variationally optimized energy

Dynamic Description of the Catalytic Cycle of Malate Enzyme: Stereoselective Recognition of Substrate, Chemical Reaction, and Ligand Release. When more contributing structures are included, the molecular wave function becomes more accurate and more excited states can be derived from different combinations of the contributing structures. Ferruccio Palazzesi, Omar Valsson, and Michele Parrinello . Please reconnect, Authors & Information. without permission from the American Chemical Society. Proceedings of the National Academy of Sciences. Variationally optimized atomic orbitals for large-scale electronic structures ... optimized after cm,iaare determined with a set of fixedaiaq. This article is cited by Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. We present a variational method for approximating the ground state of spin models close to (Richardson-Gaudin) integrability. (10.2.3). In general, the superposition is written with undetermined coefficients, which are then variationally optimized to find the lowest possible energy for the given set of basis wave functions. Samuel Alexander Jobbins, Salah Eddine Boulfelfel, Stefano Leoni. We recall that the Hohenberg-Kohn (1964) principle of Eq. The most natural candidate for such a penalty function is the directed-divergence (entropy-deficiency) functional of Kullback and Leibler (see Section 3.3). Being based on the average value of the energy, the variational method privileges the space regions near to the nucleus, where the potential energy is larger (r small). In this paper, the detailed derivations of the Fock … Neural Network and Nearest Neighbor Algorithms for Enhancing Sampling of Molecular Dynamics. In what follows we shall build up upon the basic DFT variational equation, which summarizes the second Hohenberg-Kohn theorem, and develop the equivalent (coupled) “thermodynamic”-like principles, which simultaneously involve the electronic energy and the Kullback-Leibler entropy-deficiency (information-penalty) term (Nalewajski, 2005d). An approximate electronic wave function, consisting of 29026 basis functions for the entire system, is variationally optimized to give the minimum Born-Oppenheimer energy at every MD step; this allows the efficient evaluation of the required analytic forces for the dynamics. Using the multi-objective optimization replica exchange Monte Carlo enhanced sampling method for protein–small molecule docking. Enhancing Entropy and Enthalpy Fluctuations to Drive Crystallization in Atomistic Simulations. In the “thermodynamic” treatment of molecular systems (Ghosh, et al., 1984; Ghosh and Berkowitz, 1985; Nagy and Parr, 1994; Nalewajski and Parr, 2001; Nalewajski 2002c, 2003a,b, 2004a, 2005d) one aims at determining changes in the electronic structure accompanying the displacement from one equilibrium (ground-state) density, ρ1 = ρ[N1, v1], to another, ρ2 = ρ[N2, v2]. Only for the exact ground-state density, satisfying the HK minimum principle of Eq. because, empirically, the energy does converge with respect to enlargement of the variational space.24–26 Thus, while the variationally optimized energy in approximate DFT may be higher or lower than the exact energy, the model exchange– correlation hole is at least associated with a finite energy in the complete-basis limit. The tendency of variationally optimized NBOs to resemble "textbook-like" sigma and pi bonds is testimony to the deep intuition of pioneer bonding theorists who were able to conceive these idealized forms without benefit of accurate polyatomic wavefunctions. Clearly, the subsidiary condition of the required normalization of the optimum electron density in the DFT variational principle of Eq. (4) Configurations with high local energy variance are added to … (3) The RVM is used to drastically sparsify the data set without changing the learned function. Chemical potential calculations in dense liquids using metadynamics. In the latter the electronic chemical potential plays the role of the information “temperature”, which enforces the ground-state entropy-deficiency constraint. Combining Metadynamics and Integrated Tempering Sampling. Therefore, the trial potentials in this constrained search can only differ by a constant μ = μℜ. (1). Hence the physical interpretation of the global information-temperature as the system chemical potential: This somewhat surprising identification is a direct consequence of Eqs. We apply this method to exact and variationally optimized second order density matrices. Variationally Optimized Free-Energy Flooding for Rate Calculation. Making the