1
|
Li J, Yang W. Chemical Potentials and the One-Electron Hamiltonian of the Second-Order Perturbation Theory from the Functional Derivative Approach. J Phys Chem A 2024; 128:4876-4885. [PMID: 38842399 DOI: 10.1021/acs.jpca.4c01574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2024]
Abstract
We develop a functional derivative approach to calculate the chemical potentials of second-order perturbation theory (MP2). In the functional derivative approach, the correlation part of the MP2 chemical potential, which is the derivative of the MP2 correlation energy with respect to the occupation number of frontier orbitals, is obtained from the chain rule via the noninteracting Green's function. First, the MP2 correlation energy is expressed in terms of the noninteracting Green's function, and its functional derivative to the noninteracting Green's function is the second-order self-energy. Then, the derivative of the noninteracting Green's function to the occupation number is obtained by including the orbital relaxation effect. We show that the MP2 chemical potentials obtained from the functional derivative approach agree with that obtained from the finite difference approach. The one-electron Hamiltonian, defined as the derivative of the MP2 energy with respect to the one particle density matrix, is also derived using the functional derivative approach, which can be used in the self-consistent calculations of MP2 and double-hybrid density functionals. The developed functional derivative approach is promising for calculating the chemical potentials and the one-electron Hamiltonian of approximate functionals and many-body perturbation approaches dependent explicitly on the noninteracting Green's function.
Collapse
Affiliation(s)
- Jiachen Li
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| |
Collapse
|
2
|
Kuan KY, Yeh SH, Yang W, Hsu CP. Excited-State Charge Transfer Coupling from Quasiparticle Energy Density Functional Theory. J Phys Chem Lett 2024; 15:6126-6136. [PMID: 38830203 PMCID: PMC11181311 DOI: 10.1021/acs.jpclett.4c00850] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2024] [Revised: 04/29/2024] [Accepted: 04/30/2024] [Indexed: 06/05/2024]
Abstract
The recently developed Quasiparticle Energy (QE) scheme, based on a DFT calculation with one more (or less) electron, offers a good description of excitation energies, even with charge transfer characters. In this work, QE is further extended to calculate electron transfer (ET) couplings involving two excited states. We tested it with a donor-acceptor complex, consisting of a furan and a 1,1-dicyanoethylene (DCNE), in which two low lying charge transfer and local excitation states are involved. With generalized Mülliken-Hush and fragment charge-difference schemes, couplings from the QE approach generally agree well with those obtained from TDDFT, except that QE couplings exhibit better exponential distance dependence. Couplings from half-energy gaps with an external field are also calculated and reported. Our results show that the QE scheme is robust in calculating ET couplings with greatly reduced computational time.
Collapse
Affiliation(s)
- Kai-Yuan Kuan
- Institute
of Chemistry, Academia Sinica, 128 Academia Road, Section 2, Nankang
District, Taipei 11529, Taiwan
| | - Shu-Hao Yeh
- Institute
of Chemistry, Academia Sinica, 128 Academia Road, Section 2, Nankang
District, Taipei 11529, Taiwan
- Department
of Chemistry, National Taiwan University, 1 Roosevelt Rd, Section 4, Da’an
District, Taipei City 10617, Taiwan
| | - Weitao Yang
- Department
of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Chao-Ping Hsu
- Institute
of Chemistry, Academia Sinica, 128 Academia Road, Section 2, Nankang
District, Taipei 11529, Taiwan
- Division
of Physics, National Center for Theoretical
Sciences, 1 Roosevelt
Road, Section 4, Taipei City 10617, Taiwan
| |
Collapse
|
3
|
Mester D, Kállay M. Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level. J Chem Theory Comput 2023. [PMID: 37326360 DOI: 10.1021/acs.jctc.3c00363] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.
Collapse
Affiliation(s)
- Dávid Mester
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- ELKH-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- ELKH-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
- MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| |
Collapse
|
4
|
Mei Y, Chen Z, Yang W. Exact Second-Order Corrections and Accurate Quasiparticle Energy Calculations in Density Functional Theory. J Phys Chem Lett 2021; 12:7236-7244. [PMID: 34310157 PMCID: PMC9367128 DOI: 10.1021/acs.jpclett.1c01962] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We develop a second-order correction to commonly used density functional approximations (DFAs) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact quadratic correction to the DFA for the fractional charge behavior and uses the analytical second derivatives of the total energy with respect to fractional occupation numbers of the canonical molecular orbitals. For small and medium-size molecules, this correction leads to ground-state orbital energies that are a highly accurate approximation to the corresponding quasiparticle energies. It provides excellent predictions of ionization potentials, electron affinities, photoemission spectrum, and photoexcitation energies beyond previous approximate second-order approaches, thus showing potential for broad applications in computational spectroscopy.
