main-content

## Über dieses Buch

In this Festschrift celebrating the career of Thom H. Dunning, Jr., selected researchers in theoretical chemistry present research highlights on major developments in the field. Originally published in the journal Theoretical Chemistry Accounts, these outstanding contributions are now available in a hardcover print format, as well as a special electronic edition. This volume provides valuable content for all researchers in theoretical chemistry and will especially benefit those research groups and libraries with limited access to the journal.

## Inhaltsverzeichnis

### Thom H. Dunning, Jr.: Contributions to chemical theory and computing

Thom H. Dunning, Jr., provides an outstanding example of success in science, computing, and scientific leadership. From his scientific contributions to knowledge to his developments and accomplishments that have enabled discovery, Thom’s influence upon science, computing, and the scientific community has been significant.

Angela K. Wilson, Kirk A. Peterson, David E. Woon

### The nature of the SO bond of chlorinated sulfur–oxygen compounds

Sulfur–oxygen chemistry encompasses a rich variety of chemical species and reactions. Sulfur–oxygen bonds can be quite short and strong, and historically, there has been disagreement as to the nature of the SO bond in sulfinyl groups. Early work invoked participation by the 3

d

orbitals of sulfur to explain the apparent double-bond character of sulfinyl bonds, but modern calculations have clearly established that sulfur 3

d

atomic orbitals do not participate as valence orbitals in hypervalent sulfur compounds. In prior work, we used generalized valence bond (GVB) theory to explain the features of the SO bond in the HSO/SOH structural isomers, and we extend that work here to the chlorinated analogs (ClSO/SOCl). We also use GVB theory to elucidate the nature of the bonding in Cl2SO and its higher energy structural isomer ClSOCl. We find that recoupled pair bonding, which we first introduced in our study of sulfur fluorides, is integral to describing the SO bond in all of these species. We also connect our analysis to the use of hyperconjugation to explain the backbonding in the π system in the sulfinyl halides.

Beth A. Lindquist, Thom H. Dunning

### Correlation consistent, Douglas–Kroll–Hess relativistic basis sets for the 5 p and 6 p elements

New sets of all-electron correlation consistent triple- and quadruple-zeta basis sets have been developed for the 5

p

and 6

p

elements (In–Xe, Tl–Rn). For the 5

p

elements, the spin-free Douglas–Kroll–Hess (DKH) Hamiltonian truncated at second order was used, while for the 6

p

row, DKH3 was employed. The resulting cc-pVmZDK sets (m = T,

Q

) are designed to correlate the valence

ns

and

np

electrons, but both core–valence sets (cc-pwCVmZ-DK) for (n - 1)

spd

correlation and diffuseaugmented sets (aug-cc-pVmZ-DK) for weak interactions have also been included. Benchmark DKH CCSD(T) calculations were carried out on the atoms for their first ionization potentials and electron affinities. Coupled cluster calculations of the near-equilibrium potential energy functions of 18 selected diatomic molecules were also carried out to determine their spectroscopic and thermodynamic properties. These results are extensively compared to those obtained using the analogous aug-ccp( wC)VmZ-PP basis sets with their associated small-core pseudopotentials. For the quadruple-zeta quality basis sets, the mean unsigned differences were found to be just 1.4 mÅ for re, 0.7 cm-1 for xe, and 0.2 kcal/mol for

D

e with corresponding maximum differences of 4.8 mÅ, 4.3 cm-1, and 0.7 kcal/mol, respectively. Using all-electron DKH calculations with the present basis sets as corrections to the pseudopotential approximation appears to be most accurate when (n - 1)d correlation is considered in both cases using aug-cc-pwCVQZ quality basis sets. The new DK basis sets exhibit similar basis set convergence toward the complete basis set (CBS) limit as the PP-based sets and hence should find utility in all-electron [T,

Q

] basis set extrapolations.

David H. Bross, Kirk A. Peterson

### Improved accuracy benchmarks of small molecules using correlation consistent basis sets

Improved accuracy benchmark atomization energies, equilibrium structures, and harmonic frequencies were obtained from the composite Feller–Peterson–Dixon procedure applied at the highest possible level permitted by our current hardware and software. Convergence of the 1-particle expansion was achieved through use of correlation consistent basis sets as large as aug-cc-pV8Z and aug-cc-pV9Z, followed by the application of a simple extrapolation formula in order to more closely approximate the basis set limit. Convergence of the

n

-particle expansion was addressed with a systematic sequence of coupled cluster methods up through CCSDTQ5. In 10 cases, coupled cluster theory was augmented with full configuration interaction. Each of the multiple sources of error was carefully monitored in order to minimize the overall uncertainty to the extent possible. Comparison with highquality experimental values, many of them obtained from the active thermochemical tables, reveals overall close agreement with theory.