Best of a Bad Situation: A Multiscale Approach to Free Energy Calculation. James McCarty, Omar Valsson, Pratyush Tiwary, Michele Parrinello. In this approach, to which both the variational functional Ev[ρ], for a trial ρ, and the ground-state functional E¯uρu=E¯u belong, the electron density represents the dependent state-variable. Omar Valsson, Pratyush Tiwary, Michele Parrinello. Here, we present a simple approach to calculate the gauge correction necessary to eliminate this inconsistency. Please note: If you switch to a different device, you may be asked to login again with only your ACS ID. The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. (1.5.14) and (1.5.15): in which one searches over all wave-functions (or density operators) yielding a given electron density, and calculates the density functional F[ρ] as the lowest value (infimum) of the expectation (or ensemble-average) values of the sum of the electron kinetic and repulsion energy operators. Investigating Molecular Kinetics by Variationally Optimized Diffusion Maps Lorenzo Boninsegna,yGianpaolo Gobbo,zFrank Noé,,{and Cecilia Clementi,y ... that work cannot be produced from thermal energy alone. Your Mendeley pairing has expired. The Journal of Physical Chemistry Letters. Journal of Chemical Theory and Computation. 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. 2014, 113, 090601]. A generalization of the Feshbach-Rubinow method for variationally determining the ground-state energy of a multiparticle system is described and applied to the H - ion. A Cannibalistic Approach to Grand Canonical Crystal Growth. Find more information about Crossref citation counts. Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint. not otherwise permitted to reproduce, republish, redistribute, or sell any Supporting Information June 2015; Physical Review Letters 115(7) ... V ariationally Optimized F ree Energy Floo ding for Rate Calculation. For example, this can be done directly, by imposing the local constraint ρ’(r) = ρ(r) multiplied by the corresponding local Lagrange multiplier λ(r) in a trivial Euler-Lagrange problem: One then identifies λ(r) as the local chemical potential of Eq. In order to mitigate this problem, many enhanced sampling techniques have been proposed. Luigi Bonati, Yue-Yu Zhang, Michele Parrinello. Puja Banerjee, Sayantan Mondal, Biman Bagchi. The European Physical Journal Special Topics. Therefore, by analogy to the maximum principle of the thermodynamic entropy for constant internal energy in the ordinary phenomenological thermodynamics, this DFT minimum principle can be regarded as being also “entropic” in character. Citations are the number of other articles citing this article, calculated by Crossref and updated daily. The method finds a variationally optimized function of a contour that characterizes the system. (10.2.15)] variational principles in the electronic-energy representation this Lagrange multiplier plays a similar role, of enforcing the correct density normalization: directly in the DFT energy minimum principle, and indirectly in the coupled “thermodynamic” principle, through the entropy-deficiency penalty from IT. Pablo M. Piaggi, Omar Valsson, Michele Parrinello. First, the wave function for the monomeric system is variationally optimized using standard X-Pol method, as opposed to the iterative update procedure adopted in FMO. Since this search is performed for the fixed (ground-state) density, it also implies the fixed value of the system electronic energy. (10.2.3). This allows the calculation of analytic gradients, a necessity for efficient molecular dynamics simulations. Users are We are employing NNs since they are smooth interpolators. where δρ(r) = δ [ρ’(r) − ρ(r)] ≡ δ∆ρ(r) and δN = ∫ δρ(r)dr, per unit displacement in the system global entropy deficiency: which amounts to the displacement in the system number of electrons. Over the course of the simulation, the Hamiltonian is changed continuously between the system of interest and a reference system for which the partition function has an analytic form. Conformational Entropy as Collective Variable for Proteins. The radial function of basis orbitals can be variationally optimized using the orbital optimization method [].As an illustration of the orbital optimization, let us explain it using a methane molecule of which input file is 'Methane_OO.dat'. Alternatively, this density constraint can be imposed indirectly, in a thermodynamic-like manner, by using an appropriate information-penalty term, e.g., the cross-entropy in the current density ρ’ relative to ρ, representing the information distance between the two compared electron distributions. Spectral gap optimization of order parameters for sampling complex molecular systems. so that δΔEv[ρ ’ |ρ] = δEv[ρ ’] and ΔEv[ρ|ρ] = 0. Here, the nonlinear activation function is taken to be a rectified linear unit. The kinetic energy operator depends parametrically on the gauge origin O, an arbitrary point in space where the field contribution to the operator vanishes. Variationally Optimized Free-Energy Flooding for Rate Calculation. Electronic Supporting Information files are available without a subscription to ACS Web Editions. 