Complex Energy Surface Research Articles

An explicitly correlated potential energy surface for N2-OCS complex: Out-of-plane motion and tunneling dynamics.

A four-dimensional potential energy surface (4D-PES) has been constructed for the N2-OCS complex. The PES is achieved by applying the explicitly correlated coupled cluster method, which incorporates single, double, and perturbative triple excitations [CCSD(T)-F12a], along with the augmented correlation consistent triple zeta (aug-cc-pVTZ) basis set. The rovibrational levels are precisely determined and assigned through bound state calculations and wavefunction analysis. The calculated transition frequencies reproduce the experimental observations accurately, achieving an RMSE of 0.0005cm-1 for the 23 rotational transitions (J ≤ 6, Ka ≤ 2). The R-φ contour plot of the wave function clearly demonstrates the unambiguous delocalization of the dihedral angle, and the averaged geometry of the ground vibrational state is determined to be non-planar with φ = 90°. To obtain a quantitative analysis of this phenomenon, we expanded the 3H-solution model [Guo et al., J. Quant. Spectrosc. Radiat. Transfer 309 (2023) 108711] from a three-dimensional system (Ar-AgF) to a nine-dimensional system (N2-OCS). Based on this model, the tunneling splitting was calculated to be 0.0822cm-1, which excellently matches the experimental result of 0.0817cm-1. The excellent agreement between the theoretical and experimental results suggests that the wavefunction delocalization and out-of-plane motion can be attributed to the tunneling effects in the ground vibrational state.

Collisional excitation of propyne (CH3CCH) by He atoms

Context. A detailed interpretation of the detected emission lines of environments where propyne (or methyl acetylene, CH3CCH) is observed requires access to its collisional rate coefficients with the most abundant species in the interstellar medium, namely, helium (He) or molecular hydrogen (H2). Aims. We present the first three-dimensional potential energy surface (3D PES) for the CH3CCH-He molecular complex. We study the dynamics of the collision and report the first set of rate coefficients for temperatures up to 100 K for the collisional excitation of the lowest 60 ortho rotational levels and 60 para rotational levels of CH3CCH by He atoms. Methods. We computed the 3D PES with the explicitly correlated coupled-cluster with a single-, double-, and perturbative triple-excitation method in conjunction with the augmented correlation-consistent triple zeta basis set (CCSD(T)-F12a/aug-cc-pVTZ). The 3D PES was then fitted to an analytical function and scattering computations of pure rotational (de-)excitation of CH3CCH by collision with He atoms were performed. State-to-state cross-sections were computed using the close coupling method for total energies up to 100 cm−1 and with the coupled states approximation at higher energies for both the ortho- and para- symmetries of CH3CCH. Results. The PES we obtained is characterised by a large anisotropy and a potential well depth of 51.04 cm−1. By thermally averaging the collisional cross-sections, we determined the quenching rate coefficients for kinetic temperatures up to 100 K. A strong and even Δj propensity rule at almost all collision energies is present for CH3CCH-He complex. To evaluate the impact of rate coefficients on the analysis of observations, we carried out non-local thermodynamic equilibrium radiative transfer computations of the excitation temperatures and we demonstrate that local thermodynamic equilibrium conditions are not typically fulfilled for the propyne molecule.

Computational modelling of a triaxial vibrating sample magnetometer

Magnetic Field Assisted Additive Manufacturing (MFAAM) enables 3D printing of magnetic materials of various shapes which exhibit a complex anisotropy energy surface containing contributions generated from different origins such as sample, particle, and agglomerate shape anisotropy, flow and field induced anisotropy, and particle crystal anisotropy. These novel magnet shapes require the need to measure the x, y, and z components of the magnetic dipole moment simultaneously to fully understand the magnetic reversal mechanism and unravel the complex magnetic anisotropy energy surface of 3D printed magnetic composites. This work aims to develop a triaxial vibrating sample magnetometer (VSM) by adding a z-coil set to a pre-existing biaxial VSM employing a modified Mallison coil set. The optimum size and location of the sensing coils were determined by modeling the sensitivity matrix of the z-coil set. The designed coil set was implemented using 3D printed spools, a manual coil winder, and gauge 38 copper wire. A 3D printed strontium ferrite nylon composite sample was used to estimate the sensitivity of the z-coils (50 mV/emu). The results herein are applicable for any VSM using a modified Mallison biaxial coil configuration allowing for a quick implementation on pre-existing systems.