David Feller, Kirk A. Peterson, Branko Ruscic

### Accurate ab initio potential energy curves and spectroscopic properties of the four lowest singlet states of C2

The diatomic carbon molecule has a complex electronic structure with a large number of low-lying electronic excited states. In this work, the potential energy curves (PECs) of the four lowest lying singlet states

$$\left( {X^1 \Sigma_g^ + ,\,A^1 \Pi _u ,\,B^1 \Delta_g ,\,and\,B'^1 \Sigma_g^ + } \right)$$

were obtained by high-level ab initio calculations. Valence electron correlation was accounted for by the correlation energy extrapolation by intrinsic scaling (CEEIS) method. Additional corrections to the PECs included core–valence correlation and relativistic effects. Spin–orbit corrections were found to be insignificant. The impact of using dynamically weighted reference wave functions in conjunction with CEEIS was examined and found to give indistinguishable results from the even weighted method. The PECs showed multiple curve crossings due to the

$$B^1 \Delta_g$$

state as well as an avoided crossing between the two

$$^1 \Sigma_g^ +$$

states. Vibrational energy levels were computed for each of the four electronic states, as well as rotational constants and spectroscopic parameters. Comparison between the theoretical and experimental results showed excellent agreement overall. Equilibrium bond distances are reproduced to within 0.05 %. The dissociation energies of the states agree with experiment to within ~0.5 kcal/mol, achieving “chemical accuracy.” Vibrational energy levels show average deviations of ~20 cm-1 or less. The

$$B^1 \Delta_g$$

state shows the best agreement with a mean absolute deviation of 2.41 cm-1. Calculated rotational constants exhibit very good agreement with experiment, as do the spectroscopic constants.

Jeffery S. Boschen, Daniel Theis, Klaus Ruedenberg, Theresa L. Windus

### Comparative bonding analysis of N2 and P2 versus tetrahedral N4 and P4

The nature of the chemical bonds in E2 and tetrahedral E4 (E = N, P) has been analysed with the help of an energy decomposition method. The p bonds in P

2

are not particularly weak. On the contrary, the contribution of P–P π bonding to the chemical bond in P

2

is even higher than the contribution of N–N π bonding to the chemical bond in N

2

. The higher stability of P

4

(T

d

) and the much lower stability of N

4

(T

d

) with regard to the diatomic species come from the substantially larger weakening of the N–N σ-bonds compared with the P–P σ-bonds in the tetrahedral species. The sum of the six P–P σ-bond energies in P

4

is higher than the sum of two σ- and four pbonds in two P

2

, but the six N–N σ-bonds in N

4

are weaker than two σ- and four p-bonds in two N

2

. The crucial factor that leads to the weak N–N bonds in N

4

, is the rather long N–N bonds which are 32.8 % longer than in N

2

. In contrast, the P–P bonds in P

4

are only 16.2 % longer than in P

2

. Since the equilibrium distances in E2 and E4 are determined by Pauli repulsion, it can be concluded that the origin for the different stabilities of N

4

and P

4

relative to the diatomic molecules is the exchange repulsion. The nitrogen atoms encounter stronger Pauli repulsion, because the 2

s

and 2

p

valence orbitals have a similar radius while the 3

s

and 3

p

P. Jerabek, G. Frenking

### Accurate first principles calculations on chlorine fluoride ClF and its ions ClF±

The present work focuses on the first (lightest) of the six diatomic interhalogens, namely ClF and its ions ClF

+

and ClF

-

, in an effort to better understand these interesting species. Toward this end, we have performed highly correlated all electron ab initio calculations of multireference (MRCI) and single-reference coupled-cluster calculations, employing quintuple and sextuple correlation consistent basis sets. Within the K - S ansatz, we have examined all 12 states of ClF correlating adiabatically with the first energy channel, all 23 states of ClF

+

correlating with the first three channels, and three states out of four of ClF

-

correlating with the first two channels Cl

-

+ F and Cl + F

-

. Full potential energy curves at the MRCI/quintuple zeta level have been constructed for 12, 21, and 3 states of ClF, ClF

+

, and ClF

-

, respectively. After correcting for core–subvalence and scalar relativistic effects, albeit small as expected, and spin–orbit interactions, most of our results are in excellent agreement with available experimental data. Some lingering questions have been definitely settled. Our final recommended binding energies (D

0

in kcal/mol) and equilibrium bond distances (r

e

in Å ) for

$$C1F\,\left( {X^1 \Sigma^+} \right),\,C1F^+ \,\left({X^2 \Pi } \right),\,and\,C1F^- \left({X^2 \Sigma^+} \right)$$

are [60.35, 1.6284], [67.40, 1.5357], and [29.80, 2.151], respectively. The adiabatic electron affinity of ClF,

$$C1F,\,C1F\left({X^1 \Sigma^+} \right) + e^- \to C1F^- \left({X^2 \Sigma^+} \right)$$

, is

$$EA_{ad} = 2.25 \pm 0.001$$

eV about 0.6 eV smaller than the suggested experimental value which is certainly wrong.

