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Natural Bond Orbital Analysis in the ONETEP Code: Applications to Large Protein Systems Louis P

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Natural Bond Orbital Analysis in the ONETEP Code: Applications to Large Protein Systems Louis P WWW.C-CHEM.ORG FULL PAPER Natural Bond Orbital Analysis in the ONETEP Code: Applications to Large Protein Systems Louis P. Lee,*[a] Daniel J. Cole,[a] Mike C. Payne,[a] and Chris-Kriton Skylaris[b] First principles electronic structure calculations are typically Generalized Wannier Functions of ONETEP to natural atomic performed in terms of molecular orbitals (or bands), providing a orbitals, NBO analysis can be performed within a localized straightforward theoretical avenue for approximations of region in such a way that ensures the results are identical to an increasing sophistication, but do not usually provide any analysis on the full system. We demonstrate the capabilities of qualitative chemical information about the system. We can this approach by performing illustrative studies of large derive such information via post-processing using natural bond proteins—namely, investigating changes in charge transfer orbital (NBO) analysis, which produces a chemical picture of between the heme group of myoglobin and its ligands with bonding in terms of localized Lewis-type bond and lone pair increasing system size and between a protein and its explicit orbitals that we can use to understand molecular structure and solvent, estimating the contribution of electronic delocalization interactions. We present NBO analysis of large-scale calculations to the stabilization of hydrogen bonds in the binding pocket of with the ONETEP linear-scaling density functional theory package, a drug-receptor complex, and observing, in situ, the n ! p* which we have interfaced with the NBO 5 analysis program. In hyperconjugative interactions between carbonyl groups that ONETEP calculations involving thousands of atoms, one is typically stabilize protein backbones. VC 2012 Wiley Periodicals, Inc. interested in particular regions of a nanosystem whilst accounting for long-range electronic effects from the entire system. We show that by transforming the Non-orthogonal DOI: 10.1002/jcc.23150 Introduction and observation of hydrogen bond co-operative strengthening in amides and peptides.[16] However, the applicability of first The natural bond orbital (NBO) analysis method[1,2] as imple- [3] principles methods in determining the ground state properties mented by Weinhold and coworkers in the NBO 5 program of biomolecular assemblies is hindered by the scaling of the provides chemical insights from first principles calculations by computational effort with the number of atoms in the system, transforming a ground-state quantum mechanical wavefunc- which is often cubic or greater. In this article, we address this tion into orbitals corresponding to the chemical notion of issue using a new generation of density functional theory localized Lewis-type bond and lone pairs, with their associated (DFT) approach whose computational effort scales linearly formally vacant antibonding and Rydberg orbitals. The scheme with the number of atoms. Specifically, we interface the NBO 5 involves successive transformations of the full ground-state [3] [17] analysis package with the linear-scaling DFT code ONETEP, single particle density matrix, first into a set of atom-centered [4] which has been developed for parallel computers using novel orthogonal ‘‘natural atomic orbitals’’ (NAOs), then into ‘‘natu- and highly efficient algorithms that allow calculations for sys- ral hybrid orbitals’’ (NHOs) and, finally, NBOs. The populated [18–20] tems up to tens of thousands of atoms. ONETEP is unique NBOs, formed from the diagonalization of two-center density as it achieves linear-scaling computational cost whilst preserv- matrix blocks, are maximal in their occupancies (usually 2.0), ing plane-wave accuracy, meaning that the energy and various and constitute the natural Lewis structure of the system. These computed properties can be systematically improved by orbitals are complemented by their formally unoccupied coun- increasing a single parameter equivalent to the kinetic energy terparts, whose finite occupancies represent deviation from the ideal Lewis chemical picture due to delocalization effects. The NBO method has been applied in a wide variety of [a] L. P. Lee, D. J. Cole, M. C. Payne chemical studies, from rationalizing the electronic origin of TCM Group, Cavendish Laboratory, 19 JJ Thomson Ave, Cambridge CB3 0HE, nonpairwise additivity in co-operative hydrogen-bonded clus- United Kingdom E-mail: [email protected] [5] ters, describing electronic donation between ligand and tran- [b] Chris-KritonSkylaris [6] sition metal orbitals, to explaining molecular rotational bar- School of Chemistry, University of Southampton, Highfield, Southampton riers in terms of the energetics of NBO delocalization.