Reliable Dimerization Energies for Modeling of Supramolecular Junctions.

Accurate estimates of intermolecular interaction energy, ΔE, are crucial for modeling the properties of organic electronic materials and many other systems. For a diverse set of 50 dimers comprising up to 50 atoms (Set50-50, with 7 of its members being models of single-stacking junctions), benchmark ΔE data were compiled. They were obtained by the focal-point strategy, which involves computations using the canonical variant of the coupled cluster theory with singles, doubles, and perturbative triples [CCSD(T)] performed while applying a large basis set, along with extrapolations of the respective energy components to the complete basis set (CBS) limit. The resulting ΔE data were used to gauge the performance for the Set50-50 of several density-functional theory (DFT)-based approaches, and of one of the localized variants of the CCSD(T) method. This evaluation revealed that (1) the proposed "silver standard" approach, which employs the localized CCSD(T) method and CBS extrapolations, can be expected to provide accuracy better than two kJ/mol for absolute values of ΔE, and (2) from among the DFT techniques, computationally by far the cheapest approach (termed "ωB97X-3c/vDZP" by its authors) performed remarkably well. These findings are directly applicable in cost-effective yet reliable searches of the potential energy surfaces of noncovalent complexes.

A new six-dimensional abinitio potential energy surface and rovibrational spectra for the N2-CO2 complex.

New six-dimensional abinitio potential energy surfaces (PESs) for the N2-CO2 complex, which involve the stretching vibration of N2 and the Q3 normal mode for the ν3 asymmetric stretching vibration of CO2, were constructed using the CCSD(T)-F12/AVTZ method with midpoint bond functions. Two vibrational averaged 4D interaction potentials were obtained by integrating over the two intramolecular coordinates. It was found that both PESs possess two equivalent T-shaped global minima as well as two in-plane and one out-of-plane saddle points. Based on these PESs, rovibrational bound states and energy levels were calculated applying the radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm. The splitting of the energy levels between oN2-CO2 and pN2-CO2 for the intermolecular vibrational ground state is determined to be only 0.000 09cm-1 due to the higher barriers. The obtained band origin shift is about +0.471 74cm-1 in the N2-CO2 infrared spectra with CO2 at the ν3 zone, which coincides with the experimental data of +0.483 74cm-1. The frequencies of the in-plane geared-bending for N2-CO2 at the ν3 = 0 and 1 states of CO2 turn out to be 21.6152 and 21.4522cm-1, the latter reproduces the available experimental 21.3793cm-1 value with CO2 at the ν3 zone. The spectral parameters fitted from the rovibrational energy levels show that this dimer is a near prolate asymmetric rotor. The computed microwave transitions as well as the infrared fundamental and combination bands for the complex agree well with the observed data.

Equatorial restriction of the photoinduced Jahn-Teller switch in Mn(iii)-cyclam complexes.

Ultrafast transient absorption spectra were recorded for solutions of [MnIII(cyclam)(H2O)(OTf)][OTf]2 (cyclam = 1,4,8,11-tetraazacyclotetradecane and OTf = trifluoromethanesulfonate) in water to explore the possibility to restrict the equatorial expansion following photoexcitation of the dxy ← dz2 electronic transition, often resulting in a switch from axial to equatorial Jahn-Teller distortion in MnIII complexes. Strong oscillations were observed in the excited state absorption signal and were attributed to an excited state wavepacket. The structural rigidity of the cyclam ligand causes a complex reaction coordinate with frequencies of 333, 368, 454 and 517 cm-1, and a significantly shorter compressed-state lifetime compared to other MnIII complexes with less restricted equatorial ligands. Complementary density functional theory quantum chemistry calculations indicate a switch from an axially elongated to a compressed structure in the first excited quintet state Q1, which is accompanied by a modulation of the axial tilt angle. Computed harmonic frequencies for the axial stretching mode (∼379 cm-1) and the equatorial expansions (∼410 and 503 cm-1) of the Q1 state agree well with the observed coherences and indicate that the axial bond length contraction is significantly larger than the equatorial expansion, which implies a successful restriction of the wavepacket motion. The weak oscillation observed around 517 cm-1 is assigned to a see-saw motion of the axial tilt (predicted ∼610 cm-1). The results provide insights into the structural perturbations to the molecular evolution along excited state potential energy surfaces of MnIII octahedral complexes and can be used to guide the synthesis of optically controlled MnIII-based single-molecule magnets.