Athanassios A. Vassilakis, Apostolos Kalemos, Aristides Mavridis

### Negative electron affinities from conventional electronic structure methods

If the potential V describing the interaction between an excess electron and a ground-state neutral or anionic parent is sufficiently attractive at short range, electron-attached states having positive electron affinities (EAs) can arise. Even if the potential is not attractive enough to produce a bound state, metastable electronattached states may still occur and have lifetimes long enough to give rise to experimentally detectable signatures. Low-energy metastable states arise when the attractive components of V combine with a longer-range repulsive contribution to produce a barrier behind which the excess electron can be temporarily trapped. These repulsive contributions arise from either the centrifugal potential in the excess electron’s angular kinetic energy or long-range Coulomb repulsion in the case of an anionic parent. When there is no barrier, this kind of low-energy metastable state does not arise, but improper theoretical calculations can lead to erroneous predictions of their existence. Conventional electronic structure methods with, at most, minor modifications are described for properly characterizing metastable states and for avoiding incorrectly predicting the existence of metastable states with negative EAs where no barrier is present.

Kenneth D. Jordan, Vamsee K. Voora, Jack Simons

### The V state of ethylene: valence bond theory takes up the challenge

The ground state and first singlet excited state of ethylene, so-called

N

and

V

states, respectively, are studied by means of modern valence bond methods. It is found that extremely compact wave functions, made of three VB structures for the

N

state and four structures for the

V

state, provide an

N

V

transition energy of 8.01 eV, in good agreement with experiment (7.88 eV for the

N

V

transition energy estimated from experiments). Further improvement to 7.96/7.93 eV is achieved at the variational and diffusion Monte Carlo (MC) levels, respectively, VMC/DMC, using a Jastrow factor coupled with the same compact VB wave function. Furthermore, the measure of the spatial extension of the

V

state wave function, 19.14 a

0

2

, is in the range of accepted values obtained by large-scale state-of-the-art molecular orbitalbased methods. The σ response to the fluctuations of the π electrons in the

V

state, known to be a crucial feature of the

V

state, is taken into account using the breathing orbital valence bond method, which allows the VB structures to have different sets of orbitals. Further valence bond calculations in a larger space of configurations, involving explicit participation of the σ response, with 9 VB structures for the

N

state and 14 for the

V

state, confirm the results of the minimal structure set, yielding an

N

V

transition energy of 7.97 eV and a spatial extension of 19.16 a

0

2

for the

V

state. Both types of valence bond calculations show that the

V

state of ethylene is not fully ionic as usually assumed, but involving also a symmetryadapted combination of VB structures each with asymmetric covalent π bonds. The latter VB structures have cumulated weights of 18–26 % and stabilize the

V

state by about 0.9 eV. It is further shown that these latter VB structures, rather than the commonly considered zwitterionic ones, are the ones responsible for the spatial extension of the

V

state, known to be ca. 50 % larger than the

V

state.

Wei Wu, Huaiyu Zhang, Benoît Braïda, Sason Shaik, Philippe C. Hiberty

### Comparison of multireference configuration interaction potential energy surfaces for H + O2 → HO2: the effect of internal contraction

A comparison is presented of uncontracted multireference singles and doubles configuration interaction (MRCI) and internally contracted MRCI potential energy surfaces for the reaction

$${\mathrm H}\left( {^2 {\mathrm S}} \right) + {\mathrm O}_2 \left( {^3 \Sigma _{g}^ - } \right) \to {\mathrm H}{\mathrm O}_2 \left( {^2 {\mathrm A}^{\prime\prime}} \right)$$

. It is found that internal contraction leads to significant differences in the reaction kinetics relative to the uncontracted calculations.

Lawrence B. Harding, Stephen J. Klippenstein, Hans Lischka, Ron Shepard

### Modern valence-bond description of aromatic annulene ions

Spin-coupled theory for ‘

N

electrons in

M

orbitals’ active spaces [SC(

N

,

M

)], an ab initio valence-bond (VB) approach which uses a compact and easy-to-interpret wave function comparable in quality to a ‘

N

in

M

’ complete-activespace self-consistent field [CASSCF(

N

,

M

)] construction, is used to obtain modern VB descriptions of the π-electron systems of the most important annulene rings with 4

n

+ 2 π electrons: the cyclopropenium ion, the cyclobutadiene dication and dianion, the cyclopentadienide anion, benzene, the cycloheptatrienyl cation, and the cyclooctatetraene dication and dianion in their highest-symmetry nuclear conformations. The SC wave functions for the cyclopropenium ion, cyclopentadienide anion, cycloheptatrienyl cation, cyclooctatetraene dication and dianion are shown to closely resemble the well-known SC model of the classical example of an aromatic system, benzene. The SC orbitals for the cyclobutadiene dication and dianion are more delocalized and demonstrate the ways in which SC wave functions adjust to electron-deficient and electron-rich environments. The high levels of resonance observed in all annulene ions with 4

n

+ 2 π electrons clearly demonstrate their aromaticity.

