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Szántó JK, Dietschreit JCB, Shein M, Schütz AK, Ochsenfeld C. Systematic QM/MM Study for Predicting 31P NMR Chemical Shifts of Adenosine Nucleotides in Solution and Stages of ATP Hydrolysis in a Protein Environment. J Chem Theory Comput 2024; 20:2433-2444. [PMID: 38497488 DOI: 10.1021/acs.jctc.3c01280] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2024]
Abstract
NMR (nuclear magnetic resonance) spectroscopy allows for important atomistic insights into the structure and dynamics of biological macromolecules; however, reliable assignments of experimental spectra are often difficult. Herein, quantum mechanical/molecular mechanical (QM/MM) calculations can provide crucial support. A major problem for the simulations is that experimental NMR signals are time-averaged over much longer time scales, and since computed chemical shifts are highly sensitive to local changes in the electronic and structural environment, sufficiently large averages over representative structural ensembles are essential. This entails high computational demands for reliable simulations. For NMR measurements in biological systems, a nucleus of major interest is 31P since it is both highly present (e.g., in nucleic acids) and easily observable. The focus of our present study is to develop a robust and computationally cost-efficient framework for simulating 31P NMR chemical shifts of nucleotides. We apply this scheme to study the different stages of the ATP hydrolysis reaction catalyzed by p97. Our methodology is based on MM molecular dynamics (MM-MD) sampling, followed by QM/MM structure optimizations and NMR calculations. Overall, our study is one of the most comprehensive QM-based 31P studies in a protein environment and the first to provide computed NMR chemical shifts for multiple nucleotide states in a protein environment. This study sheds light on a process that is challenging to probe experimentally and aims to bridge the gap between measured and calculated NMR spectroscopic properties.
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Affiliation(s)
- Judit Katalin Szántó
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Johannes C B Dietschreit
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Mikhail Shein
- Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 München, Germany
| | - Anne K Schütz
- Department of Chemistry, University of Munich (LMU), Butenandtstr. 5-13, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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2
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Sahu N, Khire SS, Gadre SR. Combining fragmentation method and high-performance computing: Geometry optimization and vibrational spectra of proteins. J Chem Phys 2023; 159:044309. [PMID: 37522406 DOI: 10.1063/5.0149572] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2023] [Accepted: 07/12/2023] [Indexed: 08/01/2023] Open
Abstract
Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5-10 millihartrees and 5 cm-1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future.
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Affiliation(s)
- Nityananda Sahu
- Theoretische Chemie, Philipps-Universität Marburg, 35032 Marburg, Germany
| | - Subodh S Khire
- RIKEN Center for Computational Science, Kobe 650-0047, Japan
| | - Shridhar R Gadre
- Departments of Scientific Computing, Modelling & Simulation and Chemistry, Savitribai Phule Pune University, Pune 411007, India
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3
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Negre CFA, Wall ME, Niklasson AMN. Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics. J Chem Phys 2023; 158:074108. [PMID: 36813723 DOI: 10.1063/5.0137119] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.
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Affiliation(s)
- Christian F A Negre
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Michael E Wall
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Anders M N Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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4
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Tankov I, Yankova R, Mihov D. Influence of the coordination metal on the thermal properties of double selenates: Theoretical insights and experimental study. J Mol Struct 2023. [DOI: 10.1016/j.molstruc.2022.134411] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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5
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7
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Tankov I, Yankova R. Nature of the chemical interactions in the multifunctional ionic liquid tris(2-aminothiazolium) hydrogen sulfate sulfate monohydrate. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.115366] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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8
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Esch BVD, Peters LDM, Sauerland L, Ochsenfeld C. Quantitative Comparison of Experimental and Computed IR-Spectra Extracted from Ab Initio Molecular Dynamics. J Chem Theory Comput 2021; 17:985-995. [PMID: 33512155 DOI: 10.1021/acs.jctc.0c01279] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Experimentally measured infrared spectra are often compared to their computed equivalents. However, the accordance is typically characterized by visual inspection, which is prone to subjective judgment. The primary challenge for a similarity-based analysis is that the artifacts introduced by each approach are very different and, therefore, may require preprocessing steps to determine and correct impeding irregularities. To allow for automated objective assessment, we propose a practical and comprehensive workflow involving scaling factors, a novel baseline correction scheme, and peak smoothing. The resulting spectra can then easily be compared quantitatively using similarity measures, for which we found the Pearson correlation coefficient to be the most suitable. The proposed procedure is then applied to compare the agreement of the experimental infrared spectra from the NIST Chemistry Web book with the calculated spectra using standard harmonic frequency analysis and spectra extracted from ab initio molecular dynamics simulations at different levels of theory. We conclude that the direct, quantitative comparison of calculated and measured IR spectra might become a novel, sophisticated approach to benchmark quantum-chemical methods. In the present benchmark, simulated spectra based on ab initio molecular dynamics show in general better agreement with the experiment than static calculations.
