Well-Tempered Variational Approach to Enhanced Sampling

We propose a simple yet effective iterative scheme that allows us to employ the well-tempered distribution as a target distribution for the collective variables in our recently introduced variational approach to enhanced sampling and free energy calculations [Valsson and Parrinello Phys. Rev. Lett. 2014, 113, 090601]. The performance of the scheme is evaluated for the three-dimensional free energy surface of alanine tetrapeptide where the convergence can be rather poor when employing the uniform target distribution. Using the well-tempered target distribution on the other hand results in a significant improvement in convergence. The results observed in this paper indicate that the well-tempered distribution is in most cases the preferred and recommended choice for the target distribution in the variational approach

Gas-Phase Retinal Spectroscopy: Temperature Effects Are But a Mirage

We employ state-of-the-art first-principle approaches to investigate whether temperature effects are responsible for the unusually broad and flat spectrum of protonated Schiff base retinal observed in photodissociation spectroscopy, as has recently been proposed. We first carefully calibrate how to construct a realistic geometrical model of retinal and show that the exchange–correlation M06-2X functional yields an accurate description while the commonly used complete active space self-consistent field method (CASSCF) is not adequate. Using modern multiconfigurational perturbative methods (NEVPT2) to compute the excitations, we then demonstrate that conformations with different orientations of the β-ionone ring are characterized by similar excitations. Moreover, other degrees of freedom identified as active in room-temperature molecular dynamics simulations do not yield the shift required to explain the anomalous spectral shape. Our findings indicate that photodissociation experiments are not representative of the optical spectrum of retinal in the gas phase and call for further experimental characterization of the dissociation spectra

Thermodynamical Description of a Quasi-First-Order Phase Transition from the Well-Tempered Ensemble

We explore the performance of the well-tempered ensemble combined with parallel tempering (PT-WTE) in obtaining a thermodynamical description of a given molecular system. We carefully explain the theoretical procedure employed to extract all the relevant thermodynamical quantities from a PT-WTE simulation. As a specific molecular system, we consider a Lennard–Jones cluster of 147 particles, which is a prototypical case of a finite-size system exhibiting a quasi-first-order phase transition, characterized by a range of temperatures where two distinct phases are thermodynamically stable and coexist. Two separate PT-WTE simulations, which investigate the thermodynamical behavior on different levels of detail, give equally accurate descriptions of the critical phase-coexistence region, indicating the good quality of the PT-WTE results. The positive performance observed here clearly demonstrates that the PT-WTE approach is an effective option when thermodynamical properties are needed

Hierarchical Protein Free Energy Landscapes from Variationally Enhanced Sampling

In recent work, we demonstrated that it is possible to obtain approximate representations of high-dimensional free energy surfaces with variationally enhanced sampling (Shaffer, P.; Valsson, O.; Parrinello, M. Proc. Natl. Acad. Sci., 2016, 113, 17). The high-dimensional spaces considered in that work were the set of backbone dihedral angles of a small peptide, Chignolin, and the high-dimensional free energy surface was approximated as the sum of many two-dimensional terms plus an additional term which represents an initial estimate. In this paper, we build on that work and demonstrate that we can calculate high-dimensional free energy surfaces of very high accuracy by incorporating additional terms. The additional terms apply to a set of collective variables which are more coarse than the base set of collective variables. In this way, it is possible to build hierarchical free energy surfaces, which are composed of terms that act on different length scales. We test the accuracy of these free energy landscapes for the proteins Chignolin and Trp-cage by constructing simple coarse-grained models and comparing results from the coarse-grained model to results from atomistic simulations. The approach described in this paper is ideally suited for problems in which the free energy surface has important features on different length scales or in which there is some natural hierarchy

The Crucial Role of Solvation Forces in the Steric Stabilization of Nanoplatelets

The steric stability of inorganic colloidal particles in an apolar solvent is usually described in terms of the balance between three contributions: the van der Waals attraction, the free energy of mixing, and the ligand compression. However, in the case of nanoparticles, the discrete nature of the ligand shell and the solvent has to be taken into account. Cadmium selenide nanoplatelets are a special case. They combine a weak van der Waals attraction and a large facet to particle size ratio. We use coarse grained molecular dynamics simulations of nanoplatelets in octane to demonstrate that solvation forces are strong enough to induce the formation of nanoplatelet stacks and by that have a crucial impact on the steric stability. In particular, we demonstrate that for sufficiently large nanoplatelets, solvation forces are proportional to the interacting facet area, and their strength is intrinsically tied to the softness of the ligand shell

The Crucial Role of Solvation Forces in the Steric Stabilization of Nanoplatelets

