Young - Computational chemistry
.pdfComputational Chemistry: A Practical Guide for Applying Techniques to Real-World Problems. David C. Young Copyright ( 2001 John Wiley & Sons, Inc.
ISBNs: 0-471-33368-9 (Hardback); 0-471-22065-5 (Electronic)
The Computational Chemist's
37 View of the Periodic Table
37.1ORGANIC MOLECULES
Organic molecules are the easiest to model and the easiest for which to obtain the most accurate results. This is so for a number of reasons. Since the amount of computational resources necessary to run an orbital-based calculation depends on the number of electrons, quantum mechanical calculations run fastest for compounds with few electrons. Organic molecules are also the most heavily studied and thus have the largest number of computational techniques available.
Organic molecules are generally composed of covalent bonded atoms with several well-de®ned hybridization states tending to have well-understood preferred geometries. This makes them an ideal case for molecular mechanics parameterization. Likewise, organic molecules are the ideal case for semiempirical parameterization.
This section provides a brief discussion of technical issues pertaining to modeling organic molecules. The bibliography focuses on pertinent review literature. Many computational chemistry methods can be applied to organic molecules. However, there are a few caveats to note as discussed here.
37.1.1Group Additivity Methods
One of the earliest methods for predicting the properties of organic molecules are the group additivity methods. These are systems in which a table of contributions to a particular property for each functional group is derived. The property is then estimated by adding the contribution of each functional group in the molecule. Group additivity methods are most accurate for organic systems due to the reasons cited above. Regardless of the type of molecule, group additivity techniques are only applicable when the property being predicted can be described by additive equations. This generally is most accurate for predicting the properties of monofunctional compounds. Group additivity methods are discussed in more detail in Chapter 13.
37.1.2Molecular Mechanics
A number of molecular mechanics force ®elds have been parameterized for speci®c organic systems, such as proteins or hydrocarbons. There are also a
283
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number of good force ®elds for modeling organic compounds in general. These methods can be very good for predicting the geometry of molecules and relative energies of conformers. Proteins, nucleic acids, and sugars are best described by force ®elds designed speci®cally for those compounds. Other organic compounds are described well by general-purpose organic force ®elds. Molecular mechanics methods are discussed further in Chapter 6.
37.1.3Semiempirical Methods
Many semiempirical methods have been created for modeling organic compounds. These methods correctly predict many aspects of electronic structure, such as aromaticity. Furthermore, these orbital-based methods give additional information about the compounds, such as population analysis. There are also good techniques for including solvation e¨ects in some semiempirical calculations. Semiempirical methods are discussed further in Chapter 4.
37.1.4Ab initio Methods
Ab initio methods are applicable to the widest variety of property calculations. Many typical organic molecules can now be modeled with ab initio methods, such as Hartree±Fock, density functional theory, and Mùller Plesset perturbation theory. Organic molecule calculations are made easier by the fact that most organic molecules have singlet spin ground states. Organics are the systems for which sophisticated properties, such as NMR chemical shifts and nonlinear optical properties, can be calculated most accurately.
Correlated calculations, such as con®guration interaction, DFT, MPn, and coupled cluster calculations, can be used to model small organic molecules with high-end workstations or supercomputers. These are some of the most accurate calculations done routinely. Correlation is not usually required for qualitative or even quantitative results for organic molecules. It is needed to obtain highaccuracy quantitative results.
Core potentials are seldom used for organic molecules because there are so few electrons in the core. Relativistic e¨ects are seldom included since they have very little e¨ect on the result. Ab initio methods are discussed further in Chapter 3.
37.1.5Recommendations
Organic molecule calculations can be done routinely to good accuracy on workstation-class hardware. It is advisable to examine tabulations of results in order to choose a method with acceptable accuracy and computational time for the property of interest. The trend toward having microcomputer versions of computational chemistry codes is making calculations on small organic molecules even more readily accessible.
37.2 MAIN GROUP INORGANICS, NOBLE GASES, AND ALKALI METALS 285
37.2 MAIN GROUP INORGANICS, NOBLE GASES, AND ALKALI METALS
Modeling the elements discussed in this section is fairly similar to modeling organic compounds. This is primarily because d and f orbitals play a minor role in their chemistry. When d and f orbitals do a¨ect the chemistry, their e¨ect is well de®ned and for the most part understood.