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Affiliation(s)
- Beatriz von der Esch
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Laurens D M Peters
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Lena Sauerland
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
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9
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10
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Delgado-Venegas RI, Calaminici P, Köster AM. Mixed second and third energy derivatives from auxiliary density perturbation theory. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1549339] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
| | - Patrizia Calaminici
- Departamento de Química, CINVESTAV. Avenida Instituto Politécnico Nacional 2508, México D.F., México
| | - Andreas M. Köster
- Departamento de Química, CINVESTAV. Avenida Instituto Politécnico Nacional 2508, México D.F., México
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11
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Peters LDM, Kussmann J, Ochsenfeld C. Efficient and Accurate Born-Oppenheimer Molecular Dynamics for Large Molecular Systems. J Chem Theory Comput 2017; 13:5479-5485. [PMID: 29068678 DOI: 10.1021/acs.jctc.7b00937] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An efficient scheme for the calculation of Born-Oppenheimer molecular dynamics (BOMD) simulations is introduced. It combines the corrected small basis set Hartree-Fock (HF-3c) method by Sure and Grimme [J. Comput. Chem. 2013, 43, 1672], extended Lagrangian BOMD (XL-BOMD) by Niklasson et al. [J. Chem. Phys. 2009, 130, 214109], and the calculation of the two electron integrals on graphics processing units (GPUs) [J. Chem. Phys. 2013, 138, 134114; J. Chem. Theory Comput. 2015, 11, 918]. To explore the parallel performance of our strong scaling implementation of the method, we present timings and extract, as its validation and first illustrative application, high-quality vibrational spectra from simulated trajectories of β-carotene, paclitaxel, and liquid water (up to 500 atoms). We conclude that the presented BOMD scheme may be used as a cost-efficient and reliable tool for computing vibrational spectra and thermodynamics of large molecular systems including explicit solvent molecules containing 500 atoms and more. Simulating 50 ps of maitotoxin (nearly 500 atoms) employing time steps of 0.5 fs requires ∼3 weeks on 12 CPUs (Intel Xeon E5 2620 v3) with 24 GPUs (AMD FirePro 3D W8100).
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Affiliation(s)
- Laurens D M Peters
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstr. 7, D-81377 München, Germany.,Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstr. 5-13, D-81377 München, Germany
| | - Jörg Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstr. 7, D-81377 München, Germany.,Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstr. 5-13, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstr. 7, D-81377 München, Germany.,Center for Integrated Protein Science (CIPSM) at the Department of Chemistry, University of Munich (LMU) , Butenandtstr. 5-13, D-81377 München, Germany
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12
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Helmich-Paris B, Knecht S. Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis. J Chem Phys 2017; 146:224101. [PMID: 29166042 PMCID: PMC5464961 DOI: 10.1063/1.4984591] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Accepted: 05/16/2017] [Indexed: 11/15/2022] Open
Abstract
In the present article, we show how to formulate the partially contracted n-electron valence second-order perturbation theory (NEVPT2) energies in the atomic and active molecular orbital basis by employing the Laplace transformation of orbital-energy denominators (OEDs). As atomic-orbital (AO) basis functions are inherently localized and the number of active orbitals is comparatively small, our formulation is particularly suited for a linearly scaling NEVPT2 implementation. In our formulation, there are two kinds of NEVPT2 energy contributions, which differ in the number of active orbitals in the two-electron integrals involved. Those involving integrals with either no or a single active orbital can be formulated completely in the AO basis as single-reference second-order Møller-Plesset perturbation theory and benefit from sparse active pseudo-density matrices-particularly if the active molecular orbitals are localized only in parts of a molecule. Conversely, energy contributions involving integrals with either two or three active orbitals can be obtained from Coulomb and exchange matrices generalized for pairs of active orbitals. Moreover, we demonstrate that Laplace-transformed partially contracted NEVPT2 is nothing less than time-dependent NEVPT2 [A. Y. Sokolov and G. K.-L. Chan, J. Chem. Phys. 144, 064102 (2016)] iff the all-active intermediates are computed with the internal-contraction approximation. Furthermore, we show that for multi-reference perturbation theories it is particularly challenging to find optimal parameters of the numerical Laplace transformation as the fit range may vary among the 8 different OEDs by many orders of magnitude. Selecting the number of quadrature points for each OED separately according to an accuracy-based criterion allows us to control the errors in the NEVPT2 energies reliably.
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Affiliation(s)
- Benjamin Helmich-Paris
- Section of Theoretical Chemistry, VU University Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Stefan Knecht
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland
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13
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Schurkus HF, Luenser A, Ochsenfeld C. Communication: Almost error-free resolution-of-the-identity correlation methods by null space removal of the particle-hole interactions. J Chem Phys 2017; 146:211106. [PMID: 28595410 PMCID: PMC5462614 DOI: 10.1063/1.4985085] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2017] [Accepted: 05/24/2017] [Indexed: 11/14/2022] Open
Abstract
We present a method to improve upon the resolution-of-the-identity (RI) for correlation methods. While RI is known to allow for drastic speedups, it relies on a cancellation of errors. Our method eliminates the errors introduced by RI which are known to be problematic for absolute energies. In this way, independence of the error compensation assumption for relative energies is also achieved. The proposed method is based on the idea of starting with an oversized RI basis and projecting out all of its unphysical parts. The approach can be easily implemented into existing RI codes and results in an overhead of about 30%, while effectively removing the RI error. In passing, this process alleviates the problem that for many frequently employed basis sets no optimized RI basis sets have been constructed. In this paper, the theory is presented and results are discussed exemplarily for the random phase approximation and Møller-Plesset perturbation theory.