The steric stability of inorganic colloidal particles in an apolar solvent is usually described in terms of the balance between three contributions: the van der Waals attraction, the free energy of mixing, and the ligand compression. However, in the case of nanoparticles, the discrete nature of the ligand shell and the solvent has to be taken into account. Cadmium selenide nanoplatelets are a special case. They combine a weak van der Waals attraction and a large facet to particle size ratio. We use coarse grained molecular dynamics simulations of nanoplatelets in octane to demonstrate that solvation forces are strong enough to induce the formation of nanoplatelet stacks and by that have a crucial impact on the steric stability. In particular, we demonstrate that for sufficiently large nanoplatelets, solvation forces are proportional to the interacting facet area, and their strength is intrinsically tied to the softness of the ligand shell

The Crucial Role of Solvation Forces in the Steric Stabilization of Nanoplatelets

The steric stability of inorganic colloidal particles in an apolar solvent is usually described in terms of the balance between three contributions: the van der Waals attraction, the free energy of mixing, and the ligand compression. However, in the case of nanoparticles, the discrete nature of the ligand shell and the solvent has to be taken into account. Cadmium selenide nanoplatelets are a special case. They combine a weak van der Waals attraction and a large facet to particle size ratio. We use coarse grained molecular dynamics simulations of nanoplatelets in octane to demonstrate that solvation forces are strong enough to induce the formation of nanoplatelet stacks and by that have a crucial impact on the steric stability. In particular, we demonstrate that for sufficiently large nanoplatelets, solvation forces are proportional to the interacting facet area, and their strength is intrinsically tied to the softness of the ligand shell

The Crucial Role of Solvation Forces in the Steric Stabilization of Nanoplatelets

The steric stability of inorganic colloidal particles in an apolar solvent is usually described in terms of the balance between three contributions: the van der Waals attraction, the free energy of mixing, and the ligand compression. However, in the case of nanoparticles, the discrete nature of the ligand shell and the solvent has to be taken into account. Cadmium selenide nanoplatelets are a special case. They combine a weak van der Waals attraction and a large facet to particle size ratio. We use coarse grained molecular dynamics simulations of nanoplatelets in octane to demonstrate that solvation forces are strong enough to induce the formation of nanoplatelet stacks and by that have a crucial impact on the steric stability. In particular, we demonstrate that for sufficiently large nanoplatelets, solvation forces are proportional to the interacting facet area, and their strength is intrinsically tied to the softness of the ligand shell

The Crucial Role of Solvation Forces in the Steric Stabilization of Nanoplatelets

The steric stability of inorganic colloidal particles in an apolar solvent is usually described in terms of the balance between three contributions: the van der Waals attraction, the free energy of mixing, and the ligand compression. However, in the case of nanoparticles, the discrete nature of the ligand shell and the solvent has to be taken into account. Cadmium selenide nanoplatelets are a special case. They combine a weak van der Waals attraction and a large facet to particle size ratio. We use coarse grained molecular dynamics simulations of nanoplatelets in octane to demonstrate that solvation forces are strong enough to induce the formation of nanoplatelet stacks and by that have a crucial impact on the steric stability. In particular, we demonstrate that for sufficiently large nanoplatelets, solvation forces are proportional to the interacting facet area, and their strength is intrinsically tied to the softness of the ligand shell

Rhodopsin Absorption from First Principles: Bypassing Common Pitfalls

Bovine rhodopsin is the most extensively studied retinal protein and is considered the prototype of this important class of photosensitive biosystems involved in the process of vision. Many theoretical investigations have attempted to elucidate the role of the protein matrix in modulating the absorption of retinal chromophore in rhodopsin, but, while generally agreeing in predicting the correct location of the absorption maximum, they often reached contradicting conclusions on how the environment tunes the spectrum. To address this controversial issue, we combine here a thorough structural and dynamical characterization of rhodopsin with a careful validation of its excited-state properties via the use of a wide range of state-of-the-art quantum chemical approaches including various flavors of time-dependent density functional theory (TDDFT), different multireference perturbative schemes (CASPT2 and NEVPT2), and quantum Monte Carlo (QMC) methods. Through extensive quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations, we obtain a comprehensive structural description of the chromophore–protein system and sample a wide range of thermally accessible configurations. We show that, in order to obtain reliable excitation properties, it is crucial to employ a sufficient number of representative configurations of the system. In fact, the common use of a single, ad hoc structure can easily lead to an incorrect model and an agreement with experimental absorption spectra due to cancelation of errors. Finally, we show that, to properly account for polarization effects on the chromophore and to quench the large blue-shift induced by the counterion on the excitation energies, it is necessary to adopt an enhanced description of the protein environment as given by a large quantum region including as many as 250 atoms