Peter B. Karadakov, David L. Cooper

### Bonding in PF2Cl, PF3Cl, and PF4Cl: insight into isomerism and apicophilicity from ab initio calculations and the recoupled pair bonding model

Following previous work on PF

n

and SF

n

Cl compounds, we report high-level ab initio quantum chemical calculations on PF

2

Cl, PF

3

Cl, and PF

4

Cl. Coupled cluster (CCSD(T)) calculations were used to determine the structures and energetics of the various PF

n

Cl isomers, while generalized valence bond calculations were used to gain a deeper understanding of the factors influencing the structure and energetics of the isomers. Muetterties’ rule, which predicts that more electronegative elements occupy the apical positions in pentavalent phosphorus compounds, is examined in the context of the recoupled pair bonding model, which provides invaluable insights into the bonding, structure, and reactivity of hypervalent compounds. While we found more electronegative fluorine is favored in the apical position in closed-shell PF

4

Cl, the opposite is true for PF

3

Cl and two triplet excited state isomers of PF

2

Cl, all of which are open-shell species.

Jeff Leiding, David E. Woon, Thom H. Dunning

### MULTIMODE calculations of the infrared spectra of $${\mathrm H}_7^ +$$ and $${\mathrm D}_7^ +$$ using ab initio potential energy and dipole moment surfaces

We present a new ab initio potential energy surface (PES) and a dipole moment surface (DMS) for

$${\mathrm H}_7^ +$$

in the bound region. The PES is a linear least-squares fit to 42,525 ab initio points whose energies were computed with CCSD(T)-F12b/cc-pVQZ-F12 theory, and the DMS is a fit to dipole moments calculated at MP2 level of theory. The PES and DMS describe the bound region of

$${\mathrm H}_7^ +$$

precisely. MULTIMODE (MM) calculations of the infrared spectra of

$${\mathrm H}_7^ +$$

and

$${\mathrm D}_7^ +$$

were performed using the new PES and DMS. These calculations were carried out at the lowest three stationary points using the single-reference version of MM, and only the five high-frequency modes were considered. The calculated spectra agree well with the recent experimental predissociation action spectra.

Chen Qu, Rita Prosmiti, Joel M. Bowman

### Properties of local vibrational modes: the infrared intensity

For the local (adiabatic) vibrational modes of Konkoli and Cremer (Int J Quantum Chem 67:29–40, 1998), infrared intensities are derived by setting up the appropriate adiabatic conditions. It is shown that the local mode intensities are independent of the coordinates used to describe a molecule and correctly reflect the molecular symmetry and isotope composition. Normal mode intensities are related to local mode intensities via an adiabatic connection scheme (ACS). The ACS reveals intensity changes due to local mode mixing and avoided crossings, which are easily identified and quantified. The infrared intensities of simple molecules such as H

2

O, CH

4

, O

3

, HOOH, CH

3

OH, and the water dimer are discussed, and the influence of isotopes is quantified.

Wenli Zou, Dieter Cremer

### The infrared spectra of C96H25 compared with that of C96H24

The addition of one H atom to C

96

H

24

has been studied for the neutral, cation, and anion. Hydrogen atom binding at the solo site is the most favorable for all three charge states. The solo and duo sites are significantly more strongly bound than the endo positions. One extra hydrogen atom has very little effect on the infrared spectra. It is unlikely that species with one extra hydrogen could be identified from the astronomical emission spectra.

Charles W. Bauschlicher, Alessandra Ricca

### The mechanism of the cycloaddition reaction of 1,3-dipole molecules with acetylene: an investigation with the unified reaction valley approach

The unified reaction valley approach (URVA) is used in connection with a dual-level approach to describe the mechanism of ten different cycloadditions of 1,3- dipoles XYZ (diazonium betaines, nitrilium betaines, azomethines, and nitryl hydride) to acetylene utilizing density functional theory for the URVA calculations and CCSD(T)-F12/aug-cc-pVTZ for the determination of the reaction energetics. The URVA results reveal that the mechanism of the 1,3-dipolar cycloadditions is determined early in the van der Waals range where the mutual orientation of the reactants (resulting from the shape of the enveloping exchange repulsion spheres, electrostatic attraction, and dispersion forces) decides on charge transfer, charge polarization, the formation of radicaloid centers, and the asynchronicity of bond formation. All cycloadditions investigated are driven by charge transfer to the acetylene LUMO irrespective of the electrophilic/nucleophilic character of the 1,3-dipole. However, an insufficient charge transfer typical of an electrophilic 1,3- dipole leads to a higher barrier. Energy transfer and energy dissipation as a result of curvature and Coriolis couplings between vibrational modes lead to an unusual energy exchange between just those bending modes that facilitate the formation of radicaloid centers. The relative magnitude of the reaction barriers and reaction energies is rationalized by determining reactant properties, which are responsible for the mutual polarization of the reactants and the stability of the bonds to be broken or formed.