Three-dimensional ab initio potential energy surface and predicted spectra for the CH4-Ne complex

We present a new three-dimensional potential energy surface (PES) for CH4-Ne complex. The electronic structure computations were carried out using the coupled-cluster method with singles, doubles, and perturbative triples [CCSD(T)], the augmented correlation-consistent aug-cc-pVXZ (X=T,Q) basis sets were employed with bond functions placed at the mid-point on the intermolecular axis, and the energies obtained were then extrapolated to the complete basis set limit. Analytic intermolecular PES is obtained by least-squares fitting to the Morse/Long-Range (MLR) potential function form. These fits to 664 points have root-mean-square deviations of 0.042 cm−1. The bound rovibrational levels are calculated for the first time, and the predicted infrared spectra are in good agreement with the experimental values. The microwave spectra for CH4-Ne dimer have also been predicted for the first time. The analytic PES can be used for modeling the dynamical behavior in CH4-(Ne)N clusters, and it will be useful for future studies of the collision-induced-absorption for the CH4-Ne dimer.

Collisional excitation of NH by H2: Potential energy surface and scattering calculations.

Collisional data for the excitation of NH by H2 are key to accurately derive the NH abundance in astrophysical media. We present a new four-dimensional potential energy surface (PES) for the NH-H2 van der Waals complex. The ab initio calculations of the PES were carried out using the explicitly correlated partially spin-restricted coupled cluster method with single, double, and perturbative triple excitations [RCCSD(T)-F12a] with the augmented correlation-consistent polarized valence triple zeta basis set. The PES was represented by an angular expansion in terms of coupled spherical harmonics. The global minimum corresponds to the linear structure with a well depth De = 149.10 cm-1. The calculated dissociation energy D0 is found to be 30.55 and 22.11 cm-1 for ortho-H2 and para-H2 complexes, respectively. These results are in agreement with the experimental values. Then, we perform quantum close-coupling calculations of the fine structure resolved excitation cross sections of NH induced by collisions with ortho-H2 and para-H2 for collisional energies up to 500 cm-1. We find strong differences between collisions induced by ortho-H2 and para-H2. Propensity rules are discussed. The cross sections are larger for fine structure conserving transitions than for fine structure changing ones, as predicted by theory. These new results should help in interpreting NH interstellar spectra and better constrain the abundance of NH in interstellar molecular clouds.

Ab initio study of the O3-N2 complex: Potential energy surface and rovibrational states.

The formation and destruction of O3 within the Chapman cycle occurs as a result of inelastic collisions with a third body. Since N2 is the most abundant atmospheric molecule, it can be considered as the most typical candidate when modeling energy-transfer dynamics. We report a new ab initio potential energy surface (PES) of the O3-N2 van der Waals complex. The interaction energies were calculated using the explicitly correlated single- and double-excitation coupled cluster method with a perturbative treatment of triple excitations [CCSD(T)-F12a] with the augmented correlation-consistent triple-zeta aug-cc-pVTZ basis set. The five-dimensional PES was analytically represented by an expansion in spherical harmonics up to eighth order inclusive. Along with the global minimum of the complex (De = 348.88cm-1), with N2 being perpendicular to the O3 plane, six stable configurations were found with a smaller binding energy. This PES was employed to calculate the bound states of the O3-N2 complex with both ortho- and para-N2 for total angular momentum J = 0 and 1, as well as dipole transition probabilities. The nature of the bound states of the O3-oN2 and O3-pN2 species is discussed based on their rovibrational wave functions.

Ultrafast Excited-State Dynamics of Photoluminescent Pt(II) Dimers Probed by a Coherent Vibrational Wavepacket.

Intricate potential energy surfaces (PESs) of some transition metal complexes (TMCs) pose challenges in mapping out initial excited-state pathways that could influence photochemical outcomes. Ultrafast intersystem crossing (ISC) dynamics of four structurally related platinum(II) dimer complexes were examined by detecting their coherent vibrational wavepacket (CVWP) motions of Pt-Pt stretching mode in the metal-metal-to-ligand-charge-transfer excited states. Structurally dependent CVWP behaviors (frequency, dephasing time, and oscillation amplitudes) were captured by femtosecond transient absorption spectroscopy, analyzed by short-time Fourier transformation, and rationalized by quantum mechanical calculations, revealing dual ISC pathways. The results suggest that the ligands could fine-tune the PESs to influence the proximity of the conical intersections of the excited states with the Franck-Condon state and thus to control the branching ratio of the dual ISC pathways. This comparative study presents future opportunities in control excited-state trajectories of TMCs via ligand structures.

