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Liu L, Xu Q, dos Anjos Cunha L, Xin H, Head-Gordon M, Qian J. Real-Space Pseudopotential Method for the Calculation of Third-Row Elements X-ray Photoelectron Spectroscopic Signatures. J Chem Theory Comput 2024; 20:6134-6143. [PMID: 38970155 PMCID: PMC11270745 DOI: 10.1021/acs.jctc.4c00535] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2024] [Revised: 06/18/2024] [Accepted: 06/20/2024] [Indexed: 07/08/2024]
Abstract
X-ray photoelectron spectroscopy (XPS) is a powerful characterization technique that unveils subtle chemical environment differences via core-electron binding energy (CEBE) analysis. We extend the development of real-space pseudopotential methods to calculating 1s, 2s, and 2p3/2 CEBEs of third-row elements (S, P, and Si) within the framework of Kohn-Sham density-functional theory (KS-DFT). The new approach systematically prevents variational collapse and simplifies core-excited orbital selection within dense energy level distributions. However, careful error cancellation analysis is required to achieve accuracy comparable to all-electron methods and experiments. Combined with real-space KS-DFT implementation, this development enables large-scale simulations with both Dirichlet boundary conditions and periodic boundary conditions.
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Affiliation(s)
- Liping Liu
- Department
of Chemical Engineering, Virginia Polytechnic
Institute and State University, Blacksburg, Virginia 24060, United States
| | - Qiang Xu
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Leonardo dos Anjos Cunha
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Department
of Chemistry, University of California,
Berkeley, Berkeley, California 94720, United States
| | - Hongliang Xin
- Department
of Chemical Engineering, Virginia Polytechnic
Institute and State University, Blacksburg, Virginia 24060, United States
| | - Martin Head-Gordon
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Department
of Chemistry, University of California,
Berkeley, Berkeley, California 94720, United States
| | - Jin Qian
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
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2
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Xu Q, Prendergast D, Qian J. Real-Space Pseudopotential Method for the Calculation of 1 s Core-Level Binding Energies. J Chem Theory Comput 2022; 18:5471-5478. [PMID: 36037254 PMCID: PMC9476661 DOI: 10.1021/acs.jctc.2c00474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
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We systematically studied a real-space pesudopotential
method for
the calculation of 1s core–electron binding
energies of second-row elements B, C, N, and O within the framework
of Kohn–Sham density functional theory (KS-DFT). With Dirichlet
boundary conditions, pseudopotential calculations can provide accurate
core–electron binding energies for molecular systems, when
compared with the results from all-electron calculations and experiments.
Furthermore, we report that with one simple additional nonself-consistent
calculation as a refinement step using a hybrid exchange-correlation
functional, we can generally improve the accuracy of binding energy
shifts, promising a strategy for improving accuracy at a much lower
computational cost. The specializations in the present approach, combined
with our efficient real-space KS-DFT implementation, provide key advantages
for calculating accurate core–electron binding energies of
large-scale systems.
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Affiliation(s)
- Qiang Xu
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - David Prendergast
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
| | - Jin Qian
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California94720, United States
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3
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Zheng X, Zhang C, Jin Z, Southworth SH, Cheng L. Benchmark relativistic delta-coupled-cluster calculations of K-edge core-ionization energies of third-row elements. Phys Chem Chem Phys 2022; 24:13587-13596. [PMID: 35616685 DOI: 10.1039/d2cp00993e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
A benchmark computational study of K-edge core-ionization energies of third-row elements using relativistic delta-coupled-cluster (ΔCC) methods and a revised core-valence separation (CVS) scheme is reported. High-level relativistic (HLR) corrections beyond the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), including the contributions from two-electron picture-change effects, spin-orbit coupling, the Breit term, and quantum electrodynamics effects, have been taken into account and demonstrated to play an important role. Relativistic ΔCC calculations are shown to provide accurate results for core-ionization energies of third-row elements. The SFX2C-1e-CVS-ΔCC results augmented with HLR corrections show a maximum deviation of less than 0.5 eV with respect to experimental values.
