Volume 128, Issue 3, 21 January 2008
 ARTICLES

 Theoretical Methods and Algorithms

A new parameterfree correlation functional based on an average atomic reduced density gradient analysis
View Description Hide DescriptionA new parameterfree correlation functional based on the local RagotCortona approach [J. Chem. Phys.121, 7671 (2004)] is presented. This functional rests on a single ansatz for the gradient correction enhancement factor: it is assumed to be given by a simple analytic expression satisfying some exact conditions and containing two coefficients. These coefficients are determined without implementing the functional and without using a fitting procedure to experimental data. Their values are determined by requiring that the functional gives a correct average reduced density gradient for atoms, which, to some extent, can be considered an intrinsic atomic property. The correlation functional is then coupled with the PerdewBurkeErzernhof (PBE) exchange and compared with the original PBE approach as well as with some other pure density or hybrid approaches. Standard tests for atomic and molecular systems show that our new functional significantly improves on PBE, showing very interesting properties.

The densities produced by the density functional theory: Comparison to full configuration interaction
View Description Hide DescriptionWe investigate one of the fundamental observables, electronic charge density, as produced by a number of popular functionals of the density functional theory(DFT): SVWN5, B3LYP, B3LYP, OLYP, O3LYP, BP86, B3P86, O3P86, and PBE using restricted and unrestricted orbitals. Measuring and comparing the quality of the densities could tell us more about the physical soundness of the functional models. The study is performed on the small molecules He, , LiH, in an extensive range of correlationconsistentbasis sets. We compare DFT densities to those of full configuration interaction (FCI) under the assumption that the FCI density in the largest employed basis set is sufficiently close to the exact one. For LiH and , we also compare the DFT densities to those of CCSD. The SVWN5 functional consistently shows the worst performance. The OPTX exchange functional regularly beats the Becke exchange. Among the best performers are all the hybrid functionals, the novel O3P86 being the most accurate in most cases. The popular functional B3LYP was consistently outmatched by O3LYP, and produced, in fact, some of the poorest densities among the hybrids. CCSD was found to produce much more accurate densities than any DFT functional in the case of LiH in equilibrium geometry, but was sometimes outperformed by DFT in the case of slightly stretched , where CCSD theory itself starts to break down. Surprisingly, as one stretches the molecule, BP86 and PBE improve the description of density although such behavior is not observed in other systems. We conclude by reasoning how functionals such as B3LYP, despite being quite average for density, could still be very successful in predicting thermodynamic properties.

The limits of local correlation theory: Electronic delocalization and chemically smooth potential energy surfaces
View Description Hide DescriptionLocal coupledcluster theory provides an algorithm for measuring electronic correlation quickly, using only the spatial locality of localized electronic orbitals. Previously, we showed [J. Subotnik et al., J. Chem. Phys.125, 074116 (2006)] that one may construct a local coupledcluster singlesdoubles theory which (i) yields smooth potential energy surfaces and (ii) achieves near linear scaling. That theory selected which orbitals to correlate based only on the distances between the centers of different, localized orbitals, and the approximate potential energy surfaces were characterized as smooth using only visual identification. This paper now extends our previous algorithm in three important ways. First, locality is now based on both the distances between the centers of orbitals as well as the spatial extent of the orbitals. We find that, by accounting for the spatial extent of a delocalized orbital, one can account for electronic correlation in systems with some electronic delocalization using fast correlation methods designed around orbital locality. Second, we now enforce locality on not just the amplitudes (which measure the exact electronelectron correlation), but also on the twoelectron integrals themselves (which measure the bare electronelectron interaction). Our conclusion is that we can bump integrals as well as amplitudes, thereby gaining a tremendous increase in speed and paradoxically increasing the accuracy of our LCCSD approach. Third and finally, we now make a rigorous definition of chemical smoothness as requiring that potential energy surfaces not support artificial maxima, minima, or inflection points. By looking at first and second derivatives from finite difference techniques, we demonstrate complete chemical smoothness of our potential energy surfaces (bumping both amplitudes and integrals). These results are significant both from a theoretical and from a computationally practical point of view.