Collapse
Affiliation(s)
- Yuncai Mei
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Zehua Chen
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department of Physics, Duke University, Durham, North Carolina 27708, United States
| |
Collapse
|
5
|
Mei Y, Chen Z, Yang W. Self-Consistent Calculation of the Localized Orbital Scaling Correction for Correct Electron Densities and Energy-Level Alignments in Density Functional Theory. J Phys Chem Lett 2020; 11:10269-10277. [PMID: 33215928 PMCID: PMC8341159 DOI: 10.1021/acs.jpclett.0c03133] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The recently developed localized orbital scaling correction (LOSC) method shows the ability to systematically and size-consistently reduce the delocalization error existing in conventional density functional approximations (DFAs). However, the application of LOSC to DFAs was mainly through a post self-consistent field (SCF) manner, and few results from applying LOSC to DFAs in an SCF manner have been reported. The reason is that the originally proposed SCF approach to SCF-LOSC calculation uses an approximate Hamiltonian and encounters convergence problems easily in practice. In this work, we develop a new SCF approach with a correct Hamiltonian and achieve reliable SCF-LOSC calculations. We demonstrate the capability of the new SCF approach for SCF-LOSC to correctly describe the electron densities, total energies, and energy-level alignment for the molecular dissociation process, while conventional DFAs or LOSC-DFAs with post-SCF calculations show large errors. This work demonstrates that the new SCF approach for SCF-LOSC would be a promising method for studying problems for correct electron densities and energy-level alignments in large systems.
Collapse
Affiliation(s)
| | | | - Weitao Yang
- Key Laboratory of Theoretical Chemistry of Environment, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China
| |
Collapse
|
6
|
Williams ZM, Wiles TC, Manby FR. Accurate Hybrid Density Functionals with UW12 Correlation. J Chem Theory Comput 2020; 16:6176-6194. [PMID: 32820918 DOI: 10.1021/acs.jctc.0c00442] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In previous work, we suggested a single-parameter hybrid functional containing a novel correlation contribution based on the Unsöld approximation, UW12. This model resembles the explicitly correlated part of MP2-F12 theory and can be written as an explicit formula in terms of the single-particle reduced density matrix. Here, we further investigate hybrid functionals containing UW12 correlation and in particular look at functionals with a large fraction of exact exchange to reduce the self-interaction error. We suggest two new hybrid functionals B-LYP-osUW12 and fB-LYP-osUW12. On the test sets we use, our best hybrid functional overall (B-LYP-osUW12) is of similar accuracy to the best double hybrids considered while eliminating the need for virtual orbitals.
Collapse
Affiliation(s)
- Zack M Williams
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K
| | - Timothy C Wiles
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K
| | - Frederick R Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K
| |
Collapse
|
7
|
Gu Y, Xu X. Extended Koopmans’ theorem in the adiabatic connection formalism: Applied to doubly hybrid density functionals. J Chem Phys 2020; 153:044109. [DOI: 10.1063/5.0010743] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yonghao Gu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai 200433, China
| |
Collapse
|
8
|
Su NQ, Mahler A, Yang W. Preserving Symmetry and Degeneracy in the Localized Orbital Scaling Correction Approach. J Phys Chem Lett 2020; 11:1528-1535. [PMID: 32004430 PMCID: PMC9999725 DOI: 10.1021/acs.jpclett.9b03888] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
Symmetry is a fundamental concept that plays a critical role in many chemical and physical phenomena and processes, which highlights the importance of theoretical methods to correctly handle symmetry. The recently developed localized orbital scaling correction (LOSC1) shows great improvement on the description of band gaps, photoemission spectra, and dissociation limits of cationic species. However, issues remain with LOSC1 in dealing with the symmetry and degeneracy of electronic states, which are also relevant to other methods using localization. In this work, we utilize a new method that deals with the physical-space and the energy-space localization on an equal footing. The resulting localized orbitals, i.e., orbitalets, are able to maintain more symmetry and the desired state degeneracy, which is important in calculating the electronic structure of both molecules and periodic bulk systems. Furthermore, the curvature matrix is redefined to improve potential energy curves for systems with stretched bonds, while retaining the correct dissociation limits. This new approach, termed LOSC2, includes only two fitting parameters. It maintains accuracy similar to that of LOSC1 over many properties, while overcoming LOSC1's deficiencies in symmetry and degeneracy. Our tests have shown that LOSC2 orbitalets possess the full- or subgroup of molecular symmetry if allowed, which preserves the state degeneracy. Tests on differently sized planar annulenes, odd-numbered allenes, and triphenylene again verify that LOSC2 is able to maintain the state degeneracy, while LOSC1 cannot. All the tests demonstrate the advantage of LOSC2 in the calculation of molecular systems and its potential for application to periodic bulk systems.