Full-dimensional quantum scattering calculations on ultracold atom-molecule collisions in magnetic fields: The role of molecular vibrations

Rigorous quantum scattering calculations on ultracold molecular collisions in external fields present an outstanding computational problem due to strongly anisotropic atom-molecule interactions that depend on the relative orientation of the collision partners, as well as on their vibrational degrees of freedom. Here, we present the first numerically exact three-dimensional quantum scattering calculations on strongly anisotropic atom-molecule (Li+CaH) collisions in an external magnetic field based on the parity-adapted total angular momentum representation and a new three-dimensional potential energy surface (PES) for the triplet Li-CaH collision complex using the unrestricted coupled cluster method with single, double and perturbative triple excitations [UCCSD(T)] and a large quadruple-zeta type basis set. We find that while the full three-dimensional treatment is necessary for the accurate description of Li ($M_S=1/2$)+CaH ($v=0,N=0,M_S=1/2$) collisions as a function of magnetic field, the magnetic resonance density and statistical properties of spin-polarized atom-molecule collisions are not strongly affected by vibrational degrees of freedom, justifying the rigid-rotor approximation used in previous calculations. We observe rapid, field-insensitive vibrational quenching in ultracold Li ($M_S=1/2$)+CaH ($v=1,N=0, M_S=1/2$) collisions, leading to efficient collisional cooling of CaH vibrations.

Ab initio potential energy surface and microwave spectra for Kr-NCCN complex

Ab initio potential energy surface of Kr-NCCN complex has been investigated using the coupled-cluster singles and doubles with noniterative inclusion of connected triples [CCSD(T)], which including two mixed basis sets, aug-cc-pvDz for the C and N atoms, and aug-cc-pvDz-pp for the Kr atom, containing the midbond function of 3s3p2d1f1g. The potential energy surface of Kr-NCCN complex has a T-shaped global minimum locating at R = 6.96 a0, θ = 90° with the energy of −281.677 cm−1, the two equivalent local minima with the energy of −123.513 cm−1 locating at the linear geometry for R = 10.70 a0, and two saddle points between the global and the two local minima are located at R = 10.61 a0, θ = 10.1° and 169.9° with V = −123.304 cm−1, respectively. The bound state energies up to J = 9 for Kr-NCCN are calculated based on the potential energy surface by solving the Schrödinger equation, and the microwave transition frequencies are also investigated. Finally, the calculated spectroscopic constants are obtained based on the calculated rotational energy levels. These results could provide a theoretical basis for the experimental spectra research of Kr-NCCN complex.

Calculation of Thermodynamic and Structural Characteristics of Gold and Silver Solvate Complexes

Gold and silver complexes with cyanide, thiocyanate, and thiosulfate ions have been considered. The potential energy surfaces of sorption complexes are shown. Quantum-chemical calculations of gold and silver complexes have been performed by the PM6 semi-empirical method as part of MOPAC. For eleven gold compounds, sets of potential energies have been obtained for various combinations. The potential energies for silver complexes have been calculated. As a result, data on the behavior of complex ions during sorption on anion exchange resin, the presence of energy minima, the pathways of the reaction, more accurate values of the binding energy, or the absence of sorption interaction in the system have been refined. Consideration of the sorption of gold and silver complexes from the classical standpoint of chemical kinetics made it possible to evaluate the activation energy and the nature of the interaction during the process. The thermodynamic parameters of the studied chemical processes have been calculated.

Deconstructing Vibrational Motions on the Potential Energy Surfaces of Hydrogen-Bonded Complexes

Internal vibrations underlie transient structure formation, spectroscopy, and dynamics. However, at least two challenges exist when aiming to elucidate the contributions of vibrational motions on t...