Relative energy of the high and low spin states of the ferrous complexes : CASPT2 versus density functional theory
View Description Hide DescriptionHighlevel ab initio calculations using multiconfigurational perturbation theory [complete active space with secondorder perturbation theory (CASPT2)] were performed on the transition energy between the lowest highspin (corresponding to in ) and lowspin (corresponding to in ) states in the series of sixcoordinated Fe(II) molecules , where is bis(2mercaptophenylthio)diethylamine dianion and , , , CO, and . The results are compared to (previous and presently obtained) results from density functional theory(DFT) calculations with four functionals, which were already shown previously by Casida and coworkers [Fouqueau et al., J. Chem. Phys.120, 9473 (2004);Ganzenmüller et al., ibid.122, 234321 (2005);Fouqueau et al., ibid.122, 044110 (2005);Lawson Daku et al., ChemPhysChem6, 1393 (2005)] to perform well for the spinpairing problem in these and other Fe(II) complexes, i.e., OLYP, PBE0, B3LYP, and . Very extended basis sets were used both for the DFT and CASPT2 calculations and were shown to be necessary to obtain quantitative results with both types of method. This work presents a sequel to a previous DFT/CASPT2 study of the same property in the complexes , , and [Pierloot et al., J. Chem. Phys.125, 124303 (2006)]. The latter work was extended with new results obtained with larger basis sets and including the OLYP functional. For all considered complexes, the CASPT2 method predicts the correct ground state spin multiplicity. Since experimental data for the actual quintetsinglet (free) energy differences are not available, the performance of the different DFT functionals was judged based on the comparison between the DFT and CASPT2 results. From this, it was concluded that the generalized gradient OLYP functional performs remarkably well for the present series of ferrous compounds, whereas the success of the three hybrid functionals varies from case to case.

Quantum mechanics/molecular mechanics minimum freeenergy path for accurate reaction energetics in solution and enzymes: Sequential sampling and optimization on the potential of mean force surface
View Description Hide DescriptionTo accurately determine the reaction path and its energetics for enzymatic and solutionphase reactions, we present a sequential sampling and optimization approach that greatly enhances the efficiency of the ab initio quantum mechanics/molecular mechanics minimum freeenergy path (QM/MMMFEP) method. In the QM/MMMFEP method, the thermodynamics of a complex reaction system is described by the potential of mean force (PMF) surface of the quantum mechanical (QM) subsystem with a small number of degrees of freedom, somewhat like describing a reaction process in the gas phase. The main computational cost of the QM/MMMFEP method comes from the statistical sampling of conformations of the molecular mechanical (MM) subsystem required for the calculation of the QM PMF and its gradient. In our new sequential sampling and optimization approach, we aim to reduce the amount of MM sampling while still retaining the accuracy of the results by first carrying out MM phasespace sampling and then optimizing the QM subsystem in the fixedsize ensemble of MM conformations. The resulting QM optimized structures are then used to obtain more accurate sampling of the MM subsystem. This process of sequential MM sampling and QM optimization is iterated until convergence. The use of a fixedsize, finite MM conformational ensemble enables the precise evaluation of the QM potential of mean force and its gradient within the ensemble, thus circumventing the challenges associated with statistical averaging and significantly speeding up the convergence of the optimization process. To further improve the accuracy of the QM/MMMFEP method, the reaction path potential method developed by Lu and Yang [Z. Lu and W. Yang, J. Chem. Phys.121, 89 (2004)] is employed to describe the QM/MM electrostatic interactions in an approximate yet accurate way with a computational cost that is comparable to classical MM simulations. The new method was successfully applied to two example reaction processes, the classical reaction of in solution and the second proton transfer step of the reaction catalyzed by the enzyme 4oxalocrotonate tautomerase. The activation free energies calculated with this new sequential sampling and optimization approach to the QM/MMMFEP method agree well with results from other simulation approaches such as the umbrella sampling technique with direct QM/MM dynamics sampling, demonstrating the accuracy of the iterative QM/MMMFEP method.