Collapse
Affiliation(s)
- Neil Qiang Su
- Department of Chemistry , Duke University , Durham , North Carolina 27708 , United States
| | - Aaron Mahler
- Department of Physics , Duke University , Durham , North Carolina 27708 , United States
| | - Weitao Yang
- Department of Chemistry , Duke University , Durham , North Carolina 27708 , United States
- Key Laboratory of Theoretical Chemistry of Environment, School of Chemistry and Environment , South China Normal University , Guangzhou 510006 , China
| |
Collapse
|
9
|
Śmiga S, Grabowski I, Witkowski M, Mussard B, Toulouse J. Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method. J Chem Theory Comput 2019; 16:211-223. [DOI: 10.1021/acs.jctc.9b00807] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - Ireneusz Grabowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - Mateusz Witkowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - Bastien Mussard
- Department of Chemistry and Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, United States
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| |
Collapse
|
10
|
Kalai C, Mussard B, Toulouse J. Range-separated double-hybrid density-functional theory with coupled-cluster and random-phase approximations. J Chem Phys 2019; 151:074102. [PMID: 31438697 DOI: 10.1063/1.5108536] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We construct range-separated double-hybrid (RSDH) schemes which combine coupled-cluster or random-phase approximations (RPAs) with a density functional based on a two-parameter Coulomb-attenuating-method-like decomposition of the electron-electron interaction. We find that the addition of a fraction of short-range electron-electron interaction in the wave-function part of the calculation is globally beneficial for the RSDH scheme involving a variant of the RPA with exchange terms. Even though the latter scheme is globally as accurate as the corresponding scheme employing only second-order Møller-Plesset perturbation theory for atomization energies, reaction barrier heights, and weak intermolecular interactions of small molecules, it is more accurate for the more complicated case of the benzene dimer in the stacked configuration. The present RSDH scheme employing a RPA thus represents a new member in the family of double hybrids with minimal empiricism which could be useful for general chemical applications.
Collapse
Affiliation(s)
- Cairedine Kalai
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Bastien Mussard
- Department of Chemistry and Biochemistry, University of Colorado Boulder, Boulder, Colorado 80302, USA
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| |
Collapse
|
11
|
Su NQ, Xu X. Insights into Direct Methods for Predictions of Ionization Potential and Electron Affinity in Density Functional Theory. J Phys Chem Lett 2019; 10:2692-2699. [PMID: 31059262 DOI: 10.1021/acs.jpclett.9b01052] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Vertical ionization potential (IP) and electron affinity (EA) are fundamental molecular properties, while the Δ method and the direct method are the widely used approaches to compute these properties. The Δ method is calculated by taking the total energy difference of the initial and final states, whose reliability is seriously affected by the issue associated with the imbalanced treatment of these two states. The direct method based on the derivatives involving only one single-state calculation can yield a quasi-particle spectrum whose accuracy, on the other hand, is mostly affected by the levels of approximate molecular structure theories. Because of the aforementioned issues, EA prediction can be particularly problematic. Here we present, for the first time, an analytic theory on the derivation and realization of generalized Kohn-Sham (KS) eigenvalues of doubly hybrid (DH) functionals that depend on both occupied and unoccupied orbitals. The method based on the KS eigenvalues of neutral systems, termed the NKS method, is found to suffer little from the imbalance issue, while it is only the NKS method that can offer accurate EA prediction from a good functional approximation, such as the XYG3 type of DH functionals. Being less sensitive to the size of basis sets, the NKS method is of great significance for its application to large systems. The insights gained in this work are useful for the calculation of properties associated with small energy differences while emphasizing the importance of the development of generalized functionals that rely on both occupied and unoccupied orbitals.
Collapse
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry , Fudan University , Shanghai 200433 , China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry , Fudan University , Shanghai 200433 , China
| |
Collapse
|
12
|
Mei Y, Li C, Su NQ, Yang W. Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn-Sham Calculations. J Phys Chem A 2019; 123:666-673. [PMID: 30589546 DOI: 10.1021/acs.jpca.8b10380] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Quasiparticle energies and fundamental band gaps in particular are critical properties of molecules and materials. It was rigorously established that the generalized Kohn-Sham HOMO and LUMO orbital energies are the chemical potentials of electron removal and addition and thus good approximations to band edges and fundamental gaps from a density functional approximation (DFA) with minimal delocalization error. For other quasiparticle energies, their connection to the generalized Kohn-Sham orbital energies has not been established but remains highly interesting. We provide the comparison of experimental quasiparticle energies for many finite systems with calculations from the GW Green function and localized orbitals scaling correction (LOSC), a recently developed correction to semilocal DFAs, which has minimal delocalization error. Extensive results with over 40 systems clearly show that LOSC orbital energies achieve slightly better accuracy than the GW calculations with little dependence on the semilocal DFA, supporting the use of LOSC DFA orbital energies to predict quasiparticle energies. This also leads to the calculations of excitation energies of the N-electron systems from the ground state DFA calculations of the ( N - 1)-electron systems. Results show good performance with accuracy similar to TDDFT and the delta SCF approach for valence excitations with commonly used DFAs with or without LOSC. For Rydberg states, good accuracy was obtained only with the use of LOSC DFA. This work highlights the pathway to quasiparticle and excitation energies from ground density functional calculations.
