J. Phys. Chem. 1996, 100, 18057-18064
18057
Molecular Mechanics Force Field for Platinum Coordination Complexes Thomas R. Cundari,*,1 Wentao Fu, Eddie W. Moody, Lori L. Slavin,† Leigh Anne Snyder, Shaun O. Sommerer,‡ and Thomas R. Klinckman† Department of Chemistry, UniVersity of Memphis, Memphis, Tennessee 38152, Department of Physical Sciences, Barry UniVersity, Miami Shores, Florida 33161, and Department of Chemistry, Austin Peay State UniVersity, ClarksVille, Tennessee 37044 ReceiVed: April 30, 1996; In Final Form: September 13, 1996X
A molecular mechanics study of square planar Pt(II) coordination complexes is reported. Three new ligating atom types which are representative of the σ-donor ligands prevalent in Pt(II) coordination chemistryschloride, carboxylate oxygen, and amine nitrogensare developed to extend the MM2 force field. The newly derived MM force field accurately describes the geometry of both the inner and outer coordination sphere of Pt(II) complexes. Quick and efficient modeling is obtained despite simplifications used in constructing the force field, e.g., neglect of anharmonic corrections to the bond-stretching and angle-bending potentials. The simplifications used in construction of the force field allow accurate structural prediction in a timely manner using readily available software and hardware. Additionally, the new MM force field shows the ability to predict structures, in the absence of a starting guess of the geometry from X-ray crystallography, that are subsequently found to be in good agreement with experimental geometries.
Introduction Development and application of computational methods, quantum and classical, for metals remains an active research area.2 Although, molecular mechanics (MM) has not been as widely applied to d- and f-block metals3 as nonmetals,4 several groups have investigated MM for metals including generic force fields for modeling compounds incorporating elements across the periodic table.5-7 A major effort for metal complexes has been efficient modeling of angular distortions about the metal.3,5-8 Allured et al. have described the SHAPES method,5 while Rappe´6 and Goddard7 and their co-workers have developed alternative approaches. Another technique replaces angular bending potentials about high-coordination atoms with 1,3 van der Waals interactions.8,9 Allured et al. studied square planar complexes, including those of Pt(II), although this work focused more on Rh(I).5 Rappe´ et al. included PtBr2(1,2-diaminocyclohexane) in their calibration of a universal force field.6 Molecular mechanics studies have been reported describing the interaction of Pt(II) with DNA fragments, mostly purines and related ligands because the cellular target for Pt drugs is guanine.10 These studies inspired us to investigate the utility of MM for a larger series of square planar Pt(II) complexes. A major hindrance in the application of MM to metals is the scarcity of experimental data for use in force field parametrization.3 One can divide MM parameters into two types: metric parameters, which describe the equilibrium positions of internal coordinates, e.g., bond lengths, and vibrational parameters, which describe the ease (or difficulty) of perturbing the metric parameters from their equilibrium position. Recently, development and testing of quantum mechanical (QM) methods for dand f-block metals2 has proceeded apace. A main focus of this research has been to demonstrate the reliability of QM methods for prediction of structural and vibrational data.2 Hence, it should be possible to use QM methods to estimate parameters needed to extend “organic” force fields to metal complexes.5,11 * Address correspondence to this author at the University of Memphis. † Austin Peay State University. ‡ Barry University. X Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)01240-3 CCC: $12.00
We seek to investigate such an approach for important families of metal coordination complexes. The present research focuses on square planar Pt(II) complexes with structural motifs relevant to antitumor drugs.12 Experimental interest in these complexes provides a large database of structural information with which to develop and test an MM force field. The complexes studied here are prodrugs. Experiment suggests that donor ligands (X in cisPtA2X2; A ) amine; X ) anionic donor ligand) are displaced in an aquation reaction.12a,b However, donor ligands are important in determining drug properties.12 The present force field could be used in conjunction with other methods to develop improved quantitative structure-activity relationships (QSARs), rare for metallodrugs,12f or combined with existing force fields10 to study interactions between different cis-PtA2 and DNA fragments.12g Likewise, the methodology could be extended to related square planar Pt(II) complexes, e.g., those of interest in catalytic methane conversion, since similar σ-donor ligands appear in this chemistry.13 Computational Methods Quantum Mechanics. Quantum calculations employ the GAMESS program.14 ECPs and valence basis sets (VBSs)15 are used for heavy atoms and a -31G basis for H. The 5s, 5p, 5d, 6s, and 6p orbitals are treated explicitly for platinum; for main-group elements ns and np are treated explicitly. Transition metal VBSs are quadruple- and triple-ζ for sp and d shells, respectively, while main group elements are valence double-ζ. Heavy, MG basis sets are augmented with a d function. Geometries are optimized at the restricted Hartree-Fock (RHF) level for closed-shell singlets. Vibrational frequencies are calculated at stationary points to identify them as minima or transition states. Molecular Mechanics. The molecular mechanics force field includes the following terms:4