Molecular mechanics methods have only been used to a limited extent for these classes of compounds. However, molecular mechanics methods do fairly well in describing the geometries and relative energies of compounds with these elements. It is perhaps only for historical and economic reasons that molecular mechanics has not been used more for modeling these elements. Subsequently, there are not as many force ®elds available.
Semiempirical, DFT, and ab initio methods also work well. Correlation e¨ects are sometimes included for the sake of increased accuracy, but are not always necessary. One particular case for which correlation is often necessary is ¯uorine compounds.
37.2.1Halides
Within Hartree±Fock theory, F2 has a reasonable bond length, but its total energy is higher than the sum of the energies of two F atoms. This is because correlation is a very signi®cant contribution to the valence description of ¯uorine. Correlated calculations well describe halogenated compounds. This e¨ect is seen to a lesser extent in modeling other halide atoms. Molecular mechanics works well if the charge computation scheme correctly re¯ects the electronegativity of these elements.
37.2.2Other Main Group Inorganics
Modeling the lighter main group inorganic compounds is similar to modeling organic compounds. Thus, the choice of method and basis set is nearly identical. The second-row compounds (i.e., sulfur) do have un®lled d orbitals, making it often necessary to use basis sets with d functions.
The heavier elements are a¨ected by relativistic e¨ects. This is most often accounted for by using relativistic core potentials. Relativistic e¨ects are discussed in more detail in Chapters 10 and 33.
37.2.3Noble Gases
The noble gases are mostly unreactive. In some instances, they act mostly as a place holder to ®ll a cavity. For dynamical studies of the bulk gas phase or liquid-phase noble gases, hard-sphere or soft-sphere models work rather well.
Paradoxically, compounds incorporating bonds with noble gases are di½cult to model. This is because a very accurate method is needed in order to correctly
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model what little reactivity they do have. Often, correlated ab initio calculations with polarized basis sets are used. The worst case is the dimers, such as the He2 dimer that is known experimentally to exist and have one bound vibrational level. He2 has only been modeled accurately using some of the most accurate methods known, such as quantum Monte Carlo calculations.
37.2.4Alkali Metals
The alkali metals tend to ionize; thus, their modeling is dominated by electrostatic interactions. They can be described well by ab initio calculations, provided that di¨use, polarized basis sets are used. This allows the calculation to describe the very polarizable electron density distribution. Core potentials are used for ab initio calculations on the heavier elements.
Molecular mechanics methods may work well or poorly for compounds containing alkali metals. The crucial factor is often how the force ®eld computes charges for electrostatic interactions.
37.2.5Recommendations
If these elements are included in an organic molecule, the choice of computational method can be made based on the organic system with deference to the exceptions listed in this section. If completely inorganic calculations are being performed, use a method that tends to correctly model the property of interest in organic systems.
37.3TRANSITION METALS
There is a growing interest in modeling transition metals because of its applicability to catalysts, bioinorganics, materials science, and traditional inorganic chemistry. Unfortunately, transition metals tend to be extremely di½cult to model. This is so because of a number of e¨ects that are important to correctly describing these compounds. The problem is compounded by the fact that the majority of computational methods have been created, tested, and optimized for organic molecules. Some of the techniques that work well for organics perform poorly for more technically di½cult transition metal systems.
Nearly every technical di½culty known is routinely encountered in transition metal calculations. Calculations on open-shell compounds encounter problems due to spin contamination and experience more problems with SCF convergence. For the heavier transition metals, relativistic e¨ects are signi®cant. Many transition metals compounds require correlation even to obtain results that are qualitatively correct. Compounds with low-lying excited states are di½cult to converge and require additional work to ensure that the desired states are being computed. Metals also present additional problems in parameterizing semiempirical and molecular mechanics methods.
37.3 TRANSITION METALS |
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37.3.1Molecular Mechanics Methods
In the past, when molecular mechanics methods were used for transition metals, it was by having a set of parameters for the metal that were parameterized speci®cally for one class of compounds. There have been a number of full periodic table force ®elds created, with the most successful being the UFF force ®eld. All the full periodic molecular mechanics methods still give completely unreasonable results for certain classes of compounds.
One reason for these di½culties is that metals have fairly soft bonding. This means that there is a nearly continuous range of values experimentally observed for any given metal-organic bond length. Likewise, inorganics more often exhibit distorted or ¯uxional bond angles. There is also less vibrational data available to parameterize force constants.