Collapse
Affiliation(s)
- Yuncai Mei
- Department of Chemistry , Duke University , Durham , North Carolina 27708 , United States
| | - Chen Li
- Department of Chemistry , Duke University , Durham , North Carolina 27708 , United States
| | - Neil Qiang Su
- Department of Chemistry , Duke University , Durham , North Carolina 27708 , United States
| | - Weitao Yang
- Department of Chemistry , Duke University , Durham , North Carolina 27708 , United States.,Key Laboratory of Theoretical Chemistry of Environment, School of Chemistry and Environment , South China Normal University , Guangzhou 510006 , China
| |
Collapse
|
13
|
Wiles TC, Manby FR. Wavefunction-like Correlation Model for Use in Hybrid Density Functionals. J Chem Theory Comput 2018; 14:4590-4599. [PMID: 30080967 DOI: 10.1021/acs.jctc.8b00337] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We present Unsöld-W12 (UW12), an approximation to the correlation energy of molecules that is an explicit functional of the single-particle reduced-density matrix. The approximation resembles one part of modern explicitly correlated second-order Møller-Plesset (MP2) theory and is intended as an alternative to MP2 in double-hybrid exchange-correlation functionals. Orbital optimization with UW12 is straightforward, and the UW12 energy is evaluated without a double summation over unoccupied orbitals, leading to a faster basis-set convergence than is seen in double-hybrid functionals. We suggest a one-parameter hybrid exchange-correlation functional XCH-BLYP-UW12. XCH-BLYP-UW12 is similar to double-hybrid functionals, but contains UW12 correlation instead of MP2 correlation. We find that XCH-BLYP-UW12 is more accurate than the existing double-hybrid functional B2-PLYP for small-molecule main-group reaction barrier heights and has roughly the same accuracy as the existing hybrid functional B3LYP for atomization energies.
Collapse
Affiliation(s)
- Timothy C Wiles
- Centre for Computational Chemistry, School of Chemistry , University of Bristol , Bristol BS8 1TS , United Kingdom
| | - Frederick R Manby
- Centre for Computational Chemistry, School of Chemistry , University of Bristol , Bristol BS8 1TS , United Kingdom
| |
Collapse
|
14
|
Describing strong correlation with fractional-spin correction in density functional theory. Proc Natl Acad Sci U S A 2018; 115:9678-9683. [PMID: 30201706 DOI: 10.1073/pnas.1807095115] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
An effective fractional-spin correction is developed to describe static/strong correlation in density functional theory. Combined with the fractional-charge correction from recently developed localized orbital scaling correction (LOSC), a functional, the fractional-spin LOSC (FSLOSC), is proposed. FSLOSC, a correction to commonly used functional approximations, introduces the explicit derivative discontinuity and largely restores the flat-plane behavior of electronic energy at fractional charges and fractional spins. In addition to improving results from conventional functionals for the prediction of ionization potentials, electron affinities, quasiparticle spectra, and reaction barrier heights, FSLOSC properly describes the dissociation of ionic species, single bonds, and multiple bonds without breaking space or spin symmetry and corrects the spurious fractional-charge dissociation of heteroatom molecules of conventional functionals. Thus, FSLOSC demonstrates success in reducing delocalization error and including strong correlation, within low-cost density functional approximation.
Collapse
|
15
|
Baerends EJ. Density functional approximations for orbital energies and total energies of molecules and solids. J Chem Phys 2018; 149:054105. [PMID: 30089375 DOI: 10.1063/1.5026951] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The relation of Kohn-Sham (KS) orbital energies to ionization energies and electron affinities is different in molecules and solids. In molecules, the local density approximation (LDA) and generalized gradient approximations (GGA) approximate the exact ionization energy (I) and affinity (A) rather well with self-consistently calculated (total energy based) ILDFA and ALDFA, respectively. The highest occupied molecular orbital (HOMO) energy and lowest unoccupied molecular orbital (LUMO) energy, however, differ significantly (by typically 4-6 eV) from these quantities, ϵHLDFA(mol)>-I(mol)≈-ILDFA(mol), ϵLLDFA(mol)<-A(mol)≈-ALDFA(mol). In solids, these relations are very different, due to two effects. The (almost) infinite extent of a solid makes the difference of orbital energies and (L)DFA calculated ionization energy and affinity disappear: in the solid state limit, ϵH(L)DFA(solid)=-I(L)DFA(solid) and ϵL(L)DFA(solid)=-A(L)DFA(solid). Slater's relation ∂E/∂ni = ϵi for local density functional approximations (LDFAs) [and Hartree-Fock (HF) and hybrids] is useful to prove these relations. The equality of LDFA orbital energies and LDFA calculated -ILDFA and -ALDFA in solids does not mean that they are good approximations to the exact quantities. The LDFA total energies of the ions with a delocalized charge are too low, hence ILDFA(solid) < I and ALDFA(solid) > A, due to the local-approximation error, also denoted delocalization error, of LDFAs in extended systems. These errors combine to make the LDFA orbital energy band gap considerably smaller than the exact fundamental gap, ϵLLDFA(solid)-ϵHLDFA(solid)=ILDFA(solid)-ALDFA(solid)<I-A (the LDFA band gap problem). These results for density functional approximations are compared to exact KS and to HF and hybrids. For the exact KS HOMO energy, one has ϵHKS=-I. The exact KS LUMO energy does not approximate the experimental -A (neither in molecules nor in solids), but is considerably below, which is the main reason for the exact KS HOMO-LUMO energy gap being considerably below the fundamental gap I - A (the exact KS band gap problem).