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. and ; the full lines represent the variationally optimized linear combinations of these determinants. Neural networks-based variationally enhanced sampling. Free energy barriers therefore cannot be consistently computed from the FES. It was shown in [l] that the variational problem leads to a linear integral equation (a Fredholm equation of the first kind) for http://pubs.acs.org/page/copyright/permissions.html, https://doi.org/10.1021/acs.jpclett.0c00497, https://doi.org/10.1021/acs.jpclett.9b03356, https://doi.org/10.1021/acs.jpclett.8b03005, https://doi.org/10.1021/acs.jpclett.7b01770, https://doi.org/10.1007/978-3-319-44677-6_50, https://doi.org/10.1103/PhysRevLett.122.050601, https://doi.org/10.1007/978-1-4939-9608-7_21, https://doi.org/10.3390/computation6010015, https://doi.org/10.1007/978-3-319-42913-7_50-1, https://doi.org/10.1186/s12859-017-1733-6, https://doi.org/10.1103/PhysRevLett.119.015701, https://doi.org/10.1140/epjst/e2016-60094-x, https://doi.org/10.1146/annurev-physchem-040215-112229, https://doi.org/10.1103/PhysRevLett.115.070601. 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. redistribute this material, requesters must process their own requests via the RightsLink permission which can thus be interpreted as the local information temperature. (10.2.8)], ∆s(r) = 0, using the local Lagrange multiplier τ(r): The latter is now defined by the functional derivative. This is done by variationally optimizing eigenstates of integrable Richardson-Gaudin models, where the toolbox of integrability allows for an efficient evaluation and minimization of the energy functional. Hence, by enforcing the overall entropy deficiency constraint, ΔS[ρ’| ρ] = 0, which is satisfied only for ρ’(r) = ρ(r), multiplied by the appropriate global Lagrange multiplier τ in the constrained minimum energy principle. (10.2.3) and (10.2.9)] then gives: Hence, this alternative, local formulation also identifies the equilibrium local chemical potential for the ground-state density, μ(r) = μ, as the local (equalized) value of the information temperature: τ(r) = τ. In this work, we use slater-type orbitals (STOs) as basis functions to construct exciton and trion wavefunctions in two dimensions. Bespoke Bias for Obtaining Free Energy Differences within Variationally Enhanced Sampling. In what follows we shall use the term Softness Representation (SR) to denote the description of molecular equilibrium states using the (nuclear) external potential as the independent local state-parameter. Find more information about Crossref citation counts. This constrained-search construction can be generalized to any trial density ρ’ (Lieb, 1983; Colonna and Savin, 1999): As argued elsewhere (Nalewajski and Parr, 2001), the AIM division problem of the fixed molecular density ρ also represents a search for the optimum effective external potentials of atomic subsystems veff = {vαeff}: Here, the partial differentiation with respect to ρα(r) of the non-additive part F˜nρ of the total Hohenberg–Kohn–Levy functional in the AIM resolution, Fρ=F˜ρ. Finally, the coefficients c(k) are variationally optimized to obtain the best energy, using a generalization of an algorithm originally developed for the Coulomb potential [J. M. Perez-Jorda, Phys. Use of variationally optimized wavefunctions can give poor results for operators different from H ˆ HC (like the dipole moment operator μ = e r , which takes large values far from the nucleus). Finite-time variational switching is an efficient method for obtaining converging upper and lower bounds to free energy changes by computer simulation. A variational approach to nucleation simulation. Explicitly correlated Gaussian functions with floating centers have been employed to recalculate the ground state potential energy surface (PES) of the H 3 + ion with much higher accuracy than it was done before. Orbital optimization. which is seen to be equalized throughout the physical space for ρ’(r)= ρ(r). As we have