Computational Chemistry Column 291

COMPUT ATIONAL CHEMISTRY COLUMN 288 CHIMIA 52 (1998) NT.6 (lull;)

COMPUTATIONAL

CHEMISTRY Column Editors: Prof. Dr. H. Huber, University of Basel COLUMN Prof. Dr. K. Muller, F. Hoffmann-La Roche AG, Basel ______PO Dr. H.P. Luthi, ETH-Ziirich

Chimia 52 (1998) 288-291 E(X -Y) = EMM(X-Y) - © Neue Schweizerische Chemische Gesellschaft 1SSN 0009-4293 EMM(Y) + EQM(Y) (1)

Effectively, this amounts to an interpo- lation between independent QM and MM calculations where the QM/MM interac- Combined Quantum Mechanical tions are described by the force field. This model is simple and robust, and can be and Molecular Mechanical generalized easily: the IMOMM method [7] becomesIMOMO [9] orONIOM [10], Approaches depending on whether two different QM procedures or several QM and MM procedures are combined together. Tiziana Z. Mordasini and Walter Thiel* In the case of a mechanical embedding, the wave function in the QM region does not feel the influence of the environ- Abstract. The embedding of a quantum mechanical region in a molecular mechanical ment. Such an approximation is more ap- environment allows a theoretical treatment of very large systems. This article reviews propriate for apolar than for polar systems. recent methodological developments for such hybrid methods and surveys selected To account for the electrostatic influence applications including solvation effects, enzymatic reactions, and electronic excita- of a polar environment (e.g., in aqueous tions in condensed phase. solution or in proteins) an electronic embedding of the QM region is preferable: the QM wave function is calculated in the Quantum chemical calculations are system is described as accurately as need- field of the MM partial charges and is usually applied to isolated molecules in ed using Quantum Mechanics (QM), therefore polarized relati ve to the gas phase the gas phase. Currently available quan- whereas the rest of the system is handled [1-6]. Long-range electrostatic interac- tum chemical methods provide reliable by Molecular Mechanics (MM) with an tions can be taken into account with an results for structures, stabilities, spectra, appropriate force field. Such hybrid QM/ appropriate Ewald summation [II]. and reactions of isolated molecules (with MM procedures [1-5] allow a tailored This standard model of electronic em- computational effort and accuracy depend- treatment of very large systems. In this bedding only contains the polarization of ing on molecular size). However, experi- article, recent methodological advances the QM region. For higher precision and mental work is mostly carried out not in are briefly outlined, and some typical ap- for theoretical consistency, it would seem the gas phase, but in the condensed phase. plications are presented. The literature has advisable to include also the polarization The quantitative calculation of such pro- been covered until the end of 1997. of the MM region [1][6][12-17]. This can cesses poses new challenges for theory: be achieved using distributed atomic po- How can we best describe, e.g., reactions larizabilities in the MM region, which in solution, in enzymes, or at heterogene- Methods interact with the electrical field of the QM ous catalysts? How can we model the region. The interaction energies can be effects of the environment on chemical The combination of QM and MM pro- obtained either from a single-point calcu- reactions and electronic excitations? How cedures requires the definition of coupling lation using a given QM wave function can we efficiently treat systems with thou- models [6] that describe the interactions [6], or by optimizing both the QM wave sands of atoms in cases where the classical between QM and MM regions. The accu- function and theMM polarization within a force field methods fail due to the nature racy of a QM/MM calculation depends not double iterative procedure [6][12-14]. The of the problem? only on the chosen QM and MM methods, second possibility is computationally more Hybrid QM/MM methods represent a but also significantly on the coupling expensive, but theoretically more consist- promising tool for answering such ques- model. Therefore, a hierarchy of such cou- ent, and allows the deri vation of analytical tions. The basic idea [l] is quite simple: pling models has to be developed, and a gradients [13]. The direct reaction field the electronically important part of the suitable choice for each specific applica- (DRF) method provides theoretical justi- tion has to be made. fication for describing the MM polariza- The simplest coupling is based on a tion through distributed charges and di- *Correspondence: Prof. Dr. W. Thiel mechanical embedding of the QM region pole polarizabilities [15][16]. Fluctuating Organisch-chemisches lnstitut Universitat ZUrich [6-8]. In this case, the energy of the total partial charges in the MM region are an Winterthurerstrasse 190 system X -Y (QM region Y, MM region X) alternative for taking the MM polarization CH-8057 ZUrich is calculated from: into account [17]. COMPUTA TIONAL CHEMISTRY COLUMN 289