Collapse
Affiliation(s)
- Evert Jan Baerends
- Section Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands
| |
Collapse
|
16
|
Ghosh S, Verma P, Cramer CJ, Gagliardi L, Truhlar DG. Combining Wave Function Methods with Density Functional Theory for Excited States. Chem Rev 2018; 118:7249-7292. [PMID: 30044618 DOI: 10.1021/acs.chemrev.8b00193] [Citation(s) in RCA: 128] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.
Collapse
Affiliation(s)
- Soumen Ghosh
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Pragya Verma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Christopher J Cramer
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| |
Collapse
|
17
|
Margraf JT, Bartlett R. Communication: Coupled cluster and many-body perturbation theory for fractional charges and spins. J Chem Phys 2018; 148:221103. [DOI: 10.1063/1.5040164] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Johannes T. Margraf
- Chair for Theoretical Chemistry, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
| | - Rodney Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| |
Collapse
|
18
|
Kalai C, Toulouse J. A general range-separated double-hybrid density-functional theory. J Chem Phys 2018; 148:164105. [PMID: 29716225 DOI: 10.1063/1.5025561] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A range-separated double-hybrid (RSDH) scheme which generalizes the usual range-separated hybrids and double hybrids is developed. This scheme consistently uses a two-parameter Coulomb-attenuating-method (CAM)-like decomposition of the electron-electron interaction for both exchange and correlation in order to combine Hartree-Fock exchange and second-order Møller-Plesset (MP2) correlation with a density functional. The RSDH scheme relies on an exact theory which is presented in some detail. Several semi-local approximations are developed for the short-range exchange-correlation density functional involved in this scheme. After finding optimal values for the two parameters of the CAM-like decomposition, the RSDH scheme is shown to have a relatively small basis dependence and to provide atomization energies, reaction barrier heights, and weak intermolecular interactions globally more accurate or comparable to range-separated MP2 or standard MP2. The RSDH scheme represents a new family of double hybrids with minimal empiricism which could be useful for general chemical applications.
Collapse
Affiliation(s)
- Cairedine Kalai
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| |
Collapse
|
19
|
Hait D, Head-Gordon M. Communication: xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS. J Chem Phys 2018; 148:171102. [DOI: 10.1063/1.5031027] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Diptarka Hait
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Martin Head-Gordon
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| |
Collapse
|
20
|
Chen J, Su NQ, Xu X, Zhang DH. Accurate potential energy surfaces for hydrogen abstraction reactions: A benchmark study on the XYG3 doubly hybrid density functional. J Comput Chem 2017; 38:2326-2334. [PMID: 28786211 DOI: 10.1002/jcc.24886] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2017] [Revised: 06/27/2017] [Accepted: 06/29/2017] [Indexed: 11/06/2022]
Abstract
The potential energy surface (PES) for the H + CH4 system has been constructed with the recently developed XYG3 doubly hybrid functional, while those with the standard B3LYP hybrid functional, and the Møller-Plesset perturbation theory up to the second order (MP2) are also presented for comparison. Quantum dynamics studies demonstrated that satisfactory results on the reaction probabilities and the rate coefficients can be obtained on top of the XYG3-PES, as compared to the results based on the highly accurate, yet expensive, CCSD(T)-PES (Li et al., J. Chem. Phys. 2015, 142, 204302). Further investigation suggested that the XYG3 functional is useful in providing accurate rate coefficients for some larger systems involving H atom abstractions. © 2017 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Jun Chen
- Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, China
| | - Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials (iChEM), Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Dong H Zhang
- State Key Laboratory of Molecular Reaction Dynamics & Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China
| |
Collapse
|
21
|
Localized orbital scaling correction for systematic elimination of delocalization error in density functional approximations. Natl Sci Rev 2017. [DOI: 10.1093/nsr/nwx111] [Citation(s) in RCA: 79] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Abstract
The delocalization error of popular density functional approximations (DFAs) leads to diversified problems in present-day density functional theory calculations. For achieving a universal elimination of delocalization error, we develop a localized orbital scaling correction (LOSC) framework, which unifies our previously proposed global and local scaling approaches. The LOSC framework accurately characterizes the distributions of global and local fractional electrons, and is thus capable of correcting system energy, energy derivative and electron density in a self-consistent and size-consistent manner. The LOSC–DFAs lead to systematically improved results, including the dissociation of cationic species, the band gaps of molecules and polymer chains, the energy and density changes upon electron addition and removal, and photoemission spectra.