Not all molecular mechanics methods can be adapted to metal calculations simply by adding new parameters. For example, consider a square planar Pt atom. Unlike organic atoms, some of the bond angles are 90 , whereas others are 180 . One option is to have di¨erent parameters for describing these two cases and a program that can recognize which to use. A second option is to use an angle function with two minima at 90 and 180 . In both cases, the software package must have capabilities not needed for organic molecules. Another option is to hold the Pt rigid over the course of the calculation.
Coordination creates additional problems also. Consider the metalaCp bond in a metallocene. One option is to have ®ve bonds from the metal to each carbon. A second option is to have a single bond connecting to a dummy atom at the center of the Cp ring.
One way that molecular mechanics methods have been adapted to transition metal applications is by including one orbital-based term in the force ®eld to describe the metal center. These terms are typically based on semiempirical methods or even some variation of ligand ®eld theory.
37.3.2Semiempirical Methods
There are a few semiempirical methods for modeling transition metals. These tend to have limited applicability. None has yet become extremely far-ranging in the type of system it can model accurately.
Extended HuÈckel gives a qualitative view of the valence orbitals. The formulation of extended HuÈckel is such that it is only applicable to the valence orbitals. The method reproduces the correct symmetry properties for the valence orbitals. Energetics, such as band gaps, are sometimes reasonable and other times reproduce trends better than absolute values. Extended HuÈckel tends to be more useful for examining orbital symmetry and energy than for predicting molecular geometries. It is the method of choice for many band structure calculations due to the very computation-intensive nature of those calculations.
Fenske Hall is essentially a quanti®cation of ligand ®eld theory. The interactions are primarily electrostatic in nature. It does a reasonable job of re-
288 37 THE COMPUTATIONAL CHEMIST'S VIEW OF THE PERIODIC TABLE
producing certain trends and re¯ects the very soft nature of ligand bond angles. This method must be used with caution as it sometimes oversimpli®es the nature of orbital interactions.
ZINDO is an adaptation of INDO speci®cally for predicting electronic excitations. The proper acronym for ZINDO is INDO/S (spectroscopic INDO), but the ZINDO moniker is more commonly used. ZINDO has been fairly successful in modeling electronic excited states. Some of the codes incorporated in ZINDO include transition-dipole moment computation so that peak intensities as well as wave lengths can be computed. ZINDO generally does poorly for geometry optimization.
PM3/TM is an extension of the PM3 method to transition metals. Unlike the parameterization of PM3 for organics, PM3/TM has been parameterized only to reproduce geometries. This does, of course, require a reasonable description of energies, but the other criteria used for PM3 parameterization, such as dipole moments, are not included in the PM3/TM parameterization. PM3/TM tends to exhibit a dichotomy. It will compute reasonable geometries for some compounds and completely unreasonable geometries for other compounds. It seems to favor one coordination number or hybridization for some metals.
37.3.3Ab initio Methods
Ab initio methods pose problems due a whole list of technical di½culties. Most of these stem from the large number of electrons and low-energy excited state. Core potentials are often used for heavier elements to ease the computational requirements and account for relativistic e¨ects.
Convergence problems are very common due to the number of orbitals available and low-energy excited states. The most di½cult calculations are generally those with open-shell systems and an un®lled coordination sphere. All the techniques listed in Chapter 22 may be necessary to get such calculations to converge.
Many transition metal systems are open-shell systems. Due to the presence of low-energy excited states, it is very common to experience problems with spin contamination of unrestricted wave functions. Quite often, spin projection and annihilation techniques are not su½cient to correct the large amount of spin contamination. Because of this, restricted open-shell calculations are more reliable than unrestricted calculations for metal system. Spin contamination is discussed in Chapter 27.
Electron correlation is often very important as well. The presence of multiple bonding interactions, such as pi back bonding, makes coordination compounds more sensitive to correlation than organic compounds. In some cases, the HF wave function does not provide even a qualitatively correct description of the compound. If the weight of the reference determinant in a single-reference CISD calculation is less than about 0.9, then the HF wave function is not qualitatively correct. In such cases, multiple-determinant, MSCSF, CASPT2, or MRCI calculations tend to be the most e½cient methods. The alternative is
37.4 LANTHANIDES AND ACTINIDES 289
to include triple and quadruple excitations in single-reference CI or CC calculations. In recent years, DFT methods, particularly B3LYP, have become widely used for large metal-containing systems, such as enzyme active sites. These calculations generally give results of good accuracy with reasonable computational requirements, although it is still necessary to use correlated ab initio methods at times in order to obtain more accurate results.