Solving the spinboson model of strong dissipation with flexible randomdeterministic scheme
View Description Hide DescriptionThe zerotemperature dynamics of the spinboson model with strong dissipation has been a challenging problem for more than . To solve this and quantum dynamics of dissipative systems at large, we recently proposed a mixed randomdeterministic method. This scheme has been successfully used to simulate the time evolution of the spinboson model at zero temperature for weak to moderate dissipation. For a better numerical performance, the approach is further modified so that it is flexible to convert a certain part of the random treatment to a deterministic one à la hierarchical equations. Applying the new method to the strong dissipated spinboson model at zero temperature, we observe that the population in the localized state obeys a simple decay dynamics and the time scale is proportional to the reciprocal of the cutoff frequency.

QM:QM electronic embedding using Mulliken atomic charges: Energies and analytic gradients in an ONIOM framework
View Description Hide DescriptionAn accurate firstprinciples treatment of chemical reactions for large systems remains a significant challenge facing electronic structuretheory. Hybrid models, such as quantum mechanics:molecular mechanics (QM:MM) and quantum mechanics:quantum mechanics (QM:QM) schemes, provide a promising avenue for such studies. For many chemistries, including important reactions in materials science, molecular mechanics or semiempirical methods may not be appropriate, or parameters may not be available (e.g., surface chemistry of compound semiconductors such as indium phosphide or catalytic chemistry of transition metal oxides). In such cases, QM:QM schemes are of particular interest. In this work, a QM:QM electronic embedding model within the ONIOM (our own layer integrated molecular orbital molecular mechanics) extrapolation framework is presented. To define the embedding potential, we choose the realsystem lowlevel Mulliken atomic charges. This results in a set of welldefined and unique embedding charges. However, the parametric dependence of the charges on molecular geometry complicates the energy gradient that is necessary for the efficient exploration of potential energy surfaces. We derive an efficient form for the forces where a single set of selfconsistent field response equations is solved. Initial tests of the method and key algorithmic issues are discussed.

Elimination, in electronic structure calculations, of redundant orbital products
View Description Hide DescriptionWe propose a direct method for reducing the dimension of the space of orbital products that occur, for example, in the calculation of time dependent density functional theory linear response and in Hedin’s GW approximation to the electron propagator. We do this by defining, within the linear space of orbital products, a subspace of dominant directions that are associated with a certain eigenvalue problem. These directions span the entire linear space of products with an error that decreases approximately exponentially with their number. Our procedure works best for atomic orbitals of finite range and it avoids the use of extra sets of auxiliary fit functions.

The optimal P3M algorithm for computing electrostatic energies in periodic systems
View Description Hide DescriptionWe optimize Hockney and Eastwood’s particleparticle particlemesh algorithm to achieve maximal accuracy in the electrostatic energies (instead of forces) in threedimensional periodic charged systems. To this end we construct an optimal influence function that minimizes the rootmeansquare (rms) errors of the energies. As a byproduct we derive a new realspace cutoff correction term, give a transparent derivation of the systematic errors in terms of Madelung energies, and provide an accurate analytical estimate for the rms error of the energies. This error estimate is a useful indicator of the accuracy of the computed energies and allows an easy and precise determination of the optimal values of the various parameters in the algorithm (Ewald splitting parameter, mesh size, and charge assignment order).

