal = PRA, Number =. Ehrenfest Dynamics with a Time-Dependent Density-Functional-Theory Calculation of Lifetimes and Resonant Widths of Charge-Transfer States of Li ^. 2009 , DOI =
2009
-
[283]
Moss and Wenkel Liang and Yong Feng , Journal = JCP, Number =
Xiaosong Li and Christopher L. Moss and Wenkel Liang and Yong Feng , Journal = JCP, Number =. Car-Parrinello Density Matrix Search with a First Principles Fictitious Electron Mass Method for Electronic Wave Function Optimization , Volume =. doi:10.1063/1.3155082 , Year =
-
[284]
Isborn and Xiaosong Li , Journal = JPCA, Number =
Wenkel Liang and Christine M. Isborn and Xiaosong Li , Journal = JPCA, Number =. Laser-Controlled Dissociation of C _. doi:10.1021/jp811431u , Year =
-
[285]
Isborn and Yong Feng and Stefan T
Ekateriana Badaeva and Christine M. Isborn and Yong Feng and Stefan T. Ochsenbein and Daniel R. Gamelin and Xiaosog Li , Journal = JPCC, Number =. Theoretical Characterization of Electronic Transitions in Co ^. doi:10.1021/jp900392j , Volume =
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[286]
Isborn and Xiaosong Li , Journal = JCP, Number =
Christine M. Isborn and Xiaosong Li , Journal = JCP, Number =. Modeling the Doubly Excited State with Time-Dependent Hartree--Fock and Density Functional Theories , Volume =. doi:10.1063/1.3020336 , Year =
-
[287]
Isborn and Svetlana V
Christine M. Isborn and Svetlana V. Kilina and Xiaosong Li and Oleg V. Prezhdo , Journal = JPCC, Number =. Generation of Multiple Excitons in PbSe and CdSe Quantum Dots by Direct Photoexcitation: First-Principles Calculations on Small PbSe and CdSe Clusters , Volume =. doi:10....
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[288]
Moss and Xiaosong Li , Journal = JCP, Number =
Christopher L. Moss and Xiaosong Li , Journal = JCP, Number =. First Order Simultaneous Optimization of Molecular Geometry and Electronic Wave Function , Volume =. doi:10.1063/1.2977735 , Year =
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[289]
Davies and Arumugasamy Elangovan and Philip A
Joshua A. Davies and Arumugasamy Elangovan and Philip A. Sullivan and Benjamin C. Olbricht and Denise H. Bale and Todd R. Ewy and Christine M. Isborn and Bruce E. Eichinger and Bruce H. Robinson and Philip J. Reid and Xiaosong Li and Larry R. Dalton , Journal = JACS, Number =....
-
[290]
Gamelin and Xiaosong Li , Journal = NJP, Pages =
Ekateriana Badaeva and Yong Feng and Daniel R. Gamelin and Xiaosong Li , Journal = NJP, Pages =. Investigation of Pure and Co ^. doi:10.1088/1367-2630/10/5/055013 , Year =
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[291]
Wustholz and Eric D
Kristin L. Wustholz and Eric D. Bott and Christine M. Isborn and Xiaosong Li and Bart Kahr and Philip J. Reid , Journal = JPCC, Number =. Dispersive Kinetics from Single Molecules Oriented in Single Crystals of Potassium Acid Phthalate , Volume =. doi:10.1021/jp0713559 , Year =
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[292]
Isborn and Xiaosong Li and John C
Christine M. Isborn and Xiaosong Li and John C. Tully , Journal = JCP, Pages =. TDDFT Ehrenfest Dynamics: Collisions between Atomic Oxygen and Graphite Clusters , Volume =. doi:10.1063/1.2713391 , Year =
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[293]
Tully , Journal = CPL, Number =
Xiaosong Li and John C. Tully , Journal = CPL, Number =. Ab Initio Time-Resolved Density Functional Theory for Lifetimes of Excited Adsorbate States at Metal Surfaces , Volume =. doi:10.1016/j.cplett.2007.03.041 , Year =
2007 doi
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[294]
Smith and Xiaosong Li and Alexei Markevitch and Dmitri Romanov and Robert J
Stanley M. Smith and Xiaosong Li and Alexei Markevitch and Dmitri Romanov and Robert J. Levis and H. Bernhard Schlegel , Journal = JPCA, Number =. Numerical Simulation of Nonadiabatic Electron Excitation in the Strong-Field Regime. 3. Polyacene Neutrals and Cations , Volume =....
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[295]
Bernhard Schlegel and Stanley M
H. Bernhard Schlegel and Stanley M. Smith and Xiaosong Li , Journal = JCP, Number =. Electronic Optical Response of Molecules in Intense Fields: Comparison of TD-HF, TD-CIS, and TD-CIS(D) Approaches , Volume =. doi:10.1063/1.2743982 , Year =
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[296]
Frisch , Journal = JCTC, Number =
Xiaosong Li and Michael J. Frisch , Journal = JCTC, Number =. Energy-Represented Direct Inversion in the Iterative Subspace within a Hybrid Geometry Optimization Method , Volume =. doi:10.1021/ct050275a , Year =
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[297]
Smith and Xiaosong Li and Alexei N
Stanley M. Smith and Xiaosong Li and Alexei N. Markevitch and Dmitri A. Romanov and Robert J. Levis and H. Bernhard Schlegel , Journal = JPCA, Number =. Numerical Simulation of Nonadiabatic Electron Excitation in the Strong Field Regime. 2. Linear Polyene Cations , Volume =. d...
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[298]
Tully and H
Xiaosong Li and John C. Tully and H. Bernhard Schlegel and Michael J. Frisch , Journal = JCP, Number =. Ab Initio Ehrenfest Dynamics , Volume =. doi:10.1063/1.2008258 , Year =
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[299]
Smith and Alexei N
Xiaosong Li and Stanley M. Smith and Alexei N. Markevitch and Dmitri A. Romanov and Robert J. Levis and H. Bernhard Schlegel , Issue =. A Time-Dependent Hartree-Fock Approach for Studying the Electronic Optical Response of Molecules in Intense Fields , DOI =
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[300]
Smith and Xiaosong Li and Alexei N
Stanley M. Smith and Xiaosong Li and Alexei N. Markevitch and Dmitri A. Romanov and Robert J. Levis and H. Bernhard Schlegel , Journal = JPCA, Number =. A Numerical Simulation of Nonadiabatic Electron Excitation in the Strong Field Regime: Linear Polyenes , DOI =
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