Relativistic e¨ects are signi®cant for the heavier metals. The method of choice is nearly always relativistically derived e¨ective core potentials. Explicit spin-orbit terms can be included in ab initio calculations, but are seldom used because of the amount of computational e¨ort necessary. Relativistic calculations are discussed in greater detail in Chapter 33.
Because of the existence of low-energy excited states, calculations done with the software default settings very often give results for the electronic excited states rather than the ground state. There can be a signi®cant amount of work in just computing various states of the molecule in order to ensure that the correct ground state has been determined. Chapter 25 discusses excited-state calculations and consequently the techniques to use for determining the ground state for metal systems. An initial guess algorithm based on ligand ®eld theory is perhaps most reliable.
37.4LANTHANIDES AND ACTINIDES
Lanthanide and actinide compounds are di½cult to model due to the very large number of electrons. However, they are somewhat easier to model than transition metals because the unpaired f electrons are closer to the nucleus than the outermost d shell. Thus, all possible spin combinations do not always have a signi®cant e¨ect on chemical bonding.
Relativistic e¨ects should always be included in these calculations. Particularly common is the use of core potentials. If core potentials are not included, then another form of relativistic calculation must be used. Relativistic e¨ects are discussed in more detail in Chapter 33.
37.4.1Methods
Molecular mechanics force ®elds are sometimes parameterized to describe lanthanides and actinides. This has been e¨ective in describing the shape of the molecule, but does not go very far toward giving systematic energies. A few semiempirical methods have been parameterized for these elements, but they have not seen widespread use.
Ab initio calculations with core potentials are usually the method of choice. The researcher must make a di½cult choice between minimizing the CPU time requirements and obtaining more accurate results when deciding which core potential to use. Correlation is particularly di½cult to include because of the large number of electrons even in just the valence region of these elements.
290 37 THE COMPUTATIONAL CHEMIST'S VIEW OF THE PERIODIC TABLE
Population analysis poses a particularly di½cult problem for the f block elements. This is because of the many possible orbital combinations when both f and d orbitals are occupied in the valence. Although programs will generate a population analysis, extracting meaningful information from it can be very di½cult.
BIBLIOGRAPHY
The bibliography for this chapter is perhaps the most di½cult to write. The majority of references in this entire book pertain to organic molecules. The organic references listed here are just a few of the review references pertaining speci®cally to organic chemistry. This list is incomplete, but attempts to include recent reviews, which will reference earlier work. The listing for other classes of molecules are more complete.
Some books relevant to organic chemistry are
Theoretical Organic Chemistry C. PaÂrkyaÂni, Ed., Elsevier, Amsterdam (1998).
A.K. RappeÂ, C. J. Casewit, Molecular Mechanics across Chemistry University Science Books, Sausalito (1997).
D.Hadzi, Theoretical Treatments of Hydrogen Bonding John Wiley & Sons, New York (1997).
W. B. Smith, Introduction to Theoretical Organic Chemistry and Molecular Modeling
John Wiley & Sons, New York (1996).
Modeling the Hydrogen Bond D. A. Smith, Ed., American Chemical Society, Washington (1994).
V. I. Minkin, B. Y. Simkin, R. M. Minyaev, Quantum Chemistry of Organic Compounds; Mechanisms of Reactions Springer-Verlag, Berlin (1990).
Applications of Molecular Orbital Theory in Organic Chemistry I. G. Csizmadia, Ed., Elsevier, Amsterdam (1977).
I.Fleming, Frontier Orbitals and Organic Chemical Reactions John Wiley & Sons, New York (1976).
M. J. S. Dewar, R. C. Daugherty, The PMO Theory of Organic Chemistry Plenum, New York (1975).
T. E. Peacock, The Electronic Structure of Organic Molecules Pergamon, Oxford (1972). M. J. S. Dewar, The Molecular Orbital Theory of Organic Chemistry McGraw-Hill, New
York (1969).
K. Higasi, H. Buba, A. Rembaum, Quantum Organic Chemistry John Wiley & Sons, New York (1965).
Group additivity methods are reviewed in
N.Cohen, S. W. Benson, Chem. Rev. 93, 2419 (1993).
Organic anion calculations are reviewd in
L.Radom, Applications of Electronic Structure Theory H. F. Schafer, III, Ed., 333, Plenum, New York (1977).
BIBLIOGRAPHY 291
Carbene calculations are reviewed in
H.F. Bettinger, P. v. R. Schleyer, P. R. Schreiner, H. F. Schaefer, III, Encycl. Comput. Chem. 1, 183 (1998).