[7–10] SO17 1BJ, United Kingdom More recently, the NBO method has been applied to study Contract/grant sponsor: EPSRC; Contract/grant number: EP/F032773/1; biologically relevant systems, examples including charge deter- Contract/grant sponsor: IRIDIS3 supercomputer of the University of Southampton; Contract/grant sponsor: Cambridge Commonwealth mination via natural population analysis (NPA) along an enzy- Trust; Contract/grant sponsor: EPSRC; Contract/grant sponsor: Royal matic reaction co-ordinate,[11] n ! p* backbone interactions in Society for a University Research Fellowship. [12–14] [15] proteins, hydrogen bonding in nucleic acid base pairs VC 2012 Wiley Periodicals, Inc. Journal of Computational Chemistry 2013, 34, 429–444 429 FULL PAPER WWW.C-CHEM.ORG cut-off of conventional pseudopotential plane-wave DFT PNAOs are hence ‘‘natural’’ in their molecular environment by implementations. virtue of having the most condensed occupancies whilst We begin the Methodology section by reviewing the NAO retaining free-atom AO symmetries. This lm-averaging proce- and ONETEP methods and describing our interface between ONE- dure requires free-atom angular symmetries in the initial basis, [3] TEP and the NBO 5 program that allows us to compute NBOs an issue that will be discussed in our adaptation of this and their properties from the ONETEP density matrix. We will method to ONETEP. also show how, by partitioning the density matrix obtained Subsequent steps include the division of PNAOs into ‘‘natu- from a ONETEP calculation on a large system, it is possible to ral minimal basis’’ and ‘‘natural Rydberg basis’’ (NMB and NRB) perform NBO analysis only in a small region of the large sys- sets constituting the formally occupied and unoccupied atomic tem in such a way that the NBOs obtained in this region are orbitals in the ground state configuration. The NMB PNAO set identical to those that would be obtained from NBO analysis then undergoes an occupancy-weighted symmetric orthogon- on the entire system. alization procedure OW, which serves to orthogonalize orbitals In Results, we first perform extensive validation of the prop- with a weighted-preservation of their initial shapes by mini- erties of the NBOs derived from ONETEP calculations against the mizing the Hilbert space distance: [21] quantum chemistry code GAMESS (which is officially sup- ! X ported and integrated with NBO 5), followed by several illustra- PNAO PNAO 2 À1 min f jj j/0 j/ jj ) O ¼ WðWSWÞ 2 tive applications to large systems, where we use this new i i i W i functionality in ONETEP to study local chemical properties of sev- 0 0 where h/PNAO j/PNAO i¼d ; S ¼h/PNAOj/PNAOi; W ¼ d f eral large proteins, and how these are influenced by long- i j ij ij i j ij ij j range interactions. (4) À1 € 2 Methodology OW reduces to Lowdin’s symmetric orthogonalization OL ¼ S when W ¼ 1. The weightings Wij ¼ dijfj are taken to be the ðAlÞ NAOs symmetry-averaged occupancies fi from Eq. (3), and this ensures that highly occupied orbitals retain their character In the original NBO scheme,[2] the initial ground-state single par- while low-occupancy ones are free to distort to achieve ticle density matrix P ¼h/ jq^j/ i, represented in an atom- ab a b orthogonality. local basis |/ai, is first transformed into an orthogonal NAO NRB [4] Next, the NRBs {|/i i} are Schmidt-orthogonalized (OS) representation via symmetric weighted orthogonalization, 0 with respect to the (now orthogonal) NMB space {|/NMB i}: from which all other types of orbitals (NHOs, NBOs) are derived. i X The initial functions {|/ i} are assumed to be spherical con- 0 0 0 a j/NRB ¼j/NRB À j/NMB /NMB j/NRB (5) tracted Gaussians, as commonly used in quantum chemistry. i i j j i j2NMB The full AO to NAO transformation TNAO can be summarized as[4]: NRB0 followed by a restoration of the ‘‘natural’’ character of {|/i i} by repeating NPNAO [Eq. (3)] only in the NRB space (denoted TNAO ¼ NPNAOOSNRydOWNRed (1) NRyd). The entire Hilbert space is then weighted-orthogonal- ized (OW) using the new NRB occupancies, and the ‘‘natural’’ The first step N involves the transformation of {|f i} into PNAO a character of this final NAO set is once again restored by a set of ‘‘pre-orthogonal NAOs’’ (PNAOs) by diagonalizing the repeating N (denoted N ). The NMB/NRB orthogonaliza- atom-local block of the (spin-averaged) density matrix PA of PNAO Red tion step O is crucial to ensure stability and rapid conver- atom A. However, to preserve the invariance of the entire S gence of the total NAO population on each atom (the NPA transformation T to molecular orientation with respect to NAO charges) with respect to basis set expansion, by removing Cartesian rotation of {|/ i}, an ‘‘lm-averaging’’ step is first per- a unnecessary weightings in O given to the diffuse NRBs due formed on PA and the associated overlap matrix SA as: W to their potentially large overlaps with NMBs that have satis- [4] X2lþ1 X2lþ1 factorily accommodated the electronic population. ðAlÞ 1 ðAlmÞ ðAlÞ 1 ðAlmÞ P 0 ¼ P 0 ; S 0 ¼ S 0 (2) nl;n l 2l 1 nlm;n lm nl;n l 2l 1 nlm;n lm þ m¼1 þ m¼1 ONETEP (Alm) (Alm) [17] where P and S are block diagonals sharing the same ONETEP is a linear-scaling DFT package based on the density (Al) (Al) 0 m [ l.
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