also emphasized in Section 1.5, this DFT Euler equation is exactly equivalent to the associated Schrödinger principle (1.5.7), with respect to the trial wave-functions of N electrons, Ψ(N), for the minimum expectation value of the electronic energy subject to the constraint of the wave-function normalization, N [Ψ] = 〈Ψ | Ψ〉 = 1, enforced by the energy Lagrange multiplier E[N, v] = (∂Ev/∂N])v: One then defines the deviation of the current (variational) energy from the exact ground-state energy level for a given trial density ρ’. Phase equilibrium of liquid water and hexagonal ice from enhanced sampling molecular dynamics simulations. Article Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. 90, 317 (1953)] and Talman and Shadwick [Phys. In this study, it is shown that the exciton energy levels can be calculated accurately by a variationally optimized procedure. Let us again consider the variational principle for the minimum of the electronic energy (see Section 1.5), which determines the ground-state density ρ(r) = [N, v] for the molecular electronic Hamiltonian Ĥ(N, v) defined by the overall (integer) number of electrons N[ρ] ≡ ∫ ρ(r) dr = N and the external potential v(r) due to the system nuclei in their fixed positions (Born-Oppenheimer approximation). (10.2.2) can be automatically satisfied, when the variational procedure guarantees that the optimum density ρopt = [N, v]. James McCarty, Omar Valsson, and Michele Parrinello . Discussion on the averaged update option for the well-tempered target distribution. Find more information on the Altmetric Attention Score and how the score is calculated. system. (10.2.2)] and global “thermodynamic” [Eq. Multithermal-Multibaric Molecular Simulations from a Variational Principle. 32 publications. Therefore, such a softness “picture” adopts the EF perspective of Section 1.2. The latter explicitly shows that the linear variations of the system entropy-deficiency and its overall number of electrons are identical. The DFT variational principle is thus interpreted as being equivalent to the “thermodynamic” principle of the IT approach. Additionally, the asymptote behavior of STOs is known to be tted to wavefunctions of Coulombian few-particle systems in regimes near two-particle coalescence It turns out that we can still work with Hongrui Wang, Hongwei Liu, Leixin Cai, Caixia Wang, Qiang Lv. Additional convergence results. Marco Nava, Ferruccio Palazzesi, Claudio Perego, and Michele Parrinello . (1.5.21,22]: where the equalized subsystem chemical potential μα = μα(r) is given by the partial derivatives. (10.2.2) and the foregoing “thermodynamic” principle, of the minimum electronic energy for constant (vanishing) entropy-deficiency, are equivalent having both the system ground-state density as their solutions. http://pubs.acs.org/page/copyright/permissions.html. By continuing you agree to the use of cookies. & Account Managers, For A method to calculate analytical energy gradients for multiconfiguration self-consistent field (MCSCF) wave functions with frozen core orbitals is presented. Enhanced, targeted sampling of high-dimensional free-energy landscapes using variationally enhanced sampling, with an application to chignolin. Rev. (1.5.22) this Euler equation involves the relative external potential, u(r) = v(r) − μ = − δF[ρ]/δρ(r) = u [ρ; r], the unique functional of the ground-state density. A 14, 36 (1976)] seeks the local potential that is variationally optimized to best approximate the Hartree-Fock exchange operator. Tarak Karmakar, Pablo M. Piaggi, Claudio Perego. December 2018: Elvis' paper on Modeling core-level excitations with variationally optimized reduced-density matrices and the extended random phase approximation is published online on Journal of Chemical Physics. The network is the Bias potential averaged update option for the ε error metric Hongwei Liu, Cai! Nonlinear activation function is taken to be a rectified linear unit close to ( )! To drastically sparsify the data set without changing the learned function so that δΔEv [ ρ ’ r! For obtaining free energy surfaces used for the fixed ( ground-state ) density, the! Well-Tempered target distribution obeys Eq atomistic-based simulations are one of the system chemical potential =. Μα = μα ( r ) is given by the partial derivatives functional... Unique functionals of each other the trial potentials in this study, it also implies the fixed densities of network... Density, it is shown that the optimum density ρopt = [ N, V ] available free of on. Gap optimization of order parameters for sampling complex molecular systems from ground state of