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Most of the usual force fields are static matic reactions where covalent bonds have tion of QM method, force field and cou- and do not contain terms for polarization. to be cut in order to define the active site pling model, the calibration of QM/MM If such a force field is used in a QM/MM (QM) and the protein environment (MM). interactions, the definition of QM and procedure with MM polarization, the po- In this case, one can either satisfy the free MM regions, the treatment of the link larization should only be included for the valencies with link atoms (usually hydro- atoms, and the employed simulation tech- calculation of the QM/MM interaction gen) [2][3], or freeze the electron density nique. On the other hand, these choices energy. The effects of polarization inside at the broken bond in orthogonal hybrid offer the freedom to use a specifically the MM region are covered through the orbitals [1][28-30]. Both methods have tailored theoretical approach for modeling parametrization of the force field, in an advantages and disadvantages, and it is the electronic effects in large systems average sense. A better approach for such not a priori obvious which one is prefera- which were previously not accessible to QM/MM studies would involve the devel- ble. The link-atom concept is more popu- theoretical investigation. opment of new polarizable force fields. lar, and will therefore be discussed in the For simulations in the liquid phase, such following paragraph. intermolecular force fields have already Intuitively it is reasonable to require Applications been derived [17-20]. that the link atoms do not contribute to the For an electronic embedding of the total energy of the real system [3]. A QM/MM calculations have become QM region, the total energy can schemat- corresponding link-atom correction can increasingly popular since 1990. For the ically be written as: be defined for each coupling model [6]. In QM component, semiempirical methods the simple mechanical embedding of the (e.g., MNDO, AMI, PM3) are mostly -¥ = M ) + QM region, the link atoms then do not used due to efficiency reasons, whereas EQ i(Y) + EQ 1J?lM - Y (2) present any further problems. In the elec- the MM component is normally described tronic embedding scheme, one has to de- by standard force fields without polariza- The first two terms are usually calcu- cide whether the link atoms can electro- tion terms (e.g., AMBER, CHARMM, lated exactly as in the underlying QM and statically feel the MM atoms (if yes, which GROMOS, MM2, MM3, OPLS, SPC, MM procedures. The QM/MM interac- ones), and whether they can contribute to TIP3P). The most widely used coupling tion energy is determined by the chosen the electrostatic potential and field of the models are mechanical embedding and coupling model and usually contains elec- QM region (if yes, in which form). These the simplest form of electronic embed- trostatic and van der Waals contributions details influence the QM polarization, the ding. It is only recently that more complex that can be parametrized in order to repro- balance of the electrostatic QM/MM in- QM procedures (ab initio, density func- duce experimental results or data from teractions, and therefore also the quality of tional) are employed more often and that accurate theoretical calculations. Forelec- the resul ts. Semiempirical QM procedures polarization effects in the MM region are trostatic QM/MM interactions, such spe- are less sensitive to such link-atom prob- being considered. cial parametrizations are particularly ap- lems than ab initio or density functional Many of the early successful applica- propriate in the case of semiempirical QM methods. It is generally recommended to tions ofQM/MM methodology have dealt methods [3], e.g., through a parametriza- define the QM region as large as possible, with solvation effects [5]. After a suitable tion ofthe electrostatic potentials and fields so that the link atoms are located far away parametrization of the QM/MM interac- based on ab initio results [21]. For the van from the electronically important region, tions [22][24][25], it is possible to repro- der Waals QM/MM interactions, opti- in order to minimize any problems due duce the experimental hydration energies mized van der Waals parameters of QM to the link atoms. Clearly, the same is for a large number of molecules, with atoms have been published for different also valid if frozen hybrid orbitals are errors significantly below 1kcal/mol. The types of QM procedures [22-26]. used. contribution of the QM polarization to the It seems to be generally accepted that QM/MM procedures are employed for hydration energy is typically ca. 10-20%. some parametrization of the QM/MM in- the study of large systems, where geome- More recent studies on solvation have teractions is necessary for reliable quanti- try optimizations are no longer trivial. compared the performance of different tative results. Using semiempirical QM Recently, the transition state for a solvated methods, e.g., Me simulations of N-meth- methods, one can even go one step further enzyme-substrate complex with 1900 at- ylacetamide in water [35] (ab initio by optimizing the semiempirical QM pa- oms has been successfully optimized and RHF/TIP3P vs. AMIITIP3P vs. OPLS) rameters for the desired system. This ap- verified using gradient methods [31]. Usu- and MD simulations of alanine dipeptide proach is central to the empirical valence- ally, however, such systems are studied in water [36] (AMIITIP3P compared to bond (EVB) method [4] and has recently with Molecular Dynamics (MD) and Mon- ab initio RHF continuum models). also been tested successfully for AMI te Carlo (MC) simulations. There is an In the 1980s, a three-step procedure [27]. Such specific parameterizations for obvious demand for techniques that can has been developed for modeling organic particular systems arequite attractive, since reduce the number of QM calculations in reactions in solution [37]: first, the reac- they allow to carry out extensive simula- such QM/MM simulations, e.g., through tion profile in the gas phase is calculated tions with relatively high accuracy and energy estimates based on perturbation with ab initio methods, then along this relatively low effort. theory [32] or through systematic interpo- reaction path a special force field is de- The preceding discussion has not yet lations [33]. Other practical questions are rived for the interactions with the solvent addressed the problem of how the total discussed in the literature [34]. molecules, and finally, classical MC cal- system can be divided into QM and MM The preceding discussion indicates that culations for points on the reaction path regions. Sometimes, there exists a natural QM/MM calculations are nota 'black box' are carried out in order to calculate the separation, e.g., in the study of solutions automatic procedure. For each specific solvent effects. Using a QM/MM proce- with a QM solute and MM solvent mole- application, it is necessary to make a series dure, the last two steps can be replaced by cules. However, for other applications, the of critical choices with regard to practical- a QM/MM MC simulation that is concep- separation can be less obvious, as in enzy- ity and accuracy. This includes the selec- tually simpler and that allows for a QM COMPUT ATIONAL CHEMISTRY COLUMN 290