FLAME: A library of atomistic modeling environments

FLAME is a software package to perform a wide range of atomistic simulations for exploring the potential energy surfaces (PES) of complex condensed matter systems. The available methods include molecular dynamics simulations to sample free energy landscapes, saddle point searches to identify transition states, and gradient relaxations to find dynamically stable geometries. In addition to such common tasks, FLAME implements a structure prediction algorithm based on the minima hopping method (MHM) to identify the ground state structure of any system given solely the chemical composition, and a framework to train a neural network potential to reproduce the PES from ab initio calculations. The combination of neural network potentials with the MHM in FLAME allows a highly efficient and reliable identification of the ground state as well as metastable structures of molecules and crystals, as well as of nano structures, including surfaces, interfaces, and two-dimensional materials. In this manuscript, we provide detailed descriptions of the methods implemented in the FLAME code and its capabilities, together with several illustrative examples. Program summaryProgram Title:FLAMECPC Library link to program files:http://dx.doi.org/10.17632/2t5c59rrrf.1Developer’s repository link:http://flame-code.org, https://github.com/flame-code/FLAMELicensing provisions: GPLv3Programming language: Fortran2003, C/C++, PythonExternal routines/libraries:BigDFT PSolver[1–4], Spglib[5], MPI, LaPack, BlasNature of problem: Exploring the potential energy landscapes of complex condensed matter systems, their stationary points, and their global minima.Solution method: A neural network representation of the potential energy landscape in conjunction with a library of methods to explore its features, most notably the minima hopping approach.

Protein-Protein Docking Reveals Dynamic Interactions of Tropomyosin on Actin Filaments

Experimental approaches such as fiber diffraction and cryo-electron microscopy reconstruction have defined regulatory positions of tropomyosin on actin but have not, as yet, succeeded at determining key atomic-level contacts between these proteins or fully substantiated the dynamics of their interactions at a structural level. To overcome this deficiency, we have previously employed computational approaches to deduce global dynamics of thin filament components by energy landscape determination and molecular dynamics simulations. Still, these approaches remain computationally challenging for any complex and large macromolecular assembly like the thin filament. For example, tropomyosin cable wrapping around actin of thin filaments features both head-to-tail polymeric interactions and local twisting, both of which depart from strict superhelical symmetry. This produces a complex energy surface that is difficult to model and thus to evaluate globally. Therefore, at this stage of our understanding, assessing global molecular dynamics can prove to be inherently impractical. As an alternative, we adopted a “divide and conquer” protocol to investigate actin-tropomyosin interactions at an atomistic level. Here, we first employed unbiased protein-protein docking tools to identify binding specificity of individual tropomyosin pseudorepeat segments over the actin surface. Accordingly, tropomyosin “ligand” segments were rotated and translated over potential “target” binding sites on F-actin where the corresponding interaction energetics of billions of conformational poses were ranked by the programs PIPER and ClusPro. These data were used to assess favorable interactions and then to rebuild models of seamless and continuous tropomyosin cables over the F-actin substrate, which were optimized further by flexible fitting routines and molecular dynamics. The models generated azimuthally distinct regulatory positions for tropomyosin cables along thin filaments on actin dominated by stereo-specific head-to-tail overlap linkage. The outcomes are in good agreement with current cryo-electron microscopy topology and consistent with long-thought residue-to-residue interactions between actin and tropomyosin.

Vector Exceptional Points with Strong Superchiral Fields.

Exceptional points (EPs), branch points of complex energy surfaces at which eigenvalues and eigenvectors coalesce, are ubiquitous in non-Hermitian systems. Many novel properties and applications have been proposed around the EPs. One of the important applications is to enhance the detection sensitivity. However, due to the lack of single-handed superchiral fields, all of the proposed EP-based sensing mechanisms are only useful for the nonchiral discrimination. Here, we propose theoretically and demonstrate experimentally a new type of EP, which is called a radiation vector EP, to fulfill the homogeneous superchiral fields for chiral sensing. This type of EP is realized by suitably tuning the coupling strength and radiation losses for a pair of orthogonal polarization modes in the photonic crystal slab. Based on the unique modal-coupling property at the vector EP, we demonstrate that the uniform superchiral fields can be generated with two beams of lights illuminating the photonic crystal slab from opposite directions. Thus, the designed photonic crystal slab, which supports the vector EP, can be used to perform surface-enhanced chiral detection. Our findings provide a new strategy for ultrasensitive characterization and quantification of molecular chirality, a key aspect for various bioscience and biomedicine applications.