Usteric ) ∑Us + ∑Ub + ∑Ut + ∑UvdW
(1)
The steric energy, Usteric, of a complex is the sum of individual © 1996 American Chemical Society
18058 J. Phys. Chem., Vol. 100, No. 46, 1996 bond stretching, Us; angle bending, Ub; bond torsion, Ut; and van der Waals interactions, UvdW. The force field in Chem 3D Plus16 differs slightly from the standard MM2 force field, e.g., the option for a quartic stretching term, a cutoff distance for van der Waals interactions, and a π-orbital SCF calculation for conjugated systems. A cutoff distance of 10 Å is used for van der Waals terms. The functional form of the π-conjugation correction used in Us increases the force constant, and decreases the bond length, as π-bond order increases. A Hu¨ckel molecular orbital (HMO) calculation is used to calculate π-bond orders for conjugated atoms;17 in the present work, this applies only to oxalate ligands. A steepest descent algorithm is used for geometry optimization;16 optimizations are carried out until the rms gradient is e0.010 kcal Å-1 (e0.002 kcal Å-1 for complexes with ammonia ligands). In all MM geometry optimizations, the H and lone pair (Lp) atom positions are optimized first (keeping heavy atom coordinates fixed) since these may not be accurately located in the X-ray experiment. In the second step, all atomic positions are subject to geometry optimization. Calculations are done on either a Macintosh LC 475 or Quadra 800. Further specifics about the force field are given in the following sections. A total of 50 random conformations are generated for each of the complexes studied in section 4. A spreadsheet is used to generate random Cartesian coordinates for all atoms apart from the metal and its ligating atoms; all appropriate bonds and atom types are specified. Platinum is located at the origin, while Lp pseudoatoms are positioned (1.3 Å along the z axis. The four ligating atoms are placed along the (x and (y axes at distances from the Pt equal to their equilibrium Pt-ligand bond lengths to give to a cis-PtA2X2 geometry (i.e., A-Pt-A ) X-Pt-X ) 90°). Cartesian coordinates of the remaining nonligating atoms are generated randomly with the limitation that they be within 5 Å of Pt. These 50 random geometries are then read into Chem 3D Plus16 and optimized using the following three-step protocol. First, conformations are loosely optimized to minimize structural error (rms error < 100 Å or rms gradient < 0.100 kcal Å-1). This quickly minimizes differences between actual bond lengths and bond angles and equilibrium values, flattens out “planar” atom types (e.g., carbonyl C in a carboxylate), and achieves planarity about double bonds.16 The Pt and its inner coordination sphere (including the lone-pair pseudoatoms) are fixed to the cis-PtA2X2 geometry (N-Pt-N ) A-Pt-A ) 90°; Lp-Pt-Lp ) 180°; Lp-Pt-A ) Lp-Pt-X ) 90°) during this first step. In the second step, the geometries from the first step are loosely MMoptimized (rms gradient < 0.100 kcal Å-1) with the inner coordination sphere geometry still frozen. In the third step, all 50 geometries are optimized with standard convergence criteria and no geometry constraints. This scheme provides a quick route to sampling of conformational space and ensures the cisPtA2X2 conformation of interest is obtained (as opposed to trans or non-square-planar geometries). Results and Discussion 1. Force Field Derivation. Platinum (type 784) is modified by addition of two lone pairs perpendicular to the square plane (to model the electron density in the Pt-based dz2 orbital) with an Lp-Pt-Lp angle ) 180°. There is a similar structural motif (cis-PtA2X2, A ) amine, X ) anion) in many platinum antitumor agents and indeed a general preference in the coordination chemistry of Pt(II) for hard σ-donor ligands.13,18 We therefore focus on three new ligating atom typesscoordinated carboxylate O (atom type 86), coordinated amine N (atom type 888), and chloride (atom type 12). With these ligand types,
Cundari et al. TABLE 1: MM Atom Type Parametersa,b type
R*
e
atom weight
lone pairs
12 86 784 888
2.030 1.740 2.713 1.820
0.240 0.050 0.200 0.055
34.969 15.995 194.965 14.003
0 0 2 0
a Atom types: 12 ) chloride; 86 ) coordinated carboxylate O; 784 ) square planar Pt; 888 ) coordinated amines. Platinum was modified by addition of two “lone pairs” (see text); parameters for chloride are built into the program.13 b R* is the van der Waals radius (Å), is the energy parameter (kcal mol-1), atom weight is given in AMU, and lone pairs is the number of lone pairs added to that atom type.