Energyconsistent relativistic pseudopotentials for the elements: Atomic and molecular applications
View Description Hide DescriptionRecently reported energyconsistent relativistic pseudopotentials have been used with series of matching correlation consistent basis sets in benchmark calculations of various atomic and molecular properties. The basis set convergence of the metal electron affinities and excitation energies are reported at the CCSD(T) level of theory, and the effects of valence and correlation are investigated. In addition the impact of correlating the lowlying electrons was also studied in allelectron DouglasKrollHess (DKH) calculations, which also included the ionization potentials and excitation energies. For all four atomic properties, higher order coupled cluster calculations through CCSDTQ are reported. The final calculated values are generally all within of experiment. A notable exception is the ionization potential of Tc, the currently accepted experimental value of which is suggested to be too high by about . Molecular calculations are also reported for the lowlying electronic states of ZrO and RuF, as well as the ground electronic state of . The effects of spinorbit coupling are investigated for these cases in pseudopotential calculations. Wherever possible, the pseudopotential results have been calibrated against DKH calculations with correlation consistent basis sets of triplezeta quality. In all cases the calculated data for these species are in very good agreement with experiment. In particular, the correct electronic ground state for the RuF molecule was obtained, which was made possible by utilizing systematic sequences of correlation consistent basis sets.
 Gas Phase Dynamics and Structure: Spectroscopy, Molecular Interactions, Scattering, and Photochemistry

Characterization of cyclic and linear and via anion photoelectron spectroscopy
View Description Hide DescriptionAnion photoelectron spectroscopy of and is performed using both fieldfree timeofflight and slow electron velocitymap imaging. We observe and assign transitions originating from linear/bent and cyclic anionic isomers to the corresponding neutral ground states and lowlying excited states. Transitions within the cyclic and linear manifolds are distinguished by their photoelectron angular distributions and their intensity dependence on the neutral precursor. Using calculated values for the energetics of the neutral isomers [Ochsenfeld et al., J. Chem. Phys.106, 4141 (1997)], which predict to lie lower than , the experimental results establish as the anionic ground state and place it below . Electron affinities of and are determined for and from the photodetachment transition of . Term energies for several lowlying states of and are also determined. FranckCondon simulations are used to make vibrational assignments for the bands involving . Simulations of the bands were more complicated owing to large amplitude bending motion and, in the case of the neutral state, strong RennerTeller coupling.

Calculated electronic transitions of the water ammonia complex
View Description Hide DescriptionWe have calculated vertical excitation energies and oscillator strengths of the low lying electronic transitions in , , and using a hierarchy of coupled cluster response functions [coupled cluster singles (CCS), second order approximate coupled cluster singles and doubles (CC2), coupled cluster singles and doubles (CCSD), and third order approximate coupled cluster singles, doubles, and triples (CC3)] and correlation consistent basis functions (naugccpVXZ, where and ). Our calculations indicate that significant changes in the absorption spectra of the photodissociative states of and monomers occur upon complexation. In particular, we find that the electronic transitions originating from are blueshifted, whereas the electronic transitions originating from are redshifted.

Excited electronic state decomposition of furazan based energetic materials: diaminoazoxyfurazan and its model systems, diaminofurazan and furazan
View Description Hide DescriptionWe report the first experimental and theoretical study of gas phase excited electronic state decomposition of a furazan based, high nitrogen content energetic material, diaminoazoxyfurazan (DAAF), and its model systems, diaminofurazan (DAF) and furazan . DAAF has received major attention as an insensitive high energy explosive; however, the mechanism and dynamics of the decomposition of this material are not clear yet. In order to understand the initial decomposition mechanism of DAAF and those of its model systems, nanosecond energy resolved and femtosecond time resolved spectroscopies and complete active space selfconsistent field (CASSCF) calculations have been employed to investigate the excited electronic state decomposition of these materials. The NO molecule is observed as an initial decomposition product from DAAF and its model systems at three UV excitation wavelengths (226, 236, and ) with a pulse duration of . Energies of the three excitation wavelengths coincide with the (00), (01), and (02) vibronic bands of the NO electronic transition, respectively. A unique excitation wavelength independent dissociation channel is observed for DAAF, which generates the NO product with a rotationally cold and a vibrationally hot distribution. On the contrary, excitation wavelength dependent dissociation channels are observed for the model systems, which generate the NO product with both rotationally cold and hot distributions depending on the excitation wavelengths. Potential energy surface calculations at the CASSCF level of theory illustrates that two conical intersections between the excited and ground electronic states are involved in two different excitation wavelength dependent dissociation channels for the model systems. Femtosecondpumpprobe experiments at reveal that the NO molecule is still the main observed decomposition product from the materials of interest and that the formation dynamics of the NO product is faster than . Two additional fragments are observed from furazan with mass of and employing femtosecond laser ionization. This observation suggests a fivemembered heterocyclic furazan ring opening mechanism with rupture of a CN and a NO bond, yielding NO as a major decomposition product. is not observed as a secondary decomposition product of DAAF and DAF.