Recent developments in symmetry‐adapted perturbation theory

AbstractSymmetry‐adapted perturbation theory (SAPT) is a well‐established method to compute accurate intermolecular interaction energies in terms of physical effects such as electrostatics, induction (polarization), dispersion, and exchange. With many theory levels and variants, and several computer implementations available, closed‐shell SAPT has been applied to produce numerous intermolecular potential energy surfaces for complexes of experimental interest, and to elucidate the interactions in various complexes relevant to catalysis, organic synthesis, and biochemistry. In contrast, the development of SAPT for general open‐shell complexes is still a work in progress. In the last decade, new developments from several research groups, including the author's, have greatly enhanced the capabilities of SAPT. The new and emerging approaches are designed to make SAPT more widely applicable (including interactions involving multireference systems, complexes in arbitrary spin states, and intramolecular noncovalent interactions), more accurate (enhanced description of intramolecular correlation, a better account of exchange effects, relativistic SAPT, and explicitly correlated SAPT), and more efficient (enhanced density‐fitted implementations, linear‐scaling variants, empirical dispersion, and an implementation on graphics processing units). The new developments open up avenues for SAPT applications to an unprecedented variety of weakly interacting complexes.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory Molecular and Statistical Mechanics > Molecular Interactions

Sensitization profile of cricket food-allergic or cricket tolerant patients in an entomophagous population in Niamey, Niger

Experimental approaches such as fiber diffraction and cryo-electron microscopy reconstruction have defined regulatory positions of tropomyosin on actin but have not, as yet, succeeded at determining key atomic-level contacts between these proteins or fully substantiated the dynamics of their interactions at a structural level. To overcome this deficiency, we have previously employed computational approaches to deduce global dynamics of thin filament components by energy landscape determination and molecular dynamics simulations. Still, these approaches remain computationally challenging for any complex and large macromolecular assembly like the thin filament. For example, tropomyosin cable wrapping around actin of thin filaments features both head-to-tail polymeric interactions and local twisting, both of which depart from strict superhelical symmetry. This produces a complex energy surface that is difficult to model and thus to evaluate globally. Therefore, at this stage of our understanding, assessing global molecular dynamics can prove to be inherently impractical. As an alternative, we adopted a “divide and conquer” protocol to investigate actin-tropomyosin interactions at an atomistic level. Here, we first employed unbiased protein-protein docking tools to identify binding specificity of individual tropomyosin pseudorepeat segments over the actin surface. Accordingly, tropomyosin “ligand” segments were rotated and translated over potential “target” binding sites on F-actin where the corresponding interaction energetics of billions of conformational poses were ranked by the programs PIPER and ClusPro. These data were used to assess favorable interactions and then to rebuild models of seamless and continuous tropomyosin cables over the F-actin substrate, which were optimized further by flexible fitting routines and molecular dynamics. The models generated azimuthally distinct regulatory positions for tropomyosin cables along thin filaments on actin dominated by stereo-specific head-to-tail overlap linkage. The outcomes are in good agreement with current cryo-electron microscopy topology and consistent with long-thought residue-to-residue interactions between actin and tropomyosin.

Networks of electrostatic and hydrophobic interactions modulate the complex folding free energy surface of a designed βα protein

The successful de novo design of proteins can provide insights into the physical chemical basis of stability, the role of evolution in constraining amino acid sequences, and the production of customizable platforms for engineering applications. Previous guanidine hydrochloride (GdnHCl; an ionic denaturant) experiments of a designed, naturally occurring βα fold, Di-III_14, revealed a cooperative, two-state unfolding transition and a modest stability. Continuous-flow mixing experiments in our laboratory revealed a simple two-state reaction in the microsecond to millisecond time range and consistent with the thermodynamic results. In striking contrast, the protein remains folded up to 9.25 M in urea, a neutral denaturant, and hydrogen exchange (HDX) NMR analysis in water revealed the presence of numerous high-energy states that interconvert on a time scale greater than seconds. The complex protection pattern for HDX corresponds closely with a pair of electrostatic networks on the surface and an extensive network of hydrophobic side chains in the interior of the protein. Mutational analysis showed that electrostatic and hydrophobic networks contribute to the resistance to urea denaturation for the WT protein; remarkably, single charge reversals on the protein surface restore the expected urea sensitivity. The roughness of the energy surface reflects the densely packed hydrophobic core; the removal of only two methyl groups eliminates the high-energy states and creates a smooth surface. The design of a very stable βα fold containing electrostatic and hydrophobic networks has created a complex energy surface rarely observed in natural proteins.