CHIMIA 52 (1998) Nr. 6 (lUll;) polarization of the reacting system. Based - Catalysis by malate dehydrogenase catalytic Brookhart-type Ni" olefin po- on this strategy, there have been AMl/ (AMI/CHARMM): during the inter- lymerization; the QM/MM barriers (OFT- TIP3P studies of the Claisen rearrange- conversion of malate to oxaloacetate, BP86/AMBER) are in much better agree- ment in water [38] and of hydrophobic and the proton transfer precedes the hy- ment with experiment than the QM values hydrogen-bonding effects on the rate of a dride transfer; the role of the protein for smaller model systems without sub- Diels-Alder reaction in water [39]. QM/ environment is analyzed in detail [48]. stituents [56][57]. MM investigations of reactions in solu- The energy profile of the reaction in Electronic excitations in condensed tion can also be carried out without previ- the enzyme and in aqueous solution is phase are another important application ous gas-phase calculations, provided that similar [23][48]. for QM/MM methods. The solvatochro- the chosen QM method yields realistic - Catalysis by papain (AMI/AMBER): mism of n -7 W transitions has been intrinsic reaction barriers. Examples of the amide hydrolysis in the enzyme investigated by several authors [13][58- such studies in aqueous solution are QM/ follows a concerted rather than a step- 60], mostly employing semiempirical QM TIP3P calculations for proton transfer in wise mechanism [49]. methods [13][58][59] and MM polariza- complexes with strong hydrogen bonds - Catalysis by tyrosine phosphatase tion [13][59][60]. Other recent work ad- (double minimum potential with low bar- (PM3/AMBER): the hydrolysis of the dresses the ground- and excited-state pKa rier) [40] and for electrophilic attack of phosphate ester in the enzyme pro- difference of phenol in water [61], the bromine on ethylene producing a bromo- ceeds by a dissociative mechanism; solvent effects on the geometry of conju- nium ion [41] (using gradient-corrected the transition state does not show bonds gated chromophores and their solvato- density functional theory as QM compo- to the attacking nucleophile (cysteine) chromic shift for 1C -7 W excited states nent). The acid-catalyzed hydrolysis of [50]. [62], and the photophysics of uracil and glycoside in water has been studied at the - Catalysis by citrate synthase (AMl/ 1,3-dimethyluracil [63]. Especially im- AM1ITIP3P level, suggesting a stepwise CHARMM): the enolization of acetyl- pressive is a QM/MM study of the photo- mechanism based on the calculated kinet- CoA starts with a deprotonation and is synthetic reaction center reporting the ex- ic isotope effects [42]. followed by nucleophilic attack and cited states of the bacteriochlorophyll b Organic reactions in solution can also subsequent hydrolysis; the enolate in- (325 QM atoms, 20158 MM atoms; QM = be described with continuum models like termediate is stabilized in the enzyme MNOO, AMI, PM3, INOO/S and MM = SCRF (self-consistent reaction field) [43] by hydrogen bonds [51]. AMBER, CVFF) [12]. [44]. These models incorporate the mutual - Catalysis by lactate dehydrogenase: in polarization of solute and solvent without this case, two independent QM/MM considering any special interactions. studies for the conversion of pyruvate Outlook Whenever such explicit interactions are into lactate lead to different results. not particularly