Marek Freindorf, Thomas Sexton, Elfi Kraka, Dieter Cremer

### Active Thermochemical Tables: dissociation energies of several homonuclear first-row diatomics and related thermochemical values

The current Active Thermochemical Tables (ATcT) results for the bond dissociation energies of the homonuclear diatomics H

2

, C

2

, N

2

, O

2

, and F

2

are reported and discussed. The role and origin of the distributed provenance of ATcT values is analyzed. Ramifications in terms of the enthalpies of formation of H, C, N, O, and F atoms, which are fundamental thermochemical quantities, are presented. In addition, the current ATcT bond dissociation energies and enthalpies of formation of HF, CH, CO, CN, NO, OH, CO

2

, H

2

O, and triplet and singlet CH

2

are also reported.

Branko Ruscic, David Feller, Kirk A. Peterson

### Transition metal atomic multiplet states through the lens of single-reference coupled-cluster and the equation-of-motion coupled-cluster methods

Transition metal atoms require a correct description of quasi-degeneracy and spin states, which lead to many closely lying multiplets. Before embarking on the theoretical description of transition metal complexes, the problems encountered in the atoms should be shown to be amenable to a chosen ab initio electronic structure method. It is usually thought that multi-reference methods should be a necessity for the correct description of transition metal multiplets. To the contrary, this paper explores the use of single-reference coupled-cluster theory in most of its manifestations. These include a variety of orbital choices from variationally optimal restricted open-shell references, to Brueckner orbital references, fractionally occupied references, quasi-restricted Hartree–Fock and other choices. In addition, the equation-of-motion coupled-cluster method for target multiplet states is considered. Relativistic corrections are obtained from a Douglas–Kroll–Hess fifthorder approximation which is found to be superior to effective core potentials, although there is little coupling between the relativistic effects and electron correlation.

Varun Rishi, Ajith Perera, Rodney Bartlett

### Molecular orbital interpretation of the metal–metal multiple bonding in coaxial dibenzene dimetal compounds of iron, manganese, and chromium

Both coaxial and perpendicular singlet spin state structures are found for the dibenzene dimetal complexes (C

6

H

6

)

2

M

2

(M = Fe, Mn, and Cr) using density functional theory. For (C

6

H

6

)

2

M

2

(M = Fe, Mn), the coaxial structure is the lower energy structure, whereas for (C

6

H

6

)

2

Cr

2

the perpendicular structure is the lower energy structure. These coaxial structures are predicted to have very short M–M distances of ~ 1.98 Å for (C

6

H

6

)

2

Fe

2

, ~ 1.75 Å for (C

6

H

6

)

2

Mn

2

, and ~ 1.68 Å for (C

6

H

6

)

2

Cr

2

. Investigation into the frontier molecular orbitals suggests a formal 2π Fe=Fe double bond in (C

6

H

6

)

2

Fe

2

, a σ + 2π Mn:Mn triple bond in (C

6

H

6

)

2

Mn

2

, and a σ + 2π + δ quadruple bond in (C

6

H

6

)

2

Cr

2

. This gives each metal atom in these coaxial (C

6

H

6

)

2

M

2

(M = Fe, Mn, Cr) derivatives a 16-electron configuration suggesting an 8-orbital

d

5

p

3

metal valence orbital manifold without the involvement of the s orbital. The coaxial (C

6

H

6

)

2

M

2

(M = Fe, Mn) derivatives have ideal sixfold D

6

h

symmetry. However, distortion of coaxial (C

6

H

6

)

2

Cr

2

from D

6

h

symmetry to D

2

h

symmetry is observed because of involvement of only one orbital from the {

d

(

xy

),

d

(

x

2

-

y

2

)} set of δ symmetry of each chromium atom in the

$$Cr \equiv Cr$$

Hui Wang, Dong Die, Hongyan Wang, Yaoming Xie, R. Bruce King, Henry F. Schaefer

### All electron ab initio calculations on the ScTi molecule: a really hard nut to crack

The lightest and yet completely unexplored intermetallic ScTi system has been studied by high-level ab initio methods and quantitative basis sets. We have studied in all 21

2S+1K

Λ states and constructed potential energy curves at the MRCI/cc–pvQZ computational level. The ground state of the system is of

6

Δ symmetry with

r

e

= 2.65 Å and

D

e

= 32.4 kcal/mol with respect to the adiabatic fragments or

D

e

0

= 10.4 kcal/mol with respect to the ground state atoms while its first excited state seems to be of

4

Δ symmetry with similar bonding features lying only 3 kcal/mol higher. An exceptional feature is the rather high Mulliken charge (average value of ~0.5 e

-

) transferred to Sc but the small calculated dipole moments.