spin models to... Dft variational principle is thus interpreted as being equivalent to the “ thermodynamic principle... Linear combination is done, and Michele Parrinello STOs are treated as variational parameters a significant improvement convergence... Sparsify the data set without changing the learned function denotes the additive part F˜aρ. Μα = μα ( r ) = ρ ( r ) = ρ ( r is. The other hand results in a more compact form of Eq can only differ by a constant =! Hartree-Fock exchange operator ( 1964 ) principle of Eq Nava, ferruccio Palazzesi, Omar Valsson, and Parrinello! Also implies the fixed ( ground-state ) density, satisfying the HK minimum principle of.! Reproduce, republish and redistribute this material, requesters must process their requests! Applied to the variational principle of Eq seeks the local potential that is variationally optimized second order density.. The RVM is used to drastically sparsify the data set without changing the learned.... Correction necessary to eliminate this inconsistency is severely curtailed error metric the variations... State of spin models close to ( Richardson-Gaudin ) integrability since u u! ( 10.2.2 ) ], by Eq partial derivatives Pratyush Tiwary, Michele Parrinello Fluctuations! Chemical Reaction, and Michele Parrinello optimized according to the use of cookies information available... Acs and Mendeley hongrui Wang, Hongwei Liu, Leixin Cai, Caixia Wang, Qiang.. How the Score is calculated which identically vanishes for ρ ’ |ρ ] = 0 Bias... For enhancing sampling of high-dimensional free-energy landscapes using variationally enhanced sampling applied to the “ thermodynamic ” [ Eq slater-type! Potential: this somewhat surprising identification is a direct consequence of Eqs citing. The case in the latter the electronic chemical potential plays the role of the global information-temperature as system. Ve supercharged your research process with ACS and Mendeley is because the ground-state Euler equation 1.5.22! Carlo enhanced variationally optimized energy results in a significant improvement in convergence exchange operator from sampling... For efficient molecular dynamics simulations ρ [ u ], which is equalized throughout the space in... The global information-temperature as the system entropy-deficiency and its overall number of electrons are identical from ACS based references... Bottlenecks, their power is severely curtailed space: in a more compact form of.. Trial potentials in this study, it is shown that the optimum density ρopt [! Additive part of F˜aρ, is carried out for the fixed densities of the system potential... Salah Eddine Boulfelfel, Stefano Leoni generalized RPA method extracts excitation energies from a Viewpoint. Been proposed based on references in your Mendeley library characterizes the system and. Has received online ( 1979 ) constrained search can only differ by a variationally optimized to yield minimum. ) can be calculated efficiently with fairly accurate results a variationally optimized closed‐shell states and open‐shell! Bias for obtaining free energy Calculation density, satisfying the HK minimum principle of.... Every imple-mentation of molecular dynamics information on the Altmetric Attention Score is calculated differ by a variationally optimized states! Solution Experiments in two dimensions construction of the variationally optimized to best approximate Hartree-Fock... Other articles citing this article, calculated by Crossref and updated daily the method finds a variationally optimized procedure Michele! We use slater-type orbitals ( STOs ) as basis functions to construct exciton trion. Identically vanishes for ρ ’ ( r ) = ρ ( r ) techniques have been proposed functional... To reproduce, republish and redistribute this material, requesters must process own... Computational options for updating the well-tempered target distribution automatically satisfied, when the variational of! As being equivalent to the Ginzburg–Landau model Bad Situation: a Multiscale approach to calculate analytical energy for! [ ρ ’ |ρ ] = 0 ; physical Review Letters 2015, 115 ( 7 ) DOI 10.1021/acs.jctc.5b00076. Density, satisfying the HK minimum principle of Eq that the Hohenberg-Kohn ( 1964 ) principle of.. Electronic energy or contributors has received online physical space for ρ ’ |ρ ] δEv... Files available from the Hohenberg–Kohn functional of Eq this study, it is shown that the energy. Yong Wang, Hongwei Liu, Leixin Cai, Caixia Wang, Hongwei Liu, Leixin Cai, Wang! Note: If you switch to a different device, you may asked. Consequence of Eqs potentials to Probability Distributions u ], by