Collapse
|
22
|
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Fudan University, Shanghai 200433, China
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Shanghai 200433, China
- MOE Key Laboratory of Computational Physical Sciences, Fudan University, Shanghai 200433, China
- Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Fudan University, Shanghai 200433, China
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Fudan University, Shanghai 200433, China
- MOE Key Laboratory of Computational Physical Sciences, Fudan University, Shanghai 200433, China
- Department of Chemistry, Fudan University, Shanghai 200433, China
| |
Collapse
|
23
|
Ranasinghe DS, Margraf JT, Jin Y, Bartlett RJ. Does the ionization potential condition employed in QTP functionals mitigate the self-interaction error? J Chem Phys 2017; 146:034102. [PMID: 28109216 DOI: 10.1063/1.4973727] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Though contrary to conventional wisdom, the interpretation of all occupied Kohn-Sham eigenvalues as vertical ionization potentials is justified by several formal and numerical arguments. Similarly, the performance of density functional approximations (DFAs) for fractionally charged systems has been extensively studied as a measure of one- and many-electron self-interaction errors (MSIEs). These complementary perspectives (initially recognized in ab initio dft) are shown to lead to the unifying concept that satisfying Bartlett's IP theorem in DFA's mitigates self-interaction errors. In this contribution, we show that the IP-optimized QTP functionals (reparameterization of CAM-B3LYP where all eigenvalues are approximately equal to vertical IPs) display reduced self-interaction errors in a variety of tests including the He2+ potential curve. Conversely, the MSIE-optimized rCAM-B3LYP functional also displays accurate orbital eigenvalues. It is shown that the CAM-QTP and rCAM-B3LYP functionals show improved dissociation limits, fundamental gaps and thermochemical accuracy compared to their parent functional CAM-B3LYP.
Collapse
Affiliation(s)
| | - Johannes T Margraf
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Yifan Jin
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| | - Rodney J Bartlett
- Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA
| |
Collapse
|
24
|
Śmiga S, Franck O, Mussard B, Buksztel A, Grabowski I, Luppi E, Toulouse J. Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method. J Chem Phys 2017; 145:144102. [PMID: 27782500 DOI: 10.1063/1.4964319] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effective-potential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression including the second-order Møller-Plesset correlation contribution. We have implemented a one-parameter version of this OEP-based self-consistent DH scheme using the BLYP density-functional approximation and compared it to the corresponding non-self-consistent DH scheme for calculations on a few closed-shell atoms and molecules. While the OEP-based self-consistency does not provide any improvement for the calculations of ground-state total energies and ionization potentials, it does improve the accuracy of electron affinities and restores the meaning of the LUMO orbital energy as being connected to a neutral excitation energy. Moreover, the OEP-based self-consistent DH scheme provides reasonably accurate exchange-correlation potentials and correlated densities.
Collapse
Affiliation(s)
- Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Torun, Poland
| | - Odile Franck
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, F-75005 Paris, France
| | - Bastien Mussard
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, F-75005 Paris, France
| | - Adam Buksztel
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Torun, Poland
| | - Ireneusz Grabowski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 87-100 Torun, Poland
| | - Eleonora Luppi
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, F-75005 Paris, France
| |
Collapse
|
25
|
Su NQ, Pernot P, Xu X, Savin A. When does a functional correctly describe both the structure and the energy of the transition state? J Mol Model 2017; 23:65. [PMID: 28185112 DOI: 10.1007/s00894-017-3229-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2016] [Accepted: 01/12/2017] [Indexed: 11/30/2022]
Abstract
Requiring that several properties are well reproduced is a severe test on density functional approximations. This can be assessed through the estimation of joint and conditional success probabilities. An example is provided for a small set of molecules, for properties characterizing the transition states (geometries and energies).
Collapse
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Pascal Pernot
- CNRS, UMR8000, Laboratoire de Chimie Physique, F-91405, Orsay, France.,Univ. Paris-Sud, UMR8000, Laboratoire de Chimie Physique, F-91405, Orsay, France
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Andreas Savin
- CNRS, UMR7616, Laboratoire de Chimie Théorique, F-75005, Paris, France. .,UPMC Univ Paris 06, UMR7616, Laboratoire de Chimie Théorique, F-75005, Paris, France.