Apostolos Kalemos, Aristides Mavridis

### Explicitly correlated coupled cluster benchmarks with realistic-sized ligands for some late-transition metal reactions: basis sets convergence and performance of more approximate methods

CCSD(T)-F12b benchmark calculations have been performed for the energetics and barrier heights of three late-transition metal systems, in increasing order of size: oxidative additions at bare Pd, a model for the Grubbs catalyst, and competitive CC/CH activation by a Rh(PCP) pincer complex. The results depend weakly on the basis set on the main-group atoms but are rather more sensitive to the basis set on the metal. An aug-cc-pwCVTZ-PP set on the metal combined with cc-pVTZ-F12 on the main-group elements yields barriers that are effectively converged in the basis set, but even the combination with aug-ccpwCVTZ- PP on the metal and cc-pVDZ-F12 on the main group, or of def2-TZVPP on the metal and def2-TZVP on the main group, works well enough for most benchmark purposes. Inner-shell correlation cannot be neglected for even semi-accurate work. Simple nonempirical (meta-)GGAs with D3BJ dispersion work quite well for the Grubbs and pincer cases but break down for the Pd example, which requires exact exchange. Hybrids of these same functionals, such as PBE0, TPSS0, and B3PW91, are among the best performers through rung four on Perdew’s ladder. For the Grubbs case, dispersion is very important and D3BJ clearly is superior over D2. Only the DSD double hybrids consistently perform well in the absence of dispersion corrections.

Manoj K. Kesharwani, Jan M. L. Martin

### Simulating Cl K-edge X-ray absorption spectroscopy in MCl6 2- (M = U, Np, Pu) complexes and UOCl5 - using time-dependent density functional theory

We report simulations of the X-ray absorption near edge structure at the Cl K-edge of actinide hexahalides MCl

6

2-

(M = U, Np, Pu) and the UOCl

5

complex using linear response time-dependent density functional theory extended for core excitations. To the best of our knowledge, these are the first calculations of the Cl K-edge spectra of NpCl

6

2-

and PuCl

6

2-

. In addition, the spectra are simulated with and without the environmental effects of the host crystal as well as ab initio molecular dynamics to capture the dynamical effects due to atomic motion. The calculated spectra are compared with experimental results, where available and the observed trends are discussed.

Niranjan Govind, Wibe A. de Jong

### Accurate atomization energies from combining coupled-cluster computations with interference-corrected explicitly correlated second-order perturbation theory

Interference-corrected explicitly correlated second-order perturbation theory (INT-MP2-F12) is applied to accelerate the convergence to the completebasis- set limit of coupled-cluster computations. Adding energy terms obtained from INT-MP2-F12 theory to the energies obtained from coupled-cluster singles-and-doubles (CCSD) computations yields a mean absolute deviation (MAD) from explicitly correlated CCSD results below 1 kJ/mol for a test set of 106 molecules. A composite scheme for the computation of atomization energies is assessed. This scheme is denoted as CCSD(T)?F12?INT and consists of the CCSD model with perturbative triples (CCSD(T)) supplemented with INT-MP2-F12 corrections, using a quadruple-zeta quality basis set (cc-pVQZ-F12). The composite scheme achieves chemical accuracy with respect to experimentally derived or computed reference values. Using Boys localized molecular orbitals, the MAD of the CCSD(T)?F12?INT/cc-pVQZ-F12 atomization energies from the reference values is below 1 kJ/mol for the G2/97 test set.

Konstantinos D. Vogiatzis, Robin Haunschild, Wim Klopper

### On the mutual exclusion of variationality and size consistency

Why do variational electron-correlation methods such as truncated configuration-interaction methods tend to be non-size-consistent (non-size-extensive)? Why are size-consistent (size-extensive) methods such as Møller– Plesset perturbation and coupled-cluster methods nonvariational? We conjecture that the variational and sizeconsistent properties are mutually exclusive in an ab initio electron-correlation method (which thus excludes the Hartree–Fock and density-functional methods). We analyze some key examples that support the truth of this conjecture.

So Hirata, Ireneusz Grabowski

### Accurate quadruple-ζ basis-set approximation for double-hybrid density functional theory with an order of magnitude reduction in computational cost

In the present study, we investigate a scheme for the approximation of quadruple-ζ (QZ) energies for doublehybrid density functional theory (DHDFT) procedures, using smaller double-ζ and triple-ζ basis sets. Such an approach would allow DHDFT/QZ energies to be estimated in cases where the explicit calculations might be too demanding computationally. We find this approach, denoted Q[D,T], to be very accurate for the MP2 same-spin (MP2SS) component and generally reasonable for the MP2 opposite-spin (MP2OS) component. The performance of the Q[D,T] approximation is quite insensitive to the type of basis sets used, as well as to the specific DHDFT procedure. Overall, we find that the approximation, when used in combination with the maug-cc-pVQ[D,T]Z basis sets, performs well for the calculation of relative energies. The use of explicit MP2OS/maug-cc-pVQZ energies together with the Q[D,T] MP2SS energies yields even better agreement with complete QZ energies, but at a somewhat greater computational cost. For a representative large system for DHDFT, namely C

60

, we find that the Q[D,T] approximation leads to a reduction in CPU time by more than an order of magnitude when compared with the corresponding explicit QZ calculation, with little reduction in accuracy.