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Affiliation(s)
- Xuechen Zheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Chaoqun Zhang
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
| | - Zheqi Jin
- Department of Chemistry, University College London, London, WC1E 6BT, UK
| | - Stephen H Southworth
- Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, USA
| | - Lan Cheng
- Department of Chemistry, The Johns Hopkins University, Baltimore, MD 21218, USA.
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Abou Taka A, Lu SY, Gowland D, Zuehlsdorff TJ, Corzo HH, Pribram-Jones A, Shi L, Hratchian HP, Isborn CM. Comparison of Linear Response Theory, Projected Initial Maximum Overlap Method, and Molecular Dynamics-Based Vibronic Spectra: The Case of Methylene Blue. J Chem Theory Comput 2022; 18:3039-3051. [PMID: 35472264 DOI: 10.1021/acs.jctc.1c01127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited electronic states. In this report, we show that the utilization of such a procedure within an adiabatic linear response (LR) theory framework may lead to state mixings and a breakdown of the Born-Oppenheimer approximation, resulting in a poor description of absorption spectra. In contrast, computing excited states via a self-consistent field method in conjunction with a maximum overlap model produces states that are not subject to such mixings. We show that this latter method produces vibronic spectra much more aligned with vertical gradient and molecular dynamics (MD) trajectory-based approaches. For the methylene blue chromophore, we compare vibronic absorption spectra computed with the following: an adiabatic Hessian approach with LR theory-optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlap method-optimized structures, and excitation energy time-correlation functions generated from an MD trajectory. Because of mixing between the bright S1 and dark S2 surfaces near the S1 minimum, computing the adiabatic Hessian with LR theory and time-dependent density functional theory with the B3LYP density functional predicts a large vibronic shoulder for the absorption spectrum that is not present for any of the other methods. Spectral densities are analyzed and we compare the behavior of the key normal mode that in LR theory strongly couples to the optical excitation while showing S1/S2 state mixings. Overall, our study provides a note of caution in computing vibronic spectra using the excited-state adiabatic Hessian of LR theory-optimized structures and also showcases three alternatives that are less sensitive to adiabatic state mixing effects.
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Affiliation(s)
- Ali Abou Taka
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Shao-Yu Lu
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Duncan Gowland
- Department of Physics, King's College London, London WC2R 2LS, United Kingdom
| | - Tim J Zuehlsdorff
- Department of Chemistry, Oregon State University, Corvallis, Oregon 97331, United States
| | - Hector H Corzo
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Aurora Pribram-Jones
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Liang Shi
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Hrant P Hratchian
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
| | - Christine M Isborn
- Department of Chemistry and Biochemistry, University of California Merced, Merced, California 95343, United States
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Qian J, Crumlin EJ, Prendergast D. Efficient basis sets for core-excited states motivated by Slater's rules. Phys Chem Chem Phys 2022; 24:2243-2250. [PMID: 35014633 DOI: 10.1039/d1cp03931h] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
X-Ray photoemission spectroscopy is a commonly applied characterization technique that probes the local chemistry of atoms in molecules and materials via the photoexcitation of electrons from atomic core orbitals. These measurements can be interpreted by comparison with previous literature or through the calculation of core-electron binding energies (CEBEs) for model systems. However, physically and numerically accurate description of the core-excited electronic structures demands specializations beyond routine ground state setups. Inspired by Slater's rules, we focus on developing computationally efficient and physically motivated contractions to reproduce the core-excited atomic orbitals which led to improved numerical accuracy of calculated CEBEs. When applied to carbon 1s excitations in a wide range of molecules, these core-excited basis sets produce total energy differences (ΔSCF) using a hybrid exact-exchange density functional (B3LYP) that can reproduce core-excitation energies within experimental accuracy (∼0.1 eV). Due to missing relativistic effects, heavier elements (N, O) exhibit slightly larger systematic absolute errors, but still maintain a satisfactory 0.2 eV mean average error for relative CEBEs. We also connect the known variability in the core level binding energy with local atomic charge to demonstrate how the transferability of a given model should be measured against a diverse test set. We conclude by exploring one outlier, CO, and the outlook for extending this approach to other elements.