TABLE 2: Bond-Stretching Parametersa,b bond type
KS
length
bond dpl
1-86 1-888 3-86 12-784 20-784c 23-888 86-784 784-888
5.360 5.100 5.050 2.052 5.000 6.100 2.960 1.535
1.402 1.438 1.338 2.293 1.310 1.020 2.000 2.000
0.440 0.040 -0.200 0.000 0.000 -0.760 0.000 0.000
a KS is the force constant of the particular bond type (mdyn Å-1); length is the equilibrium bond length (Å); bond dpl is the bond dipole (D). b Atom types: 1 ) alkane C; 3 ) carbonyl C; 12 ) Cl; 20 ) lone pair; 23 ) amine H; 86 ) coordinated carboxylate O; 784 ) square planar Pt; 888 ) coordinated amine N. c The Pt-Lp equilibrium bond length was set to 1.30 Å, i.e., the Pt covalent radius. Different Pt-Lp force constants and equilibrium bond lengths were investigated and found to have a minimal effect on the resulting geometries over a wide range of values.
MM calculations can, for example, be performed on ≈40% of the 206 platinum complexes classified as Selected Agent Compounds in National Cancer Institute (NCI) in vivo tests of antitumor activity.19 In derivation of the force field there are two types of parameters: metal-dependent and metal-independent. Metalindependent parameters are assumed not to change upon coordination of the ligand to the metal, and thus, standard MM2 parameters are used.4,16 For example, a coordinated amine nitrogen (atom type 888) is equivalenced to a noncoordinated amine nitrogen (atom type 8). Derivation of metal-dependent parameters is outlined below. Van der Waals. The van der Waals parameters for ligating atoms are taken from values for nonligating analogues (for N, O, and Cl) and from built-in parameters for square planar Pt.16 The van der Waals parameters for new atom types are collected in Table 1. Bond Stretching. The force constants for Pt-ligand bonds are calculated from restricted Hartree-Fock calculations, employing effective core potentials,15 on the model compounds cis-platin, and cis-diammine(oxalato)platinum(II). The force constants are not scaled. The quantum methods employed have been widely applied to numerous and varied transition metal complexes.2e X-ray crystallographic data18 was used in the determination of Pt-ligand equilibrium bond lengths. Newly defined bond stretching parameters are given in Table 2. Angle Bending. There are two types of metal-dependent, angle-bending potentials, X-Pt-Y and Pt-X-Y. The former are modeled with 1,3 van der Waals terms.8 The latter are estimated from organic analogues, e.g., C(alkane)-X-Y and modified as needed to improve the agreement between X-ray and MM structures. New angle-bending parameters are collected in Table 3. Torsion. There are two varieties of metal-dependent torsions: X-Y-Z-Pt and X-Y-Pt-Z. The latter involve
Platinum Coordination Complexes
J. Phys. Chem., Vol. 100, No. 46, 1996 18059
TABLE 3: Angle Bendinga,b
TABLE 4: Torsional Parametersa,b
angle type
KS
-XR2-
-XRH-
-XH2-
dihedral type
V1
V2
V3
1-1-86 1-1-888 3-1-888 5-1-86 5-1-888 86-1-86 1-3-86 3-3-86 7-3-86 22-3-86 3-22-3 3-86-784 1-888-1 1-888-23 1-888-784 23-888-23 23-888-784
0.700 0.570 1.045 0.540 0.500 0.460 0.650 0.700 0.800 0.650 0.450 0.600 0.630 0.500 0.630 0.500 0.500
107.500 109.470 110.740 106.700 108.800 99.900 107.100 124.300 122.000 107.100 125.400 109.900 107.700 109.470 107.700 104.500 109.470
107.700 108.800 0.000 106.700 0.000 97.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
107.400 109.500 0.000 106.700 0.000 102.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
1-1-86-1 5-1-86-1 1-1-888-1 1-1-888-23 1-1-888-784 3-1-888-23 3-1-888-784 5-1-888-1 5-1-888-23 5-1-888-784 7-3-3-86 86-3-3-86 7-3-22-3 86-3-22-3 86-3-22-22 1-3-86-784 3-3-86-784 7-3-86-784 22-3-86-784 1-1-1-86 1-1-1-888 5-1-1-86 5-1-1-888 6-1-1-86 6-1-1-888 86-1-1-888 888-1-1-888 1-1-3-86 3-1-3-86 5-1-3-86 12-1-3-86 888-1-3-7 888-1-3-86