### A perspective on the localizability of Hartree–Fock orbitals

A common perception about molecular systems with a nonlocal electronic structure (as manifested by a nonlocal Hartree–Fock (HF) density matrix), such as conjugated p-systems, is that they can only be described in terms of nonlocal molecular orbitals. This view is mostly founded on chemical intuition, and further, this view is strengthened by traditional approaches for obtaining local occupied and virtual orbital spaces, such as the occupied Pipek–Mezey orbitals, and projected atomic orbitals. In this article, we discuss the limitations for localizability of HF orbitals in terms of restrictions posed by the delocalized character of the underlying density matrix for the molecular system and by the orthogonality constraint on the molecular orbitals. We show that the locality of the orbitals, in terms of nonvanishing charge distributions of orbitals centered far apart, is much more strongly affected by the orthogonality constraint than by the physical requirement that the occupied orbitals must represent the electron density. Thus, the freedom of carrying out unitary transformations among the orbitals provides the flexibility to obtain highly local occupied and virtual molecular orbitals, even for molecular systems with a nonlocal density matrix, provided that a proper localization function is used. As an additional consideration, we clear up the common misconception that projected atomic orbitals in general are more local than localized orthogonal virtual orbitals.

Ida-Marie Høyvik, Kasper Kristensen, Thomas Kjærgaard, Poul Jørgensen

### Computing optical rotation via an N-body approach

Properties of four chiral compounds—(

S

)- methyloxirane, (

S

)-methylthiirane, (

S

)-2-chloropropionitrile, and (

M

)-dimethylallene—centered in a solvation shell of six to seven water molecules have been computed using time-dependent density functional theory at several wavelengths using a many-body expansion. Interaction energies, total system dipole moments, and dynamic dipole polarizabilities converge rapidly and smoothly, exhibiting only minor oscillations with higher-body contributions. At three-body truncation of the expansion, errors in such properties as compared to the full cluster typically fall to less than 1 % (and much smaller in most cases). Specific optical rotations, however, are found to converge much more slowly and erratically, requiring five-body contributions to obtain errors less than 5 % in three of four test cases, and six-body terms for (

S

)-methylthiirane. The source of this behavior is found to be the wide variation of both magnitude and sign of the specific rotation with changes in the configuration of individual solute/solvent clusters. Thus, unlike simpler properties such as energies or dipole moments, where each fragment makes a small, same-sign contribution to the total property, specific rotations typically involve much larger contributions that partly cancel in the many-body expansion. Thus, the computational costs of molecular dynamics simulations of explicit solvation, for example, will be only partially alleviated by such expansions.

Taylor J. Mach, T. Daniel Crawford

### Quantitative estimation of uncertainties from wavefunction diagnostics

Coupled–cluster calculations with large basis sets are used widely to make predictions of gas–phase thermochemistry. Wavefunction diagnostics are sometimes used to indicate whether or not there is problematic multireference character that may cause errors. Here, we investigate whether existing diagnostics, as well as diagnostics proposed by us, can be used to estimate these errors quantitatively. We calculate the atomization energy of 50 molecules, including known multireference molecules such as CN, C

2

, O

3

,

ortho

c

0

2

,

T

1,

D

1, and %TAE[(T)] diagnostics, we assess the Hartree–Fock HOMO–LUMO gap, maximum occupation number defect, fi rst vertical excitation energy, a direct estimate of multireference effects, and combinations of diagnostics as indicators of errant thermochemistry.

Matthew K. Sprague, Karl K. Irikura

### What makes differences between intra- and inter-molecular charge transfer excitations in conjugated long-chained polyene? EOM-CCSD and LC-BOP study

We performed intra- and inter-molecular charge transfer (CT) excitation calculations of H2N– (CH=CH)

n

–NO

2

(

a

) and its equidistant H2N–H…H–NO2 (

b

) using EOM-CCSD (

n

= 1–9), time-dependent (TD) long-range corrected (LC) density functional theory (DFT) (

n

= 1–10). It was shown that LC-BOP and LCgau-BOP outperform all the tested DFT functionals on inter- and intra-CT excitation energy and oscillator strength, regardless of CT interaction distance (R). Decomposition of TD-DFT optical excitation energies of (

a

) and (

b

) into HOMO–LUMO gap and excitonic binding energy disclosed that HOMO–LUMO gap reduction resulting from delocalization of HOMO and LUMO through bridged polyene conjugation is mainly responsible for the decreasing of intra-molecular CT excitation energy with chain number, while inter-molecular CT increases linearly with -1/