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Affiliation(s)
- Jin Qian
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.,Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - Ethan J Crumlin
- Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
| | - David Prendergast
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
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Besley NA. Density Functional Theory Calculations of Core-Electron Binding Energies at the K-Edge of Heavier Elements. J Chem Theory Comput 2021; 17:3644-3651. [PMID: 34042434 DOI: 10.1021/acs.jctc.1c00171] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
The capability to determine core-electron binding energies (CEBEs) is vital in the analysis of X-ray photoelectron spectroscopy, and the continued development of light sources has made inner shell spectroscopy of heavier elements increasingly accessible. Density functional theory is widely used to determine CEBEs of lighter elements (boron-fluorine). It is shown that good performance of exchange-correlation functionals for these elements does not necessarily translate to the calculation of CEBEs for the heavier elements from the next row of the periodic table, and in general, larger errors are observed. Two strategies are explored that improve the accuracy of the calculated CEBEs. The first is to apply element and functional dependent energy corrections, and the second is a reparametrization of a short-range corrected functional. This functional is able to reproduce experimental phosphorus and sulfur K-edge CEBEs with an average error of 0.15 eV demonstrating the importance of reducing the self-interaction error associated with the core electrons and represents progress toward a density functional theory calculation that performs equally well for ionization at the K-edge of all elements.
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Affiliation(s)
- Nicholas A Besley
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, U.K
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Rishi V, Perera A, Bartlett RJ. A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory. J Chem Phys 2020; 153:234101. [DOI: 10.1063/5.0023862] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Affiliation(s)
- Varun Rishi
- Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Ajith Perera
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J. Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
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Carter-Fenk K, Herbert JM. State-Targeted Energy Projection: A Simple and Robust Approach to Orbital Relaxation of Non-Aufbau Self-Consistent Field Solutions. J Chem Theory Comput 2020; 16:5067-5082. [DOI: 10.1021/acs.jctc.0c00502] [Citation(s) in RCA: 38] [Impact Index Per Article: 9.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- Kevin Carter-Fenk
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - John M. Herbert
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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Hait D, Head-Gordon M. Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining Sub-electronvolt Error from a Restricted Open-Shell Kohn-Sham Approach. J Phys Chem Lett 2020; 11:775-786. [PMID: 31917579 DOI: 10.1021/acs.jpclett.9b03661] [Citation(s) in RCA: 74] [Impact Index Per Article: 18.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We present the use of the recently developed square gradient minimization (SGM) algorithm for excited-state orbital optimization to obtain spin-pure restricted open-shell Kohn-Sham (ROKS) energies for core excited states of molecules. The SGM algorithm is robust against variational collapse and offers a reliable route to converging orbitals for target excited states at only 2-3 times the cost of ground-state orbital optimization (per iteration). ROKS/SGM with the modern SCAN/ωB97X-V functionals is found to predict the K-edge of C, N, O, and F to a root mean squared error of ∼0.3 eV. ROKS/SGM is equally effective at predicting L-edge spectra of third period elements, provided a perturbative spin-orbit correction is employed. This high accuracy can be contrasted with traditional time-dependent density functional theory (TDDFT), which typically has greater than 10 eV error and requires translation of computed spectra to align with experiment. ROKS is computationally affordable (having the same scaling as ground-state DFT and a slightly larger prefactor) and can be applied to geometry optimizations/ab initio molecular dynamics of core excited states, as well as condensed phase simulations. ROKS can also model doubly excited/ionized states with one broken electron pair, which are beyond the ability of linear response based methods.
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Affiliation(s)
- Diptarka Hait
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry , University of California , Berkeley , California 94720 , United States
- Chemical Sciences Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry , University of California , Berkeley , California 94720 , United States
- Chemical Sciences Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
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