Ground state structures and excited state dynamics of pyrrolewater complexes: Ab initio excited state molecular dynamics simulations
View Description Hide DescriptionStructures of the ground state pyrrole clusters are investigated using ab initio calculations. The chargetransfer driven femtosecond scale dynamics are studied with excited stateab initiomolecular dynamics simulations employing the completeactivespace selfconsistentfield method for pyrrole clusters. Upon the excitation of these clusters, the charge density is located over the farthest water molecule which is repelled by the depleted electron cloud of pyrrole ring, resulting in a highly polarized complex. For pyrrole, the charge transfer is maximized (up to ) around and then oscillates. For pyrrole, the initial charge transfer occurs through the space between the pyrrole and the Hbonded water molecule and then the charge transfer takes place from this water molecule to the Hbonded water molecule. The total charge transfer from the pyrrole to the water molecules is maximized (up to ) around .

The barrier height of the reaction revisited: Coupledcluster and multireference configurationinteraction benchmark calculations
View Description Hide DescriptionLarge scale coupledcluster benchmark calculations have been carried out to determine the barrier height of the reaction as accurately as possible. The best estimates for the barrier height of the linear and bent transition states amount to 2.16 and , respectively. These values include corrections for core correlation, scalarrelativistic effects, spinorbit effects, as well as the diagonal BornOppenheimer correction. The CCSD(T) basisset limits are estimated using extrapolation techniques with augmented quintuple and sextuplezeta basis sets, and remaining electron errors are determined using coupledcluster singles, doubles, triples, quadruples calculations with up to augmented quintuplezeta basis sets. The remaining uncertainty is estimated to be less than . The coupledcluster results are used to calibrate multireference configurationinteraction calculations with empirical scaling of the correlation energy.

Quantum scattering of SiS with : Potential energy surface and rate coefficients at low temperature
View Description Hide DescriptionRotational excitation of the interstellar species SiS with is investigated. We present a new four dimensional potential energy surface for the system. Both molecules were treated as rigid rotors. Potential was obtained from the electronic structure calculations using a single and doubleexcitation coupled cluster method with perturbative contributions from connected triple excitations [CCSD(T)]. The four atoms were described using the augccpVTZ basis sets.Bond functions were placed at middistance between the SiS center of mass and the center of mass of for a better description of the van der Waals interaction. Additionally, at seven characteristic geometries, we calculated perturbational components of the interaction energy using symmetryadapted perturbation theory approach to explain the anisotropy of the potential energy surface. Coupledstate calculations of the inelastic integral cross sections of SiS in collisions with para and ortho were calculated at low energies. After Boltzmann thermal averaging, rate coefficients were obtained for temperatures ranging from . Significant differences exist between para and ortho results. The strongest collisioninduced rotational SiS transitions are the transitions with for collisions with para and the transitions with for collisions with ortho.