0.400 0.000 -0.200 0.000 -0.200 0.000 0.000 0.000 0.000 0.000 0.000 0.000 -0.130 0.000 0.400 -2.500 -2.500 -1.660 -2.500 0.100 0.100 0.000 -0.150 0.000 0.000 0.000 -0.400 0.400 0.000 0.000 0.000 0.000 0.000
0.520 0.000 0.730 0.120 0.730 0.000 0.000 0.000 0.000 0.000 11.100 11.100 0.904 0.000 -0.300 1.390 1.390 8.980 1.390 0.100 0.400 0.000 0.000 -0.600 0.000 0.000 -1.100 -0.300 0.000 0.000 2.600 0.000 0.000
0.467 0.530 0.800 0.100 0.800 0.000 0.000 0.520 0.250 0.520 0.000 0.000 0.050 -0.417 -0.070 0.000 0.000 0.000 0.000 0.180 0.500 0.180 0.150 0.300 0.000 0.000 1.200 -0.070 -0.417 -0.016 0.000 0.000 0.000
a KS is the force constant of the particular angle type (mdyn Å-1 rad-2); -XR2-, -XRH-, and -XH2- are the equilibrium bond angles (deg) depending on whether the central atom (X) is bonded to H or some other heavy group (R). b Atom types: 1 ) alkane C; 3 ) carbonyl C; 5 ) H; 7 ) carbonyl O; 8 ) amine N; 12 ) chlorine; 20 ) lone pair; 22 - cyclopropane C; 23 ) amine H; 86 ) coordinated carboxylate O; 784 ) square planar Pt; 888 ) coordinated amine N.
rotation about metal-ligand bonds and are often assumed to be small and set to zero.3a The former are approximated by assuming the metal plays a spectator role in determining the torsional potential about the X-Y bond; M-X-Y-Z torsional potentials are often assumed to be equal to C(alkane)-X-Y-Z potentials,3a which are usually available when X, Y, and Z are nonmetal atoms. Newly defined torsions are collected in Table 4. Out-of-plane bending terms, also called improper torsions, at square planar Pt and carbonyl C (atom type ) 3) are given in Table 5. 2. Force Field Preliminaries. Our goal is to accurately predict the structure of Pt(II) coordination complexes using a minimum of terms above and beyond the basic Allinger MM2 force field.4 Test calculations were carried out on the Pt(II) complexes in Figure 1.18 Geometry optimizations were first carried out using cubic, and quartic terms in Us as well as stretch-bend, Usb, terms. Similarly, a sextic correction to a normal harmonic potential was used for Ub. Torsional potentials are described using a standard, three-term Fourier series expansion. The vdW terms are calculated using a modified Buckingham potential function (UvdW ) A exp(-Br) - C/r6; A, B, and C are adjustable parameters). These choices represent the default options in Chem 3D Plus.16 Test molecules were initially optimized starting from X-ray coordinates for heavy atoms (H atoms and lone pairs are added as required) using force field options outlined in the previous paragraph. Subsequently, geometries are reoptimized ignoring cubic and quartic corrections to Us, ignoring the sextic correction to Ub, and omitting Usb potentials. Very small changes in geometry are noticed whether or not Us and Ub were described with a harmonic potential. In the most extreme case (1618n) the root-mean-square (rms) deviation in heavy atom positions between the geometries resulting from the two MM optimization schemes is only 0.04 Å. In general for the test complexes, the rms deviation in heavy atom positions is e0.02 Å. These test calculations point to the suitability of harmonic Us and Ub potentials for MM modeling of these Pt(II) complexes, and this approximation was used in subsequent calculations. 3. Application of the Force Field to Platinum(II) Complexes. With derivation of the force field as described above it is now possible to study a wide variety of Pt(II) coordination
a V , V and V are the 1-, 2-, and 3-fold barriers (kcal mol-1) for 1 2 3 rotation about a bond. All torsions of the form X-Pt-Y-Z have V1 ) V2 ) V3 ) 0 kcal mol-1. b Atom types: 1 ) alkane C; 3 ) carbonyl C; 5 ) H; 6 ) alcohol O; 7 ) carbonyl O; 12 ) chlorine; 20 ) lone pair; 22 - cyclopropane C; 23 ) amine H; 86 ) coordinated carboxylate O; 784 ) square planar Pt; 888 ) coordinated amine N.
