Analytical First and Second Derivatives for a Fully Polarizable QM/Classical Hamiltonian

Lipparini, Filippo; Cappelli, Chiara; Scalmani, Giovanni; Mitri, Nicola De; Barone, Vincenzo

doi:10.1021/ct300635c

Cited by 70 publications

(134 citation statements)

References 83 publications

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“…13,15 Methods rooted into the density functional theory (DFT) and its time-dependent extension (TD-DFT) are robust enough to provide reliable electronic structure results. 16−18 Besides, their coupling with molecular mechanics (MM) force fields 19,20 and polarizable continuum models (PCM) 21,22 to embed the active region (e.g., the chromophore) to get a reliable description of the environment are paving the way to the treatment of larger and larger systems both in the gas phase and in solution. 23−25 Regarding the actual computation of vibronic spectra, both time-independent (TI) 26−28 and time-dependent (TD) 29 −31 routes have been proposed.…”

Section: Introductionmentioning

confidence: 99%

Accurate Simulation of Resonance-Raman Spectra of Flexible Molecules: An Internal Coordinates Approach

Baiardi

Bloino

Barone

2015

J. Chem. Theory Comput.

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The interpretation and analysis of experimental resonance-Raman (RR) spectra can be significantly facilitated by vibronic computations based on reliable quantum-mechanical (QM) methods. With the aim of improving the description of large and flexible molecules, our recent time-dependent formulation to compute vibrationally resolved electronic spectra, based on Cartesian coordinates, has been extended to support internal coordinates. A set of nonredundant delocalized coordinates is automatically generated from the molecular connectivity thanks to a new general and robust procedure. In order to validate our implementation, a series of molecules has been used as test cases. Among them, rigid systems show that normal modes based on Cartesian and delocalized internal coordinates provide equivalent results, but the latter set is much more convenient and reliable for systems characterized by strong geometric deformations associated with the electronic transition. The so-called Z-matrix internal coordinates, which perform well for chain molecules, are also shown to be poorly suited in the presence of cycles or nonstandard structures.

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Section: Introductionmentioning

confidence: 99%

Accurate Simulation of Resonance-Raman Spectra of Flexible Molecules: An Internal Coordinates Approach

Baiardi

Bloino

Barone

2015

J. Chem. Theory Comput.

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“…7 There are notable exceptions which combined a polarizable force field for the MM fragment with semiempirical quantum chemistry for the QM fragment. [8][9][10][11][12] Combinations of higher-level QM treatments (density functional a) Electronic mail: gerald.mathias@physik.uni-muenchen.de theory 13,14 (DFT) or ab initio quantum chemistry) with PMM force fields were either restricted to the energetics of static systems, [15][16][17][18][19][20][21][22][23] to small molecular clusters, [24][25][26][27][28][29] or describe the dynamics only in parts of the simulation system. 30,31 Other approaches augment DFT atoms with self-consistent polarization terms (SCP-DFT) to correct the deficiencies of the longrange electrostatics and dispersion description within certain exchange-correlation functionals.…”

Section: Introductionmentioning

confidence: 99%

Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations

Schwörer

Breitenfeld

Tröster

et al. 2013

The Journal of Chemical Physics

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Hybrid molecular dynamics (MD) simulations, in which the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10 3 -10 5 molecules, pose a challenge. A corresponding computational approach should guarantee energy conservation, exclude artificial distortions of the electron density at the interface between the DFT and PMM fragments, and should treat the long-range electrostatic interactions within the hybrid simulation system in a linearly scaling fashion. Here we describe a corresponding Hamiltonian DFT/(P)MM implementation, which accounts for inducible atomic dipoles of a PMM environment in a joint DFT/PMM self-consistency iteration. The long-range parts of the electrostatics are treated by hierarchically nested fast multipole expansions up to a maximum distance dictated by the minimum image convention of toroidal boundary conditions and, beyond that distance, by a reaction field approach such that the computation scales linearly with the number of PMM atoms. Short-range over-polarization artifacts are excluded by using Gaussian inducible dipoles throughout the system and Gaussian partial charges in the PMM region close to the DFT fragment. The Hamiltonian character, the stability, and efficiency of the implementation are investigated by hybrid DFT/PMM-MD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM. © 2013 AIP Publishing LLC. [http://dx

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“…The equilibrium between the charge interactions and the differences in the atomic electronegativities represents the physical basis of the electronegativity equalization principle, which defines, in turn, the FQ model. The QM/FQ model has recently been extended by some of the present authors to the evaluation of analytical first and second derivatives, response equations, magnetic perturbations with gauge independent atomic orbitals (GIAO) and excitation energies at the equation of motion coupled cluster singles and doubles (EOM‐CCSD) level, and has been shown to give remarkable agreement with experimental findings in various applications in the field of computational spectroscopy . In the polarizable QM/FQ approach, the interaction energy is analogous to eq.…”

Section: Theorymentioning

confidence: 72%

“…As mentioned in The QM/FQ Model section, the gradients of E MM and E LJ are already available and have not been modified in this work. Regarding the other contributions, following previous works on this topic, the gradient of the energy in eq. with respect to a QM atomic coordinates reads

E_{0}^{x} = E^{SCF, x} + a_{c} E^{PT 2, x},

where the SCF term reads

E^{SCF, x} = 〈 {boldh}^{x} D 〉 + \frac{1}{2} 〈 {boldG}^{(x)} (D) D 〉 + \tilde{boldq} {boldV}^{(x)} (D) - 〈 W {boldS}_{o o}^{x} 〉,

where

〈 〉

denotes the usual trace operation.…”

Section: Theorymentioning

confidence: 99%

Analytical gradients for MP2, double hybrid functionals, and TD‐DFT with polarizable embedding described by fluctuating charges

2015

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A polarizable quantum mechanics (QM)/ molecular mechanics (MM) approach recently developed for Hartree–Fock (HF) and Kohn–Sham (KS) methods has been extended to energies and analytical gradients for MP2, double hybrid functionals, and TD‐DFT models, thus allowing the computation of equilibrium structures for excited electronic states together with more accurate results for ground electronic states. After a detailed presentation of the theoretical background and of some implementation details, a number of test cases are analyzed to show that the polarizable embedding model based on fluctuating charges (FQ) is remarkably more accurate than the corresponding electronic embedding based on a fixed charge (FX) description. In particular, a set of electronegativities and hardnesses has been optimized for interactions between QM and FQ regions together with new repulsion–dispersion parameters. After validation of both the numerical implementation and of the new parameters, absorption electronic spectra have been computed for representative model systems including vibronic effects. The results show remarkable agreement with full QM computations and significant improvement with respect to the corresponding FX results. The last part of the article provides some hints about computation of solvatochromic effects on absorption spectra in aqueous solution as a function of the number of FQ water molecules and on the use of FX external shells to improve the convergence of the results. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

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Analytical First and Second Derivatives for a Fully Polarizable QM/Classical Hamiltonian

Cited by 70 publications

References 83 publications

Accurate Simulation of Resonance-Raman Spectra of Flexible Molecules: An Internal Coordinates Approach

Accurate Simulation of Resonance-Raman Spectra of Flexible Molecules: An Internal Coordinates Approach

Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations

Analytical gradients for MP2, double hybrid functionals, and TD‐DFT with polarizable embedding described by fluctuating charges

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