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Affiliation(s)
- Henry F Schurkus
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Arne Luenser
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry and Center for Integrated Protein Science Munich (CIPSM), Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 Munich, Germany
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14
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Luenser A, Schurkus HF, Ochsenfeld C. Vanishing-Overhead Linear-Scaling Random Phase Approximation by Cholesky Decomposition and an Attenuated Coulomb-Metric. J Chem Theory Comput 2017; 13:1647-1655. [DOI: 10.1021/acs.jctc.6b01235] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Arne Luenser
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstrasse
5-13, D-81377 Munich, Germany
- Center for Integrated Protein Science Munich (CIPSM), Butenandtstrasse
5-13, D-81377 Munich, Germany
| | - Henry F. Schurkus
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstrasse
5-13, D-81377 Munich, Germany
- Center for Integrated Protein Science Munich (CIPSM), Butenandtstrasse
5-13, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry,
Department of Chemistry, University of Munich (LMU), Butenandtstrasse
5-13, D-81377 Munich, Germany
- Center for Integrated Protein Science Munich (CIPSM), Butenandtstrasse
5-13, D-81377 Munich, Germany
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15
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Sahu N, Gadre SR. Vibrational infrared and Raman spectra of polypeptides: Fragments-in-fragments within molecular tailoring approach. J Chem Phys 2017; 144:114113. [PMID: 27004868 DOI: 10.1063/1.4943966] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
The present work reports the calculation of vibrational infrared (IR) and Raman spectra of large molecular systems employing molecular tailoring approach (MTA). Further, it extends the grafting procedure for the accurate evaluation of IR and Raman spectra of large molecular systems, employing a new methodology termed as Fragments-in-Fragments (FIF), within MTA. Unlike the previous MTA-based studies, the accurate estimation of the requisite molecular properties is achieved without performing any full calculations (FC). The basic idea of the grafting procedure is implemented by invoking the nearly basis-set-independent nature of the MTA-based error vis-à-vis the respective FCs. FIF has been tested out for the estimation of the above molecular properties for three isomers, viz., β-strand, 310- and α-helix of acetyl(alanine)nNH2 (n = 10, 15) polypeptides, three conformers of doubly protonated gramicidin S decapeptide and trpzip2 protein (PDB id: 1LE1), respectively, employing BP86/TZVP, M06/6-311G**, and M05-2X/6-31G** levels of theory. For most of the cases, a maximum difference of 3 cm(-1) is achieved between the grafted-MTA frequencies and the corresponding FC values. Further, a comparison of the BP86/TZVP level IR and Raman spectra of α-helical (alanine)20 and its N-deuterated derivative shows an excellent agreement with the existing experimental spectra. In view of the requirement of only MTA-based calculations and the ability of FIF to work at any level of theory, the current methodology provides a cost-effective solution for obtaining accurate spectra of large molecular systems.
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Affiliation(s)
- Nityananda Sahu
- Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208 016, India
| | - Shridhar R Gadre
- Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208 016, India
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16
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Delgado-Venegas RI, Mejía-Rodríguez D, Flores-Moreno R, Calaminici P, Köster AM. Analytic second derivatives from auxiliary density perturbation theory. J Chem Phys 2016; 145:224103. [PMID: 27984884 DOI: 10.1063/1.4971292] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Rogelio Isaac Delgado-Venegas
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
| | - Daniel Mejía-Rodríguez
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
| | - Roberto Flores-Moreno
- Departamento de Química, Universidad de Guadalajara, Boulevard Marcelino García Barragán 1421, Guadalajara, Jalisco 44430, Mexico
| | - Patrizia Calaminici
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
| | - Andreas M. Köster
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740, México D.F. 07000, Mexico
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Luenser A, Kussmann J, Ochsenfeld C. Computation of indirect nuclear spin–spin couplings with reduced complexity in pure and hybrid density functional approximations. J Chem Phys 2016; 145:124103. [DOI: 10.1063/1.4962260] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Arne Luenser
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU Munich) and Center for Integrated Protein Science Munich (CIPSM, LMU Munich), Butenandtstr. 5–13, D-81377 Munich, Germany
| | - Jörg Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU Munich) and Center for Integrated Protein Science Munich (CIPSM, LMU Munich), Butenandtstr. 5–13, D-81377 Munich, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU Munich) and Center for Integrated Protein Science Munich (CIPSM, LMU Munich), Butenandtstr. 5–13, D-81377 Munich, Germany
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18
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Nagy PR, Koltai J, Surján PR, Kürti J, Szabados Á. Resonance Raman Optical Activity of Single Walled Chiral Carbon Nanotubes. J Phys Chem A 2016; 120:5527-38. [DOI: 10.1021/acs.jpca.6b04594] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Péter R. Nagy
- MTA-BME
Lendület Quantum Chemistry Research Group, Department of Physical
Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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