TABLE 5: Out-of-Plane Bendinga,b bond type
KS
bond type
KS
3-86 784-12 784-20
0.800 0.800 0.800
784-86 784-888
0.800 0.800
a KS is the out-of-plane bending force constant (kcal deg-2). b Atom types: 3 ) carbonyl C; 12 ) chlorine; 20 ) lone pair; 86 ) coordinated carboxylate O; 784 ) square planar Pt; 888 ) coordinated amine N.
complexes given the importance of hard σ-donor ligands in Pt(II) coordination chemistry. All of the complexes in Figure 118 have reported antitumor activity. Other researchers have used MM to study Pt(II) complexes.5,6,10 However, to our knowledge, there has been no systematic evaluation of MM with regards to structural prediction for a wide variety of Pt(II) complexes with non-purine ligands. In the present work, square planar Pt(II) complexes with coordinated amine, carboxylate, or chloride ligands, for which X-ray structural data is available,18 are studied (Figure 1). a. Description of the Inner Coordination Sphere. The rms deviation in atomic positions provides a quick assessment of agreement between MM structures and X-ray data (Table 6). Hydrogen atom positions are neglected due to difficulties in locating them in the X-ray experiment. The average rms deviation between heavy atom positions for the inner coordination sphere (i.e., Pt and its four ligating atoms, rmsPtL4) is 0.08 ( 0.05 Å for the test complexes. As a comparison, two crystal structures for cis-platin have been reported, 718f and 6.18e These two complexes have rmsPtL4 ) 0.05 Å. The same rmsPtL4 is
18060 J. Phys. Chem., Vol. 100, No. 46, 1996
Cundari et al.
Figure 1. Square planar Pt(II) complexes used in construction and validation of the force field. Hydrogen atoms are removed for clarity in this and subsequent figures. Numbers correspond to those in the text and ref 18.
seen for the two independent cis-diammine(valinato-N,O)platinum(II) fragments in the unit cell of 20.18p No complex shows an rmsPtL4 deviation significantly (i.e., two standard deviations above the average) higher than the rest. The complexes with the highest deviations between MM and X-ray geometries for the Pt coordination sphere are 1718o and 1918p (rmsPtL4 ) 0.16 and 0.17 Å, respectively). Complex 19 is one of three structures (with 20 and 18) with an amino acid coordinated to a cis-diammineplatinum(II) moiety; rmsPtL4 ) 0.06 Å for 20, and rmsheavy ) 0.13 Å for 18. Likewise, there seems to be no trend toward higher rmsPtL4 for cis-diammineplatinum(II) complexes (rmsPtL4 ) 0.10 Å (6), 0.06 Å (7), 0.03 Å (10), 0.05 Å (11), and 0.01 Å (23). This suggests that there is no shortcoming in the force field for description of amino acid or diammine complexes. Complex 17 is a malonate; other malonates (5, 10) have rmsPtL4 e 0.03 Å. Related complexes with ethylenediamine spacers (or derivatives) show very good
agreement with experiment: rmsPtL4 ) 0.02 and 0.03 Å (for the two [Pt(en)2]2+ conformers in 8), 0.05 Å (15 and 21), 0.06 Å (12), 0.10 Å (2), 0.13 Å (4), and 0.02 (5). Even in the extreme case, 17, the average difference between MM and X-ray metric data for the inner coordination sphere is 0.01 Å (