Experimental and theoretical study of the photodissociation of bromo3fluorobenzene
View Description Hide DescriptionThe UV photodissociation of bromo3fluorobenzene under collisionless conditions has been studied as a function of the excitation wavelength between 255 and . The experiments were performed using ultrafast pumpprobe laser spectroscopy. To aid in the interpretation of the results, it was necessary to extend the theoretical framework substantially compared to previous studies, to also include quantum dynamical simulations employing a twodimensional nuclear Hamiltonian. The nonadiabaticpotential energy surfaces (PES) were parameterized against highlevel MSCASTP2 quantum chemical calculations, using both the C–Br distance and the outofplane bending of the bromine as nuclear parameters. We show that the wavelength dependence of the photodissociation via the channel, accessible with a pulse, is captured in this model. We thereby present the first correlation between experiments and theory within the quantitative regime.

Predicting the infrared transition intensities in the Ar–HF complex: The key role of the dipole moment surface accuracy
View Description Hide DescriptionThe method proposed earlier for the generation of the fulldimensional energy surface for van der Waals complexes [P. Jankowski, J. Chem. Phys.121, 1655 (2004)] is used to obtain a fulldimensional dipole momentsurface for the atomdiatom complex in calculations based on the coupledcluster with single, double, and noniterative triple excitation approach and the augccpVQZ basis sets. This surface has been employed to calculate transition intensities of the infrared spectra of Ar–HF. Special attention has been paid to study the problem of relative intensities of the different bands which have not been properly predicted within the longrange models of the dipole moment [A. E. Thornley and J. M. Hutson, J. Chem. Phys.101, 5578 (1994)]. The intensities calculated with the present dipole momentsurface agree very well with the experimental data, which indicate that the shortrange interactions significantly affect the dipole momentsurface and the calculated intensities. To investigate the role of the accuracy of the dipole momentsurface on infrared transition intensities in atomdiatom complexes, four models of increasing complexity are studied. Their performance is shown to strongly depend on the region of the interaction energy surface probed by the initial and final states of the individual transitions.

Electronic structure and bonding of the transition metal borides, MB, , Ti, V, Cr, Mn, Fe, Co, Ni, and Cu through all electron ab initio calculations
View Description Hide DescriptionThe electronic structure and bonding of the ground and some lowlying states of all first row transition metalborides (MB), ScB, TiB, VB, CrB, MnB, FeB, CoB, NiB, and CuB have been studied by multireference configuration interaction (MRCI) methods employing a correlation consistent basis set of quintuple cardinality (5Z). It should be stressed that for all the above nine molecules, experimental results are essentially absent, whereas with the exception of ScB and CuB the remaining seven species are studied theoretically for the first time. We have constructed full potential energy curves at the MRCI/5Z level for a total of 27 lowlying states, subsequently used to extract binding energies, spectroscopic parameters, and bonding schemes. In addition, some 20 or more states for every MB species have been examined at the MRCI/4Z level of theory. The ground state symmetries and corresponding binding energies (in kcal/mol) are , 76; , 65; , 55; , 31; , 20; , 54; , 66; , 79; and , 49.

Water clusters , , in external electric fields
View Description Hide DescriptionStructural evolution of water clusters, , , induced by a uniform static external electric field is studied within the density functional theory. The electric field is seen to stretch the intermolecular hydrogen bonds in the water clusters, eventually breaking them at some characteristic threshold value, triggering a conformational transformation to a lower energy. The transformed configurations appear as local minima on the cluster’s multidimensional potential energy landscape with the applied field as an extra coordinate. This transformation is accompanied by a rather abrupt increase in the electric dipole moment over and above its steady, albeit nonlinear increase with the applied field. The overall effect of the applied field is the “opening up” of three dimensional morphologies of water clusters to form linear, branched, or netlike structures by making the dipolar water monomers align along the field axis. Consequently, the number of hydrogen bonds in a cluster decreases, in general, with an increase in the field strength. It has been observed that moderately low fields (Field strength ) markedly alter the ordering of the lowest energy configurations.