R

, which is wholly due to the decrease in excitonic energy between HOMO and LUMO. We found that success of exchange correlation functional on long-distanced intra-molecular CT calculations depends on correct descriptions of (1) Koopmans’ energy of donor and acceptor and (2) excitonic energy between donor and acceptor, and (3) correct farnucleus asymptotic behavior, -1/

R

. We found that LC scheme can satisfy (3), but needs an appropriate choice of long-range parameter able to satisfy (1) and (2). On the other hand, the pure, conventional hybrid, and screened hybrid functionals show near-zero intra- and intermolecular excitonic energy regardless of R, which means optical band gap coincide with HOMO–LUMO gap. Therefore, we conclude that 100 % long-range Hartree– Fock exchange inclusion is indispensable for correct descriptions of intra-molecular CT excitations as well as inter-molecular CT.

Jong-Won Song, Kimihiko Hirao

### Unimolecular and hydrolysis channels for the detachment of water from microsolvated alkaline earth dication (Mg2+, Ca2+, Sr2+, Ba2+) clusters

We examine theoretically the three channels that are associated with the detachment of a single water molecule from the aqueous clusters of the alkaline earth dications, [M(H

2

O)

n

]

2+

, M = Mg, Ca, Sr, Ba,

n

≤ 6. These are the unimolecular water loss (M

2+

(H

2

O)

n

-1

+ H

2

O) and the two hydrolysis channels resulting the loss of hydronium ([MOH(H

2

O)

n

-2

]

+

+ H

3

O

+

) and Zundel ([MOH(H

2

O)

n

-3

]

+

+ H

3

O

+

(H

2

O)) cations. Minimum energy paths (MEPs) corresponding to those three channels were constructed at the Møller–Plesset second order perturbation (MP2) level of theory with basis sets of doubleand triple-ζ quality. We furthermore investigated the water and hydronium loss channels from the mono-hydroxide water clusters with up to four water molecules, [MOH (H

2

O)

n

]

+

, 1 ≤

n

≤ 4. Our results indicate the preference of the hydronium loss and possibly the Zundel-cation loss channels for the smallest size clusters, whereas the unimolecular water loss channel is preferred for the larger ones as well as the mono-hydroxide clusters. Although the charge separation (hydronium and Zundel-cation loss) channels produce more stable products when compared to the ones for the unimolecular water loss, they also require the surmounting of high-energy barriers, a fact that makes the experimental observation of fragments related to these hydrolysis channels difficult.

Evangelos Miliordos, Sotiris S. Xantheas

### Stacking of the mutagenic DNA base analog 5-bromouracil

The potential energy surface of the stacked 5-bromouracil/uracil (BrU/U) dimer has been investigated in the gas phase and in solution (water and 1,4-dioxane), modeled by a continuum solvent using the polarizable continuum model. Minima and transition states were optimized using DFT (the M06-2X density functional and the 6-31+G(d) basis set). Six stacked gas-phase BrU/U minima were located: four in the face-to-back orientation and two face-to-face. The global minimum in the gas phase is a face-to-face structure with a twist angle of 60° and a zero-point energy-corrected interaction energy of -10.7 kcal/mol. The BrU/U potential energy surface is geometrically and energetically similar to that of U/U (Hunter and Van Mourik in J Comput Chem 33:2161, 2012). Energy calculations were also performed on experimental geometries of stacked dimers (47 containing BrU stacking with either adenine, cytosine, guanine or thymine and 51 containing thymine also stacking with one of those four bases) taken from DNA structures in the Protein Data Bank. Single-point interaction energies were computed at different levels of theory including MP2, CCSD(T) and DFT using the mPW2PLYP-D doublehybrid functional augmented with an empirical dispersion term, using basis sets ranging from aug-cc-pVDZ to augcc-pVQZ. No strong evidence was found for the suggestion that the mutagenicity of BrU is due to enhanced stacking of BrU compared to the corresponding stacked dimers involving thymine.

Leo F. Holroyd, Tanja van Mourik

### Quantum Monte Carlo investigation of the H-shift and O2-loss channels of cis-2-butene-1-peroxy radical

Owing to importance in combustion processes, O

2

-loss and 1, 6-H-shift in

cis

-2-butene-1-peroxy radical have been investigated. Energies for these processes and the barrier height of the latter are computed using the diffusion Monte Carlo (DMC) method. The DMC energy for the 1, 6-H-shift was determined to be 4.56 ± 0.19 kcal/mol with barrier height of 26.79 ± 0.20 kcal/mol. The energy for O

2

-loss was found to be 14.93 ± 0.24 kcal/mol. Quantitative differences between the fi ndings of the present study and previous CBS- QB 3 results indicate a discrepancy between high-level methods for the resonance-stabilized radicals. Further study is needed to identify the origin of these differences.

Zhiping Wang, Dmitry Yu Zubarev, William A. Lester
Weitere Informationen