Carbocations are reviewed in
D. H. Aue, Encycl. Comput. Chem. 1, 210 (1998).
Carbohydrates are reviewed in
A. D. Brench, Encycl. Comput. Chem. 1, 233 (1998).
Cyclodextrins are reviewed in
C. Jaime, Encycl. Comput. Chem. 1, 644 (1998).
Diels-Alder reactions are reviewed in
J. Bertran, V. Branchadell, A. Oliva, M. Sodupe, Encycl. Comput. Chem. 3, 2030 (1998).
J.J. Dannenberg, Advances in Molecular Modeling 2, 1, D. Liotta, Ed., JAI New York (1990).
Organic diradicals are reviewed in
W. T. Borden, Encycl. Comput. Chem. 1, 709 (1998).
Electron transfer in organic molecules is reviewed in
K. D. Jordan, M. N. Paddon-Row, Encycl. Comput. Chem. 2, 826 (1998).
Enthalpy of hydration of organic molecules is reviewed in
D. W. Rodgers, Encycl. Comput. Chem. 2, 920 (1998).
Heat of formation for organic molecules is reviewed in
Y. Fan, Encycl. Comput. Chem. 2, 1217, (1998).
Hydrogen bonding is reviewed in
J. E. Del Bene, Encycl. Comput. Chem. 2, 1263 (1998).
J.-H. Lii, Encycl. Comput. Chem. 2, 1271 (1998).
J. J. P. Stewart, Encycl. Comput. Chem. 2, 1283 (1998).
P.A. Kollman, Applications of Electronic Structure Theory H. F. Schaefer, III, Ed., 109, Plenum, New York (1977).
Hyperconjugation is reviewed in
C.J. Cramer, Encycl. Comput. Chem. 2, 1294 (1998).
Photochemistry is reviewed in
M. A. Robb, M. Olivucci, F. Bernardi, Encycl. Comput. Chem. 3, 2057 (1998).
292 37 THE COMPUTATIONAL CHEMIST'S VIEW OF THE PERIODIC TABLE
Proton a½nity is reviewed in
S. Gronert, Encycl. Comput. Chem. 3, 2283 (1998).
Organic heterocyclic reactions are reviewed in
G.L. Heard B. F. Yates, Encycl. Comput. Chem. 4, 2420 (1998).
Rotational barriers are reviewed in
K.B. Wiberg, Encycl. Comput. Chem. 4, 2518 (1998).
L.Goodman, V. Pophristic, Encycl. Comput. Chem. 4, 2525 (1998).
Carbohydrate solvation is reviewed in
J. W. Brady, Encycl. Comput. Chem. 4, 2609 (1998).
Other review articles pertaining to organic chemistry are
J.CatalaÂn, J. L. G. de Paz, Computational Chemistry: Structure, Interactions and Reactivity Part A S. Fraga, Ed., 434, Elsevier, Amsterdam (1992).
Sources giving discussions generally applicable to main group inorganics are
J.A. Alonso, L. C. BalbaÂs, Density Functional Theory III R. F. Nalewajski, Ed., 119, Springer, Berlin (1996).
P.Comba, T. W. Hambly, Molecular Modeling of Inorganic Compounds VCH, Weinheim (1995).
J.K. Burdett, Molecular Shapes: Theoretical Models of Inorganic Stereochemistry John Wiley & Sons, New York (1980).
G. Doggett, The Electronic Structure of Models: Theory and Applications to Inorganic Molecules Pergamon, Oxford (1972).
Bromine containing compounds are discussed in
S.Guha, J. S. Francisco, Computational Chemistry Reviews of Current Trends Volume 3
75, J. Leszczynski, Ed., World Scienti®c, Singapore (1999).
Fluctional Processes in boranes and carboranes are reviewed in
M. L. McKee, Encycl. Comput. Chem. 2, 1002 (1998).
The He2 problem is examined in
J. B. Anderson, C. A. Traynor, B. M. Boghosian, J. Chem. Phys. 99, 345 (1993).
Isolobal relationships are reviewed in
E.D. Jemmis, K. T. Giju, Encycl. Comput. Chem. 2, 1149 (1998).
Molecular mechanics modeling of main group inorganics is reviewed in
A.K. RappeÂ, C. J. Casewit, Molecular Mechanics across Chemistry University Science Books, Sausalito (1997).