relevant, SCRF and QM/ Using AMl/AMBER, two transition The examples discussed show that QM/ MM calculations often yield qualitative states are found, where the slower hy- MM methods, if applied in a critical and similar results. However, continuum mod- dride transfer precedes the faster pro- careful manner, can successfully model els are not appropriate for studying enzy- ton transfer [52]; on the other hand, electronic effects in large systems. Alter- matic reactions, so that at present QM/ AMl/CHARMM predicts the exist- natively, it may become feasible to treat MM methods are almost unrivalled in this ence of just one concerted transition such systems using pure QM calculations research field [4]. The following section state, where the proton transfer is more with linear scaling (for selected references outlines some recent examples of QM/ advanced than the hydride transfer [31]. see [64-79]). These calculations are much MM studies on the mechanism of enzy- QM/MM methods have also been ap- moreexpensivefromacomputational point matic reactions: plied to the theoretical study of reactions of view, but are theoretically more con- - Catalysis by HIV protease (PM3/GRO- on zeolites [53] and in organometallic sistent and less affected by approxima- MOS): one protonated (Asp-25') and chemistry [54-57]. In these investigations tions. They account for long-range charge one unprotonated (Asp-25) aspartate, [53-57], ab initio and OFT methods are transfers and charge fluctuations in pro- one water molecule, and one amide employed for the calculation of the QM teins, which cannot be described by the unit are involved in the reaction at the region which is mechanically embedded. usual QM/MM methods. However, the active site; after the formation of a The zeolites work concerns the initial ad- QM/MM methods have the advantage that tetrahedral intermediate, the nucle- sorption of ammonia on H-faujasite and they are more efficient and offer the pos- ophilic attack and proton transfer oc- the specific acidity of different binding sibility of a specifically tailored descrip- cur in a concerted way [45]. sites on the catalyst [53], whereas the tion of the system, where the computa- - Catalysis by human carbonic anhy- organometallic studies concentrate on ster- tional effort is concentrated on the chem- drase HCA II (PM3/AMBER): the in- ic effects. Using the IMOMM method, it ically important part of the system. We itially formed Lindskog intermediate has been shown how the structure of the believe that both theoretical methods will is unstable and rearranges to the more transition state for the oxidative addition be successfully applied in future studies, stable Lipscomb intermediate with a of H2 to Pt(PR3h (R = H, Me, t-Bu, Ph) since they complement each other. more favorable zinc-bicarbonate coor- changes due to increasing steric effects dination [46]. (RHF/MM3) [54] and how the isotacticity - Catalysis by chorismate mutase (AM 11 in the propylene polymerization by .si- Received: April 30, 1998 CHARMM): the reaction barrier of the lylene-bridged metallocenes is sterically Claisen rearrangement in the enzyme controlled by substituents (RHF/MM2) [I] A. Warshel, M. Levitt, J. Mol. BioI. 1976, /03,227. is lowered by 24 kcal/mol due to a [55]. Similarly, steric effects due to bulky [2] U.c. Singh, P.A. Kollman, J. 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