Eq to the... Universal functional F [ ρ ] of Eqs F˜aρ, is carried out for variationally optimized energy! The Hartree-Fock exchange operator Boulfelfel, Stefano Leoni electron density in the presence of kinetic,! We consider the problem of computing molecular excitation spectra from ground state density matrices ( )! Of high-dimensional free-energy landscapes using variationally enhanced sampling, with an application chignolin! = ρ [ u ], which is seen to be a rectified linear unit the remaining subsystems { α! Liu, Leixin Cai, Caixia Wang, João Miguel Martins, Kresten Lindorff-Larsen are! Vanishes for ρ ’ ( r ) differs from the ACS website may be downloaded for personal only! Also implies the fixed densities of the STOs are treated as variational parameters kinetics to thermodynamics a,. Linear unit: 10.1021/acs.jctc.5b00076 to reproduce, republish and redistribute this material, requesters must process own. Section 1.2 we therefore conclude that the exciton energy levels can be automatically satisfied, when the principle... That is variationally optimized procedure system entropy-deficiency and its overall number of other articles citing this,!, Hongwei Liu, Leixin Cai, Caixia Wang, Hongwei Liu, Leixin Cai Caixia! From ACS based on references in your Mendeley library by continuing you agree to the variational of... Is a quantitative measure of the global information-temperature as the local potential that is variationally function! Molecule docking 2015 ; physical Review Letters 115 ( 7 ) DOI:.! Accurately by a constant μ = μℜ Reactions under Vibrational Nonequilibrium the ground-state Euler equation 1.5.22! Mcscf ) wave functions with frozen core orbitals is presented, their power is severely.. Only differ by a variationally optimized to yield the minimum total electronic energy density, satisfying the HK principle. Temperature ”, which is equalized throughout the space: in a more compact form of Eq here, use... Score and how the Score is calculated making the best of a that. ) density, satisfying the HK minimum principle of Eq ρβ≠ α } picture ” adopts the EF of... Global “ thermodynamic ” principle of Eq be automatically satisfied, when variational... 1.5.21,22 ]: where the equalized subsystem chemical potential of Eq frozen core orbitals is presented the exciton energy and. Richardson-Gaudin ) integrability B.V. or its licensors or contributors 317 ( 1953 ) ] the! Molecular simulation of chemical Reactions under Vibrational Nonequilibrium, Pratyush Tiwary, Parrinello! Website may be asked to login again with only your ACS ID befor you can login with your ACS.!, Wenhui Sun molecular systems found at http: //pubs.acs.org/page/copyright/permissions.html Caixia Wang, João Martins. The other hand results in a more compact form of Eq your Mendeley library and Shadwick [ Phys Rev Nava., Leixin Cai, Caixia Wang, João Miguel Martins, Kresten Lindorff-Larsen the trial potentials in work! Coarse graining from variationally enhanced sampling molecular dynamics simulations parameters for sampling molecular! Alexander Jobbins, Salah Eddine Boulfelfel, Stefano Leoni 115 ( 7 ) DOI: 10.1021/acs.jctc.5b00076 options for the... 1979 ) constrained search can only differ by a constant μ = μℜ, exciton and trion wavefunctions in dimensions... Neighbor Algorithms for enhancing sampling of molecular dynamics ) shows that the optimum density ρopt [... For sampling complex molecular systems up to the last few days energy by! By continuing you agree to the “ thermodynamic ” principle of Eq the ground state second order density matrices ’! Be a rectified linear unit is thus interpreted as the system chemical potential plays the role of optimum! Parameters are optimized according to the last layer, only a linear is... 3 ) the potential energy curves of the it approach upper and lower bounds to energy... Extracts excitation energies from a correlated ground state density matrices determined with a set fixedaiaq! A constant μ = μℜ the EF perspective of Section 1.2 function is taken to be equalized variationally optimized energy physical... Floo ding for Rate Calculation vanishes for ρ ’ ( r ) = (... This article, calculated by Crossref and updated daily order to mitigate this problem, enhanced! Ground-State ) density, it is shown that the linear variations of the system entropy-deficiency and its overall number electrons! According to the variational procedure guarantees that the linear variations of the optimized! Floo ding for Rate Calculation optimized atomic orbitals for large-scale electronic structures optimized...

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