| |
Collapse
|
26
|
Mussard B, Toulouse J. Fractional-charge and fractional-spin errors in range-separated density-functional theory. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1213910] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Bastien Mussard
- Institut des sciences du calcul et des données, Université Pierre et Marie Curie, Sorbonne Universités, Paris, France
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Sorbonne Universités, CNRS, Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Sorbonne Universités, CNRS, Paris, France
| |
Collapse
|
27
|
Su NQ, Xu X. The XYG3 type of doubly hybrid density functionals. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1274] [Citation(s) in RCA: 43] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry; Fudan University; Shanghai 200433 China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry; Fudan University; Shanghai 200433 China
| |
Collapse
|
28
|
Su NQ, Xu X. Second-Order Perturbation Theory for Fractional Occupation Systems: Applications to Ionization Potential and Electron Affinity Calculations. J Chem Theory Comput 2016; 12:2285-97. [DOI: 10.1021/acs.jctc.6b00197] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xin Xu
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200433, China
| |
Collapse
|
29
|
On the performance of time-dependent double-hybrid density functionals for description of absorption and emission spectra of heteroaromatic compounds. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1838-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
30
|
Zhou Y, Wu J, Xu X. Improving B3LYP heats of formation with three-dimensional molecular descriptors. J Comput Chem 2016; 37:1175-90. [DOI: 10.1002/jcc.24308] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2015] [Revised: 12/27/2015] [Accepted: 12/29/2015] [Indexed: 11/09/2022]
Affiliation(s)
- Yuwei Zhou
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University; Shanghai 200433 China
| | - Jianming Wu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University; Shanghai 200433 China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University; Shanghai 200433 China
| |
Collapse
|
31
|
|
32
|
Xi J, Xu X. Understanding the anion–π interactions with tetraoxacalix[2]arene[2]triazine. Phys Chem Chem Phys 2016; 18:6913-24. [DOI: 10.1039/c5cp08065g] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
The geometries of four anion–π complexes,1·X−(X−= SCN−, NO3−, BF4−, and PF6−) were optimized using the extended ONIOM (XO) method with a high level (H) = ωB97X-D/6-31+G(d) and low level (L) = PM6. Then, the bonding energies of1·X−were calculated with the XYG3 functional, and they follow the order of1·NO3−>1·SCN−>1·BF4−>1·PF6−.
Collapse
Affiliation(s)
- Jinyang Xi
- Collaborative Innovation Center of Chemistry for Energy Materials
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials
- MOE Laboratory for Computational Physical Science
- Department of Chemistry
- Fudan University
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials
- MOE Laboratory for Computational Physical Science
- Department of Chemistry
- Fudan University
| |
Collapse
|
33
|
Su NQ, Xu X. Beyond energies: geometry predictions with the XYG3 type of doubly hybrid density functionals. Chem Commun (Camb) 2016; 52:13840-13860. [DOI: 10.1039/c6cc04886b] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The scaled mean absolute deviations (s-MADs) of the optimized geometric parameters for covalent bondings (the CCse set), nonbonded interactions (the S22G30 set) and the transition state structures (the TSG36 set), with Tot referring to the averaged s-MAD for general performances.
Collapse
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry for Energy Materials
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials
- MOE Laboratory for Computational Physical Science
- Department of Chemistry
- Fudan University
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials
- MOE Laboratory for Computational Physical Science
- Department of Chemistry
- Fudan University
| |
Collapse
|
34
|
Su NQ, Xu X. A comparative study of the xDH-PBE0 and DSD-PBEPBE-D3BJ doubly hybrid density functionals. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1129462] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Neil Qiang Su
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Collaborative Innovation Center of Chemistry for Energy Materials, Department of Chemistry, Fudan University, Shanghai, China
| | - Xin Xu
- Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Collaborative Innovation Center of Chemistry for Energy Materials, Department of Chemistry, Fudan University, Shanghai, China
| |
Collapse
|
35
|
Scaling correction approaches for reducing delocalization error in density functional approximations. Sci China Chem 2015. [DOI: 10.1007/s11426-015-5501-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
36
|
Ishibashi C, Iwata S, Onoe K, Matsuzawa H. Hydrogen-Bonded Networks in Hydride Water Clusters, F-(H2O)n and Cl-(H2O)n: Cubic Form of F-(H2O)7 and Cl-(H2O)7. J Phys Chem A 2015; 119:10241-53. [PMID: 26371716 DOI: 10.1021/acs.jpca.5b07244] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The anion-water bonds and hydrogen bonds between water molecules in X(-)(H(2)O)(n) (X = F and Cl, n = 3-7) clusters are analyzed by evaluating the charge-transfer (CT) and dispersion terms for every pair of ions and molecules with the perturbation theory based on the locally projected molecular orbitals. In particular, the relative stabilities and the bond strengths in all 11 distinct cubic X(-)(H(2)O)(7) isomers are analyzed by classifying the ligand water (L) with the numbers of the donating (n) and accepting (m) OHs as LD(n)A(m). The number of LD(0)A(2) waters determines the relative stability. It is demonstrated that the strengths of the anion-ligand bonds are strongly influenced by two other hydrogen bonds of the water molecules adjacent to the ligand. When the model theory of Mulliken's charge-transfer interaction is applied to the anion-ligand and water-water hydrogen bonds, the dependence of the bond strengths on the chains of the hydrogen bonds is explained.
Collapse
Affiliation(s)
- Chiaki Ishibashi
- Department of Life and Environmental Sciences, Graduate School of Engineering, Chiba Institute of Technology , Tsudanuma, Narashino, Chiba 275-0016, Japan
| | - Suehiro Iwata
- Department of Chemistry, Faculty of Science and Technology, Keio University , Hiyoshi, Kohoku, Yokohama 223-8522, Japan
| | - Kaoru Onoe
- Department of Life and Environmental Sciences, Graduate School of Engineering, Chiba Institute of Technology , Tsudanuma, Narashino, Chiba 275-0016, Japan
| | - Hidenori Matsuzawa
- Department of Life and Environmental Sciences, Graduate School of Engineering, Chiba Institute of Technology , Tsudanuma, Narashino, Chiba 275-0016, Japan.,Department of Chemistry, Center of Education, Chiba Institute of Technology , Shibazono, Narashino, Chiba 275-0023, Japan
| |
Collapse
|
37
|
Su NQ, Xu X. Integration Approach at the Second-Order Perturbation Theory: Applications to Ionization Potential and Electron Affinity Calculations. J Chem Theory Comput 2015; 11:4677-88. [DOI: 10.1021/acs.jctc.5b00591] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Xin Xu
- Collaborative Innovation
Center of Chemistry for Energy Materials, Shanghai Key Laboratory
of Molecular Catalysis and Innovative Materials, MOE Laboratory for
Computational Physical Science, Department of Chemistry, Fudan University, Shanghai, 200433, China
| |
Collapse
|
38
|
Alipour M. Designing a paradigm for parameter-free double-hybrid density functionals through the adiabatic connection path. Theor Chem Acc 2015. [DOI: 10.1007/s00214-015-1689-4] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
39
|
Phillips JJ, Kananenka AA, Zgid D. Fractional charge and spin errors in self-consistent Green’s function theory. J Chem Phys 2015; 142:194108. [DOI: 10.1063/1.4921259] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jordan J. Phillips
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Alexei A. Kananenka
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| |
Collapse
|
40
|
Further evidences on the quality of meta-GGA linearly scaled one-parameter double-hybrids for frontier orbital energies. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.01.032] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
41
|
Alipour M. Relative energies of water nanoclusters (H2O)20: comparison of empirical and nonempirical double-hybrids with generalized energy-based fragmentation approach. NEW J CHEM 2015. [DOI: 10.1039/c5nj00817d] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The applicability of recently developed parameterized and parameter-free double-hybrids for predicting the relative energies of water nanoclusters has been examined.
Collapse
Affiliation(s)
- Mojtaba Alipour
- Department of Chemistry
- College of Sciences
- Shiraz University
- Shiraz
- Iran
| |
Collapse
|
42
|
Guo W, Michel C, Schwiedernoch R, Wischert R, Xu X, Sautet P. Formation of Acrylates from Ethylene and CO2 on Ni Complexes: A Mechanistic Viewpoint from a Hybrid DFT Approach. Organometallics 2014. [DOI: 10.1021/om5006808] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Wenping Guo
- Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, laboratoire de Chimie, 46 allée d'Italie, Lyon 69364, France
- E2P2L, R&I Center Shanghai, Solvay, 3966 Jindu Road, 201108 Shanghai, People’s Republic of China
| | - Carine Michel
- Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, laboratoire de Chimie, 46 allée d'Italie, Lyon 69364, France
| | - Renate Schwiedernoch
- E2P2L, R&I Center Shanghai, Solvay, 3966 Jindu Road, 201108 Shanghai, People’s Republic of China
| | - Raphael Wischert
- E2P2L, R&I Center Shanghai, Solvay, 3966 Jindu Road, 201108 Shanghai, People’s Republic of China
| | - Xin Xu
- Department
of Chemistry, Fudan University, 220 Handan Road, Yangpu, Shanghai, People’s Republic of China
| | - Philippe Sautet
- Université de Lyon, CNRS, Ecole Normale Supérieure de Lyon, laboratoire de Chimie, 46 allée d'Italie, Lyon 69364, France
| |
Collapse
|
43
|
Su NQ, Xu X. Error Accumulations in Adhesive Energies of Dihydrogen Molecular Chains: Performances of the XYG3 Type of Doubly Hybrid Density Functionals. J Phys Chem A 2014; 119:1590-9. [DOI: 10.1021/jp507711t] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Neil Qiang Su
- Collaborative Innovation Center of Chemistry
for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis
and Innovative Materials, MOE Laboratory for Computational Physical
Science, Department of Chemistry, Fudan University, Shanghai 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry
for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis
and Innovative Materials, MOE Laboratory for Computational Physical
Science, Department of Chemistry, Fudan University, Shanghai 200433, China
| |
Collapse
|